JP2723505B2 - Filter function spreading device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial applications]   The present invention relates to an apparatus for expanding a filter function, and more particularly to a digital function.
Used in convolution processing required for noise removal of signal
Filter function that can perform convolution processing at high speed.
The present invention relates to a filter developing device for decomposing into filters. [Prior art]   Conventionally, for example, a one-dimensional image signal sequence [i (n); n = 0, ± 1,
± 2, ..., ± I ±, for example, the gain characteristic G (ω) is an even function
Image signal as a result of applying a filter with
Signal sequence {θ (n); n = 0, ± 1, ± 2, ..., ± I},
The first step is to make the filter function size N odd.
And the second step is a filter function f (n); n = 0, 1,
..., N-1 , And as a third step, the resulting image signal sequence (Taku Arimoto, “Digital processing of signals and images”
”, Sangyo Tosho Co., Ltd., p.155.). [Problems to be solved by the present invention]   However, in the above conventional method, the gain characteristic G
To express (ω), the filter function f (n)
The size N must be set large enough. The result
As a result, the processing unit that executes the above equation (2) is sized according to the accuracy
Have to convolve the changing filter function of
Therefore, when the above processing unit is configured by hardware,
It gets complicated. Also, in the conventional method,
The phase characteristic θ (ω) of the θ (ω) = e^{-i ・ (N-1) ω / 2}; i is the imaginary unit (3) And convolve a filter function with real-valued frequency characteristics
There is a drawback that you can not.   An object of the present invention is to provide a file having a real-valued frequency characteristic of an even function.
Filter functions of a certain size that can be easily realized
Fast convolution using hardware that convolves the ruta function
Into a group of window functions of a certain size
It is an object of the present invention to provide a ruta deployment device. [Means to solve the problem]   According to the first aspect of the present invention, the filter function expanding apparatus includes
Frequency characteristic storage means for storing a wave number characteristic function;
The wave number characteristic function is represented by a large convolution of the window function group.
Number storage means for storing the number of window functions
And the above-mentioned window function is converted to a value of zero outside a certain range.
The window function is the size of the range when approximated by
Size storage means for storing as the size of
Zero area storage means for storing a variable indicating the degree;
Variable indicating the degree of approximation obtained and the stored window
From the size of the function and the number of window functions, the area width
Area width calculation means for determining, and storing the area width for determination
Area width storage means for storing, and storing the stored area width
Wave of harmonic oscillator using number of remembered window functions
Determine a group of functions, the frequency characteristic function of the filter,
Calculate the expansion coefficient when expanding with the wave function group as the basis
And the calculated expansion coefficient group.
Expansion coefficient storage means for storing the area width and
The number of stored window functions and the stored expansion
From the coefficient group, the angle in the frequency characteristic function determined by them
The part of the polynomial about the square of frequency is
Expanded by the product of the quadratic polynomial group for the square of frequency,
Coefficient calculating means for calculating a coefficient group of powers,
Coefficient storage means for storing a coefficient group to be processed,
A variable indicating the stored degree of approximation and the stored window;
Of the window function and the number of the stored window functions
And the stored coefficient group of each power of the quadratic polynomial group
To generate a window function group for multi-superposition
Window function group generating means.   A filter function expanding device according to a second aspect of the present invention includes a filter function expanding device.
Frequency characteristic storage means for storing a wave number characteristic function;
The wave number characteristic function is represented by a large convolution of the window function group.
If the window function is outside the range, the value is zero
, The size of the range, when approximated by
Size storage means for storing as the size of a number;
Zero area storage means for storing a variable indicating the degree of
Stores the area width that defines the spread of the function in frequency space
Area width storage means and the stored degree of approximation.
Variables and the magnitude of the stored window function and the storage
The frequency characteristic function from the window width
The number of the window functions described above when expressed by multiple superposition of functions
Means for calculating the number of stages,
A number-of-stages storage means for storing the number of numbers;
Using the bandwidth and the number of the stored window functions,
The wave function group of the sum oscillator is determined, and the frequency characteristic of the filter is determined.
The expansion when the sex function is expanded using the wave function group as a basis.
A wave function expanding means for calculating an open coefficient; and
Expansion coefficient storage means for storing an expansion coefficient group;
Area width, the number of the stored window functions and the
Frequency characteristics determined by stored expansion coefficients
A polynomial about the square of the angular frequency in the function
Is the product of the quadratic polynomial for the square of the angular frequency.
Coefficient calculation means to calculate the coefficient group to be expanded by
And coefficient storage for storing the calculated power coefficient group.
Means, said stored area width and said stored window.
Using the number of functions and the stored coefficient group,
A window that generates a group of window functions for superposition
It has function group generation means.   A filter function expanding device according to a third aspect of the present invention provides a filter function expanding device.
Frequency characteristic storage means for storing a wave number characteristic function;
The wave number characteristic function is represented by a large convolution of the window function group.
Number storage means for storing the number of window functions
And the above-mentioned window function is converted to a value of zero outside a certain range.
The window function is the size of the range when approximated by
Size storage means for storing as the size of
Zero area storage means for storing a variable indicating the degree;
Variable indicating the degree of approximation obtained and the stored window
From the size of the function and the number of window functions, the area width
Area width calculation means for determining, and storing the area width for determination
Area width storage means for storing, and storing the stored area width
Using the number of remembered window functions, the wave of the harmonic oscillator
A dynamic function group is defined, and the frequency characteristic function of the filter is
Calculate the expansion coefficient when expanding the wave function group as a basis
Wave function expanding means, and the calculated expansion coefficient group
Expansion coefficient storage means for storing, the stored area width;
The number of the stored window functions and the stored
From the open coefficient group, the frequency characteristic function
The part that is a polynomial about the square of the angular frequency is
Expanded by the product of the quadratic polynomial group for the square of angular frequency
Coefficient calculating means for calculating a power coefficient group,
Coefficient storage means for storing the calculated coefficient group,
Of the stored area width and the stored window function
Number and coefficient of each power of the stored second-order polynomial group
Generate a group of window functions for multi-superposition using groups
It has means for generating a window function group.   According to a fourth aspect of the present invention, a filter function expanding apparatus includes
Frequency characteristic storage means for storing a wave number characteristic function;
The wave number characteristic function is represented by a large convolution of the window function group.
Number storage means for storing the number of window functions
And the above-mentioned window function is converted to a value of zero outside a certain range.
The window function is the size of the range when approximated by
Size storage means for storing as the size of
Zero area storage means for storing a variable indicating the degree;
Variable indicating the degree of approximation obtained and the stored window
From the size of the function and the number of window functions, the area width
Area width calculation means for determining, and storing the area width for determination
Area width storage means for storing, and storing the stored area width
Using the number of remembered window functions, the wave of the harmonic oscillator
A dynamic function group is defined, and the frequency characteristic function of the filter is
Calculate the expansion coefficient when expanding the wave function group as a basis
Wave function expanding means, and the calculated expansion coefficient group
Expansion coefficient storage means for storing, and the stored expansion coefficient
A group and a variable indicating the degree of approximation stored and the stored
Frequency determined by the magnitude of the window function
A polynomial for the square of the angular frequency in the characteristic function
Is the second-order polynomial for the square of the angular frequency
Coefficient calculation to calculate the power coefficient group by expanding with the product of the group
Output means and a storage unit for storing the calculated coefficient group.
Number storage means, and a variable indicating the stored degree of approximation;
The magnitude of the stored window function and the stored
The number of window functions and the stored second-order polynomial group
Using the coefficient group of each power of
Window function group generating means for generating a command function group
I have. [Action]   The principle of the present invention will be described step by step.   First, as an actual function, an even function real-valued frequency adjustment function
Note that F (w) is an even function.
The wave functions of harmonic oscillators that form a perfect orthogonal system Of the wave functions that are even functions of It is expressed as   Next, as a second step, the above equation (5) is calculated by summing 2k + 1 terms
Approximate It is expressed as The third step is to define the Hermite polynomial Σ on the right-hand side of equation (6)
Unfold.   Further, the expression (6-1) is Summarized in terms of the same order And transform. That is, equation (6) is And transform. However It is.   Next, as the fourth stage The above equation (8) becomes Is transformed. on the other hand Can represent any polynomial of degree 2k with respect to W
From that, b_j, C_jIs appropriately selected, the above equation (9-
2) Can be expressed as Based on this, equation (8) is It is expressed as   Next, as the fifth stage And G_j(Ω) is defined and the above equation (9) is F (ω) = P_4k｛G₁(Ω) · G_Two(Ω) …… G_k(Ω)｝ (1
1) It is expressed as   As the sixth step, the inverse Fourier transform of the equation (10) is F_i(X) (12) And the function G in the frequency domain₁(Ω), G
_Two(Ω), ………, G_k(Ω) product G₁(Ω) · G_Two(Ω)…
… G_kThe inverse Fourier transform of (ω) is G in the time domain.
₁(Ω), G_Two(Ω), ………, G_k(Ω) each inverse foo
Rie transform f_i(X), f_i(X), ………, f_kMultiplex of (x)
Inverse Fourier transform and multiple convolution, which are equivalent to convolution
Using the general property of the F (ω)
-Transform L (x) L (x) ≡P_4k｛F₁(x)^*f_Two(x)^*............^*f_k(x)｝ (13) It is expressed as   As the seventh step, the inverse Fourier transform of the above equation (10) is obtained.
You. First Inverse Fourier transform of Ask for. And variable conversion, Is obtained. by the way Because Becomes However It is. next Inverse Fourier transform of Ask for. Same as when calculating equation (14-1) And variable conversion Becomes even here Was used. next Inverse Fourier transform of Ask for.   Do the same when calculating equations (14-1) and (14-6) And variable conversion Becomes The integral part of equation (14-10) is In Although, With, Because Becomes Use the above equations (14-4), (14-8), and (14-13)
When you are Inverse Fourier transform of Becomes even here Was used. That is, the above equation (14-13) is converted to the fourth and second order
Lumite polynomial Using Can be expressed as In the above equation (14) And f at | x | → ∞_j(X) → 0
Noting that,At f_j(X) 0 Is adjusted by adjusting σ so that
Is L. For example Is assumed to be sufficiently zero. Ie It is. At this time By choosing σ By doing Becomes That is, in the above equation (14), By choosing Function f of the equation (13) outside the region_j(X), j = 1,2,
…, K is converged to zero.   Finally, as an eighth step, the function group f_j(X) converges to zero
Integer sequence in the area of the above equation (17) −M, −M + 1, ..., M−1, M Where M is the largest integer satisfying the above equation (17). Is a number whose length is L sampled from the function group of the above equation (14).
Columns ｛F_j(−M), f_j(-M + 1), ..., f_j(M-1), f_j
(M)｝ (19) j = 1,2,…, k , The frequency characteristic is F (ω).
It is possible to express the filter function by multiple superposition of the function group (19)
To make it possible. [Example]   Next, embodiments of the present invention will be described in detail with reference to the drawings.
I will tell.   FIG. 1 shows an embodiment of the first invention. Fig. 1
The embodiment of the first invention is constituted by a computer or the like.
Control means 1000 for controlling each means and display means 1010 such as a CRT
And a signal composed of, for example, a memory that stores an image signal sequence
The storage means 1020 stores these image signal sequences in a window function.
Sequences of a length determined by the number and the size of the window function, etc.
Calculating means 1150 for calculating by means of
Temporary storage means 1160 for temporarily storing the generated sequence,
The sequence stored in the storage unit 1160 is stored in the signal storage unit 1020.
And copying means 1170 for storing
Screen of the display means 1010 showing the sequence stored in the number storage means 1020
The frequency characteristics of the filter
Frequency characteristic storage means 1060 for storing the sex function,
Stage number storage means 1040 for storing the number of window functions;
Size storage means 1050 for storing the size of the bind function,
A zero area storage unit 1030 for storing the accuracy of division.   These stage number storage means 1040 and zero area storage means 1030
It is connected to the area width calculation means 1070. Area width calculation means
1070 is close to the number of window functions and the size of the window function.
The area width is determined from a variable representing the degree of similarity. Area width memory
Means 1080 stores the area width determined by the area width calculation means.
Wave function expansion means 1090 stores the area width storage means 1040
Using the number of window functions, the wave function group of the harmonic oscillator
Frequency characteristic memory for each of the wave functions
Calculate the expansion coefficient group of the frequency characteristic function stored in step 1060
You. The expansion coefficient storage means 1100 is calculated by the wave function expansion means 1090.
The output expansion coefficient group is stored. The power coefficient calculation means 1110
Area width and step number storage means 10 stored in area width storage means 1080
Means for storing the number of window functions and expansion coefficients stored in 40
A second-order polynomial is generated using the expansion coefficient group stored in 00.
You. The exponent coefficient storage unit 1120 generates the exponent coefficient calculation unit 1110.
The coefficient group of the resulting quadratic polynomial is stored. Window functions
The generating unit 1130 is configured to store the approximation stored in the null region storage unit 1030.
Variables representing degrees and windows stored by size storage means 1050
The window size stored by the function size and stage number storage means 1040
Second-order polynomial stored in number and power coefficient storage means 1120
The window function stored by the size storage means using the coefficient group of
Generate a sequence of lengths determined by the size of the number, and
Is supplied to the window group storage means 1140.
I have.   Next, the operation of the embodiment of the first invention will be described. No.
An embodiment of the invention is, for example, a one-dimensional image signal sequence. ｛ⁱ0,ⁱ1,…,ⁱl｝, l is a positive integer (20) The real value of an even function whose frequency response is illustrated in Fig. 5A
function F (ω) = 1, | ω | ≦ ω_c                   (twenty one)         = 0, | ω | <ω_c And the result of convolving the filter function F (ω)
In the above example, as the first stage of preprocessing,
The image signal sequence to be read is stored in a signal storage
Stored in stage 1020, for example, a memory
To the zero area storage means 1030 As a parameter value of a variable indicating the degree of approximation that satisfies
For example, 4 is stored, and as the third stage of the preprocessing, for example, a memory is stored.
Function to be folded into the number-of-stages storage means 1040 composed of
For example, 5 is stored as the value of the number k of the
Size storage means 1050 composed of, for example, a memory as a floor
Is a positive odd number as the window size L to be folded
Is stored in the memory as a fifth stage of the preprocessing.
The obtained frequency characteristic storage means 1060 is represented by the above equation (21).
The frequency characteristic function F (ω) Δω = 0.01 (23) The sequence shown in Fig. 5B sampled for each ｛F_j= 1; j = -m, -m + 1, ..., m-1, m｝ (24)   Where m is m · Δω ≦ ω_cWrite the largest integer that satisfies
Remember   The processing starts when the control unit 1000 activates the area width calculation unit 1070.
Begin. The activated area width calculating means 1070 is a zero area storing means.
Constant ξ stored in 1030 and c
The number k of window functions and the size stored in the size storage means 1050.
Region size か ら from the size L of the For example, in the area width storage means 1080 composed of memory
The processing is terminated after storing the area width Θ. Area width calculation means 10
When 70 has completed the processing, the control means 1000 starts the wave function expansion procedure.
Activate step 1090. The activated wave function expanding means 1090 is
The window stored by the stage number storage means 1040 as one stage
Number of functions k and area stored by the area width storage means 1080
Wave relation of 2k + 1 harmonic oscillators defined by width Θ
Group of numbers   Where Hj (y) is the j-order Hermite polynomial for y
Within the domain of the frequency characteristic function F (ω).
3) 2k + 1 sequence groups sampled for each Δω of 3) ｛Φ_2j, Η = φ_2j(Δω · η); η = -m, -m + 1, ..., m
-1, m｝ (27)                                   j = 0,, 1, ..., 2k Is calculated and held, and as a second step, the frequency characteristic function F
(Ω) And the expansion coefficient group ｛a_2j｝
(23) The Δω stored in the frequency characteristic storage means 1060
The sequence of expression (24), the sequence of expression (27), and the number of stages storage means
From the number k of window functions stored in 1040And the third step is to use the above equation (28)
A set of expansion coefficients that are determined, for example, expansion coefficients composed of memory
The information is stored in the storage unit 1100, and the process ends.   When the wave function expansion means 1090 completes the processing, the control means 10
00 activates the exponent coefficient calculating means 1110. Start the above
The coefficient calculating means 1110 includes a region width storing means as a first stage.
The area width 1080 stored by 1080 and the step storage means 1040 store
The number k of window functions to be
The sequence of equation (28) remembered and the equation (7-1)
Consisting of the coefficient group of the formula (8-1) obtained from the coefficient group
Coefficient group t_2j= P_2j/ p_4k; j = 0,1, ..., 2k (30) 2k of W generated using For example, the Barestow method (Kazuo Isoda, Yutaka Ohno, “FORTRAN
Handbook for Numerical Calculations by Ohm ”, Ohmsha, PP.428-431,
1971.) Set of two sequences obtained by transforming into the form ｛B_j; j = 1,2,…, k｝, ｛c_j; j = 1,2,…, k｝ (33) , And as the second step, the sequence group of the above equation (33) is compared.
Stored in the coefficient storage means 1120 which should be a memory.
The process ends.   When the power coefficient calculating means 1110 completes the processing, the control means 10
00 activates the window function group generation means 1130. Started
The window function group generation means 1130 performs the first step
The variable ξ representing the degree of approximation stored in the storage means 1030 and the size
Represents the size of the window function stored by the
The odd (L) and power coefficient storage means 1120 stores the above equation (3
The two sets of number series shown in 3) and the number-of-stages storage means 1040 store
K window function groups determined from the number k of window functions For example, a k-number sequence group having a length L is As shown in Fig. 6  Where [x] is the largest integer not exceeding an arbitrary number x, j =
1,2,…, k, and so on.
The above-mentioned formula (3)
6) The k-number sequence group and the window stored in the stage number storage means 1040
Window number and size stored by the command function
The processing is terminated after storing the magnitude of the function.   Control when window function group generation means 1130 finishes processing
The means 1000 activates the calculating means 1150. Activated operator
Step 1150 is performed by the window group storage means 1140 as the first step.
The number k of window functions to remember and the size L of the window function
Is read and stored as signal storage means 1020 as a second stage.
数 i₀, i₁, ..., i_l｝ And window group storage means 1140
1st sequence to store From Generates a sequence of numbers, for example, temporary storage composed of memory
Stored in the means 1160, and starts the copying means 1170 as the second stage
Waits for the copying means 1170 to stop, and repeats the above process.
Number of window functions stored in the window group storage unit 1140
And terminate the process. The duplication started by the arithmetic means 1150
The copying means 1170 signals the sequence stored in the temporary storage means 1160 as a signal.
The processing is stored in the storage means 1020 and stopped.   When the calculating means 1150 completes the processing, the control means 1000 displays
The indicating means 1010 is activated. The activated display means 1010 indicates the signal
The sequence of numbers stored by the storage means 1020 is displayed on the screen.
Is completed.   Next, FIG. 2 shows an embodiment of the second invention. In FIG.
In the second embodiment, the control means 1000 includes a signal
Storage means 1020, arithmetic means 1150, temporary storage means 1160, display means
A stage 1010 and a copying means 1170,
Step 1030, frequency characteristic storage means 1060, and size storage means
Includes step 1050. Each of these means is a part of the first invention.
Since the function is the same as that of the embodiment, a detailed description thereof will be omitted.
You. The area width storage means 1080 stores the area width. Number of stages
The calculating means 2000 calculates the approximation stored in the zero area storing means 1030.
Variables representing degrees and windows stored by size storage means 1050
Function size and area width stored by the area width storage means 1080
Determine the number of window functions after decomposition from. Step number memory
Step 1040 is the number of window functions determined by the step number calculation means 2000.
Is stored. The wave function expanding means 1090 is the area width storing means 10
The area width stored by 80 and the window stored by the step number storage means 1040
The wave functions of the harmonic oscillator using the number of
The frequency characteristic memory for each of these wave functions
Calculate expansion coefficient group of frequency characteristic function stored by means 1060
I do. The expansion coefficient storage means 1100 stores the wave function expansion means 1090
The calculated expansion coefficient group is stored. Power coefficient calculation means 1110
Is the area width and the number of steps stored in the area width storage means 1080
Means for storing the number of window functions and expansion coefficients stored in 1040
Generate a second-order polynomial using the expansion coefficients stored in the 1100
You. The exponent coefficient storage unit 1120 generates the exponent coefficient calculation unit 1110.
The coefficient group of the resulting quadratic polynomial is stored. Window functions
The generation unit 1130 determines the region width stored in the region width storage unit 1080
The number and power of window functions stored in the stage number storage unit 1040
Using the coefficient group of the quadratic polynomial stored in the coefficient storage means 1120
Size of the window function stored by the size storage means 1050
Generates a sequence of lengths determined by
It is configured to store in the group storage means 1140.   The operation of the embodiment of the second invention will be described. Second
In the embodiment of the present invention, for example, the image signal
The frequency characteristic in the column is, for example, the above equation (21) illustrated in FIG. 5A.
Convolved the filter function, which is the real-valued function of the even function of
In the example of displaying the result, as the first stage of the preprocessing, the expression (2
An image signal sequence represented by 0) is constituted by a memory, for example.
Stored in the signal storage means 1020 as the second stage of the preprocessing.
For example, the zero area storage means 1030 constituted by a memory
For example, 4 is stored as the value of ξ that satisfies equation (22),
As a third stage of processing, for example, a size
In the storage means 1050, the size of the window to be folded is L
If a positive odd number is stored, for example,
The above formula is stored in the frequency characteristic storage means 1060 composed of a memory.
For example, the frequency characteristic function F (ω) expressed by
FIG. 5B shows an example in FIG. 5B sampled for each Δω of the above equation (23) within the defined area.
The sequence of the above equation (24) is stored, and the fifth stage of the preprocessing is performed.
For example, in the area width storage means 1080 constituted by a memory
Is the frequency characteristic function F (ω) expressed by the above equation (21).
Compare the domain width に 対 す る for the wave function of a developing harmonic oscillator
For example, it is stored as 0.1.   The process starts when the control means 1000 activates the step number calculation means 2000.
Round. The activated stage number calculation means 2000 is a zero area storage means 1030.
Is stored by the size storage means 1050.
Size of the command function and the area stored by the area width storage means 1080.
From the area width Θ, the number k of window functions Where [x] is the largest integer that does not exceed x For example, the number-of-stages storage means 1040 constituted by a memory
And the process ends. Step number calculation means 2000
Upon completion, the control means 1000 invokes the wave function expansion means 1090.
Move.   The activated wave function expanding means 1090 is a step
Number k and area of window function stored in number storage means 1040
Defined using the area width す る stored by the width storage means 1080
Wave function group of 2k + 1 harmonic oscillators shown in the above equation (26)
And the above equation (27) generated from Δω of the above equation (23)
Calculate and hold 2k + 1 sequence groups, and as a second stage
The sequence obtained by the frequency characteristic storage means 1060 and the sequence
The sequence group of the above equation (27), Δω of the above equation (23) and the number of stages
Using the number k of window functions stored in the storage means 1040
The expansion coefficient group shown in the above equation (28) can be stored in a memory, for example.
The generated expansion coefficient is stored in the expansion coefficient storage means 1100 and the processing is terminated.
You.   When the wave function expansion means 1090 completes the processing, the control means 10
00 activates the exponent coefficient calculating means 1110. The person who should have started
The number calculation means 1110 is used as the first stage by the area width storage means 1010.
The area width が stored by 80 and the step storage means 1040 store
Stored in the number k of window functions and expansion coefficient storage means 1100
Of the equation (28) and the equation (7-1)
In the above equation (8-1) obtained from the coefficient group of the Lumiet polynomial,
Using the coefficient group of the above equation (30) defined using the coefficient group
The 2k order equation of W shown in the above equation (31) generated by
Using the Bearstow method, the shape is transformed into the form of the above equation (32).
The sequence group of the above equation (33) is configured by a memory, for example.
This is stored in the exponent coefficient storage unit 1120, and the processing is terminated.   When the power coefficient calculating means 1110 completes the processing, the control means 10
00 activates the window function group generation means 1130. Started
Window function group generating means 1130, as a first stage,
Area width す る stored by width storage means 1080 and step number storage means 1040
Means for storing the number k of window functions and power coefficient
K stored in the number sequence group of the equation (33) stored in 20
Function group And the length L stored by the size storage means 1050 and the equation (35)
As shown in FIG. 6, k sets of sequence groups are calculated using Δx of
(36), and as a second step, for example, using a memory
In the configured window group storage means 1140, k of the above equation (36) is stored.
A window function stored by a set of series and a stage number storage means 1040
Window function stored by the number k and size storage means 1050
Is stored, and the process ends.   Control when window function group generation means 1130 finishes processing
The means 1000 activates the calculating means 1150. Activated computing means
1150 is stored in the window group storage means 1140 as the first stage.
The number of window functions k and the size L of the window function
Before the signal is stored by the signal storage means 1020 as the second stage.
The sequence represented by the expression (20) and the window group storage unit 1140 are
From the first sequence shown in equation (37) to be stored,
Generates the sequence shown in (38) and is composed of, for example, a memory
It is stored in the temporary storage means 1160, and as a second stage, the copying means 11
Activate 70 and wait for this copying means 1170 to stop,
The window group storing means 1140 stores the above process.
The processing is performed a number of times, and the processing is terminated. Calculation means 1150
The copying means 1170 started by the temporary storage means 1160 is stored.
The sequence to be performed is stored in the signal storage unit 1020 and the operation is stopped.   When the calculation means 1150 completes the processing, the control means 1000
The display means 1010 is activated. The activated display means 1010
The sequence stored by the number storage means 1020 is displayed on the screen, and
The whole process ends.   Next, FIG. 3 shows an embodiment of the third invention. In FIG.
In the third embodiment, the control means 1000 includes a signal
Storage means 1020, arithmetic means 1150, temporary storage means 1160, display means
A stage 1010 and a copying means 1170,
Step 1030, step number storage means 1040, frequency characteristic storage means 1060 and
And a size storage means 1050. Each of these hands
The step has a function similar to that of the first and second embodiments.
Therefore, the detailed description is omitted. Area width calculation means 1070
Is the number of steps storage means 1040, the size storage means 1050,
Connected to the area storage means 1030, and stored in the stage number storage means 1040.
The number and size of window functions to be stored
Window size and null area storage means 1030 store
The area width is determined from a variable indicating the degree of approximation. Area width
The storage unit 1080 stores the region width determined by the region width calculation unit 1070.
I do. The wave function expansion means 1090 is recorded by the area width storage means 1080.
Window width stored in the storage area width and step number storage means 1040
The wave function group of the harmonic oscillator is determined using the number of
Frequency characteristic storage means 1060 for each of the wave function groups
Calculates the expansion coefficient group of the frequency characteristic function stored by. Exhibition
The open coefficient storage means 1100 outputs the wave function expansion means 1090
The expansion coefficient group is stored. Exponent coefficient calculating means 1110 calculates the area width
The area width stored in the storage unit 1100 and the number of steps storage unit 1040 are recorded.
The number of window functions to be stored and the expansion coefficient
A second-order polynomial is generated using the expansion coefficient group stored. Should
The coefficient storage unit 1120 stores the data generated by the power coefficient calculation unit 1110.
The coefficient group of the degree polynomial is stored. Window function group generation means
1130 is the area width and the number of steps stored in the area width storage means 1080
Means and number of window functions stored by means 1040
The size is calculated using the coefficient group of the quadratic polynomial stored in the means 1120.
Determined by the size of the window function stored by storage means 1050
Generates a sequence of lengths and stores the sequence in a window group storage
It is configured to supply the stage 1140.   The operation of the third embodiment will be described. Third
In the embodiment of the present invention, for example, the image signal
The frequency characteristic in the column is, for example, the above equation (21) illustrated in FIG. 5A.
Convolve the filter function which is the real-valued function of the even function shown in
In this example, the first step of the preprocessing is
The image signal sequence represented by the equation (20) is composed of, for example, a memory.
Stored in the stored signal storage means 1020, the second stage of the preprocessing and
Then, for example, the zero area storage means 1030 composed of a memory
For example, 4 is stored as the value of ξ that satisfies the expression (22),
As a third stage of the pre-processing, for example, a
The size L of the window to be folded
For example, store a positive odd number and compare it as the fourth stage of preprocessing.
For example, the frequency characteristic storage means 1060 constituted by a memory
The frequency characteristic function F (ω) expressed by the equation (21)
In FIG. 5B, which is sampled for each Δω of the equation (23) within the domain,
The sequence of the above-described equation (24) is stored, and the fifth stage of the preprocessing is performed.
As a floor, for example, a stage number storage means 1040 constituted by a memory
Is 10 as the value of the number k of window functions to be folded.
Is stored.   The processing starts when the control unit 1000 activates the area width calculation unit 1070.
Begin. The activated area width calculating means 1070 is a zero area storing means.
Constant ξ stored in 1030 and c
The number k of window functions and the size stored in the size storage means 1050.
The area width Θ is determined from the size L of the
For example, stored in the area width storage means 1080 composed of memory
And terminate the processing.   When the area width calculation means 1070 ends the processing, the control means 1000
Activates the wave function expansion means 1090. Activated wave function
The expansion means 1090 is stored in the stage number storage means 1040 as the first stage.
The number k of window functions to be stored and the area width storage means 1080 are recorded.
Equation (26) defined using the area width Θ
The wave function group of 2k + 1 harmonic oscillators and Δ in equation (23)
2k + 1 number sequence group shown in the above equation (27) generated from ω
Is calculated and stored, and as a second step, frequency characteristic storage means
The sequence stored by the 1060 and the window stored by the
The number k of command functions, the sequence group of the equation (27) and the equation (2
3) Expansion coefficient group shown in the above equation (28) obtained from Δω
Is stored in the expansion coefficient storage means 1100 constituted by a memory, for example.
Then, the processing ends.   The wave function expanding means 1090 ends the processing.   When the power coefficient calculating means 1110 completes the processing, the control means 10
00 activates the exponent coefficient calculating means 1110. The person who should have started
The number calculation means 1110 is used as a first step by the area width storage means 1080.
The area width す る to be stored and the window
Number k of expansion functions and expansion coefficient storage means 1110
(28) and the Hermite of the formula (7-1)
The coefficient group of the equation (8-1) obtained from the coefficient group of the polynomial is
Generated using the coefficient group of the equation (30) defined using
The 2k order equation of W shown in the above equation (31) is, for example,
Using the tow method, the above equation obtained by transforming the equation (32)
For example, the sequence group of equation (33) is a power coefficient constituted by a memory.
The information is stored in the storage unit 1120, and the process is terminated. Power coefficient calculation
When the means 1110 completes the processing, the control means 1000
The number group generating means 1130 is started. Activated window functions
The generating means 1130 is provided as a first step.
The area width が stored by 80 and the number of steps stored by the
The number k of bind functions and power coefficient storage means 1120 store
Equation (40), defined using the sequence of Equation (33)
The k window function groups and the size storage means 1050 are recorded.
The size L of the window function to be stored and Δx of the above-mentioned equation (35)
Fig. 6 shows k sets of sequence groups whose length is L from
In the second step, for example, the memory
In the window group storage means 1140 composed of
The window function stored in the k-number sequence group and the stage number storage means 1040
The window function stored by the number storage unit 1050
The number L is stored, and the process ends.   Control when window function group generation means 1130 finishes processing
The means 1000 activates the calculating means 1150. Activated operator
Step 1150 is stored in the window group storage means 1140 as the first step.
The number k of window functions and the size L of the window function
Read, and stored by the signal storage means 1020 as the second stage
The numerical sequence shown in the above equation (20) and the window group storage means 1140 are recorded.
From the first sequence shown in equation (37),
Generates the sequence shown in (38) and is composed of, for example, a memory
It is stored in the temporary storage means 1160, and as a second stage, the copying means 11
Activate 70 and wait for the copying means 1170 to stop.
A window function that stores the process in the window group storage unit 1140
Is performed the number of times, and the process ends. By the calculation means 1150
The activated copy unit 1170 stores the temporary storage unit 1160
The sequence is stored in the signal storage unit 1020, and the operation is stopped.   When the calculating means 1150 completes the processing, the control means 1000 displays
The indicating means 1010 is activated. The activated display means 1010 indicates the signal
The sequence of numbers stored by the storage means 1020 is displayed on the screen.
Is completed.   Next, FIG. 4 shows an embodiment of the fourth invention. In FIG.
Here, one embodiment of the fourth invention is the control means 1000,
Storage means 1020, arithmetic means 1150, temporary storage means 1160, display means
Step 1010 includes a copying means 1170 and further includes a zero area storage means 103
0, stage number storage means 1040, frequency characteristic storage means 1060 and
And size storage means 1050. Each of these means
Has the same function as the embodiment of the first to third inventions.
The detailed description of is omitted. The area width calculating means 1070
Each of the means 1030, 1040 and 1050 is connected similarly to the embodiment of the invention.
The window function stored in the number-of-stages storage means 1040 is continued.
Window function stored by the number and size storage means 1050
And the degree of approximation stored by the zero area storage means 1030
The area width is determined from the variables to be expressed. The area width storage means 1080
The area width determined by the area width calculation means 1070 is stored. Hado
The number expansion means 1090 is the area width stored in the area width storage means 1080
And the number of window functions stored in the stage number storage means 1040
To determine the wave functions of the harmonic oscillator.
The frequency characteristic storage means 1060 stores the frequency
A group of expansion coefficients of the wave number characteristic function is calculated. Expansion coefficient memory
Step 1100 stores the expansion coefficient group output by the wave function expansion unit 1090.
Remember. The exponent coefficient calculating means 1110 is provided with the expansion coefficient storing means 11
The expansion coefficient group stored in 00 and the zero area storage means 1030 store
The variable indicating the degree of approximation and the size storage means 1050 store the variable.
Generate a second-order polynomial using the magnitude of the window function
You. The exponent coefficient storage unit 1120 generates the exponent coefficient calculation unit 1110.
The coefficient group of the resulting quadratic polynomial is stored. Window functions
The generating unit 1130 is configured to store the approximation stored in the null region storage unit 1030.
Variables representing degrees and windows stored by size storage means 1050
The window size stored by the function size and stage number storage means 1040
Second-order polynomial stored in number and power coefficient storage means 1120
Window stored in the size storage means 1050 using the coefficient group of
Generate a sequence of lengths determined by the size of the
The columns are supplied to window group storage means.   The operation of the embodiment of the fourth invention will be described. Fourth
In the embodiment of the present invention, for example, the image signal
The frequency characteristic in the column is, for example, the above equation (21) illustrated in FIG. 5A.
Convolved the filter function, which is the real-valued function of the even function of
In the example of displaying the result, the above expression is used as the first stage of the preprocessing.
The image signal sequence represented by (20) is composed of, for example, a memory.
Stored in the stored signal storage means 1020 and used as the second stage of preprocessing.
For example, the zero area storage means 1030 constituted by a memory
For example, 4 is stored as the value of ξ that satisfies Expression (22), and
As the third stage of processing, for example, the size configured in the memory
Example of the size L of the window to be folded in the storage means 1050
For example, a positive odd number is stored, and as a fourth stage of preprocessing, for example,
The above formula is stored in the frequency characteristic storage means 1060 constituted by a memory.
For example, the frequency characteristic function F (ω) expressed by
FIG. 5B shows an example in FIG. 5B sampled for each Δω of the above equation (23) within the defined area.
The sequence of the above equation (24) is stored, and the fifth stage of the preprocessing is performed.
For example, in the stage number storage means 1040 constituted by a memory,
For example, 10 is written as the value k of the number of window functions to be folded.
Remember.   The processing starts when the control unit 1000 activates the area width calculation unit 1070.
Begin. The activated area width calculating means 1070 is a zero area storing means.
Constant ξ stored in 1030 and c
The number k of window functions and the size stored in the size storage means 1050.
From the size L of the window function and the area width Θ,
For example, it is recorded in the area width storage means 1080 composed of memory.
Then, the processing ends.   When the area width calculation means 1070 ends the processing, the control means 1000
Activates the wave function expansion means 1090.   The activated wave function expanding means 1090 is a step
Number K and area of window function stored in number storage means 1040
Before being defined using the area width stored by the width storage means 1080
The wave function group of 2K + 1 harmonic oscillators shown in equation (26) and
Expression (27) generated from Δω in Expression (23)
Calculate and hold 2K + 1 sequence groups, and as a second step,
The sequence and the number-of-stages storage means 10 stored in the wavenumber characteristic storage means 1060
The number k of window functions stored in 40 and obtained in the first step
Equation (27) and Δω in Equation (23)
The expansion coefficient group shown in the above equation (28) is constituted by a memory, for example.
Is stored in the expanded coefficient storage means 1100 and the processing is terminated.
You.   When the wave function expansion means 1090 completes the processing, the control means 10
00 activates the exponent coefficient calculating means 1110. The person who should have started
The number calculation means 1110 calculates the accuracy stored in the zero area storage means 1030.
And the number k of window functions stored in the stage number storage means 1040,
The size L of the window function stored in the size storage means 1050
And the series of sequences stored by the expansion coefficient storage means 1100 and the formula
From the coefficient group of the Hermite polynomial shown in (7-1)
Coefficient group Generated using the coefficient group of the equation (30) generated from
The 2k following equation of W shown in the equation (31)
The above equation obtained by transforming into the form of the above equation (32) using the c method
The group of numbers in (33) is written, for example, as a coefficient
This is stored in the storage unit 1120, and the processing ends.   When the power coefficient calculating means 1110 ends the processing, the control
Stage 1000 activates window function group generation means 1130. Start-up
The generated window function group generation means 1130 performs zero
Accuracy が stored by area storage means 1030 and size storage means 10
Window function size L and power coefficient storage function 50
Determined from the series represented by the equation (33) stored in the step 1120
The k window function groups and the size notation shown in the above equation (34)
The size L and the number of stages of the window function stored in the storage means 1050
The length is greater than the number k of window functions stored by the storage means 1040.
The k sets of sequence groups L are represented by, for example, Δ
Using the above x, as shown in FIG.
In the second stage, for example, a window composed of memory
The group storage means 1140 stores the k sets of sequence groups and the number of stages in the above equation (36).
Record the number k and size of the window functions stored in the storage means 1040
The size L of the window function stored by the storage means 1050 is stored.
To end the processing.   Control when window function group generation means 1130 finishes processing
The means 1000 activates the calculating means 1150. Activate arithmetic means 11
50 is stored in the window group storage means 1140 as the first stage
Read the number k of window functions and the size L of the window function
As a second stage, the above equation stored by the signal storage means 1020
The sequence shown in (20) and the window group storage means 1140 are stored.
From the first sequence shown in the above equation (37),
Generates a numerical sequence to indicate and temporarily stores, for example, a memory
Stored in the means 1160, and starts the copying means 1170 as the second stage
And waits for the copying means 1170 to stop.
Of the window functions stored in the window group storage unit 1140
Perform several times and end the process. By this arithmetic means 1150
When activated, the copying means 1170 stores the sequence stored in the temporary storage means 1160.
Is stored in the signal storage means 1020 and the operation is stopped.   When the calculating means 1150 completes the processing, the control means 1000 displays
The indicating means 1010 is activated. The activated display means 1010 indicates the signal
The sequence of numbers stored by the storage means 1020 is displayed on the screen.
Is completed.   As described above, in the embodiments of the first to fourth inventions,
Although the decomposition device of the dimensional filter has been described, in general,
Two-dimensional filters are one-dimensional by decomposing singular values
Effective application field of the present invention
(William K. Pratt, “Intelligent image proces
sing display terminal ", Proceedings of SPIE-The Int
ernational Society for Optical Engineering, Volume
199, Advances in Display Technology, 1979, PP.189-19
Four. [The invention's effect]   As described above, even function frequency characteristics can be
Group of window functions of the specified size
It is possible to disassemble it. On the other hand, fixed size
Filters can be easily converted to hardware using conventional technology
You. Therefore, according to the present invention, the above filter function can be easily obtained.
Hardware.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1, FIG. 2, FIG. 3, and FIG. 4 are block diagrams showing one embodiment of the first, second, third and fourth inventions, and FIG. FIG. 5B shows an example of a frequency characteristic of a function, FIG.
The figure shows an example of sampling of frequency characteristics, and FIG. 6 shows an example of a sequence group to be convolved. 1030: Zero area storage means, 1040: Stage number storage means, 1050
…… Size storage means, 1060 …… Frequency characteristic storage means, 10
70... Area width calculation means, 1080... Area width storage means, 1090
…… Wave function expansion means, 1100 …… Expansion coefficient storage means, 11
10 ... power coefficient calculating means, 1120 power coefficient storing means,
1130: Window function group generation means, 1140: Window group storage means, 2000: Step number calculation means.

Claims (1)

(57) [Claims] Frequency characteristic storage means for storing a frequency characteristic function of the filter; number-of-stages storage means for storing the number of window functions when the frequency characteristic function is represented by a large number of convolutions of a group of window functions; A size storage means for storing the size of the range as the size of the window function when approximated to take a value of zero outside the range; a zero area storage means for storing a variable indicating the degree of the approximation; An area width calculation unit that determines an area width from the stored variable indicating the degree of approximation, the size of the stored window function, and the number of the window functions, and an area width storage unit that stores the determined area width And a wave function group of a harmonic oscillator using the stored region width and the stored number of window functions, and the frequency characteristic function of the filter is defined as the wave function A wave function expansion means for calculating an expansion coefficient when the number group is expanded on the basis, an expansion coefficient storage means for storing the calculated expansion coefficient group, and a storage area width and the stored window function. From the number and the stored expansion coefficient group, the part that is a polynomial about the square of the angular frequency in the frequency characteristic function determined by them is expanded by the product of the quadratic polynomial group about the square of the angular frequency, and Coefficient calculating means for calculating the coefficient group of, coefficient storing means for storing the calculated coefficient group, a variable indicating the stored degree of approximation, the size of the stored window function, and Wind function group generation for generating a window function group for multi-superposition using the number of stored window functions and each stored power coefficient group of the stored second-order polynomial group Comprising a stage deployment device of the filter function, characterized by decomposing the filter function to window function group of a certain size with the given frequency characteristic. 2. Frequency characteristic storage means for storing a frequency characteristic function of the filter, and a case where the frequency function is approximated by taking a value of zero outside a certain range, when the window function is represented by a large amount of convolution of a group of window functions. Size storage means for storing the size of the range as the size of the window function, zero area storage means for storing a variable indicating the degree of approximation, and an area width for defining the spread of the wave function in the frequency space. From the stored variable indicating the degree of approximation, the size of the stored window function, and the stored region width, the frequency characteristic function is represented by multiplication of the window function. A number-of-stages calculating means for determining the number of the window functions in the case, a number-of-stages storing means for storing the determined number of the window functions, and the stored region width. Wave function expansion means for determining a wave function group of the harmonic oscillator using the number of the stored wind functions, and calculating expansion coefficients when the frequency characteristic function of the filter is expanded based on the wave function group. When,
Expansion coefficient storage means for storing the calculated expansion coefficient group; and an angular frequency in a frequency characteristic function determined from the stored area width, the number of stored window functions, and the stored expansion coefficient group. A coefficient calculation means for calculating a coefficient group to be expanded by multiplying a part which is a polynomial about the square of the quadratic polynomial for the square of the angular frequency, and storing the calculated coefficient group. Power function storage means, a window function group generation means for generating a window function group for multiple superimposition using the stored area width, the stored number of window functions, and the stored power coefficient group, And a filter function decomposing device which decomposes a filter function having a given frequency characteristic into a group of window functions having a predetermined size. 3. Frequency characteristic storage means for storing a frequency characteristic function of the filter; number-of-stages storage means for storing the number of window functions when the frequency characteristic function is represented by a large number of convolutions of a group of window functions; A size storage means for storing the size of the range as the size of the window function when approximated to take a value of zero outside the range; a zero area storage means for storing a variable indicating the degree of the approximation; An area width calculation unit that determines an area width from the stored variable indicating the degree of approximation, the size of the stored window function, and the number of the window functions, and an area width storage unit that stores the determined area width Using the stored region width and the stored number of window functions, a wave function group of a harmonic oscillator is determined, and a frequency characteristic function of the filter is defined as A wave function expansion unit that calculates an expansion coefficient when the expansion is performed based on the function group, an expansion coefficient storage unit that stores the calculated expansion coefficient group, and a storage area width and the stored window function. From the number and the stored expansion coefficient group, the part that is a polynomial about the square of the angular frequency in the frequency characteristic function determined by them is expanded by the product of the quadratic polynomial group about the square of the angular frequency, and Coefficient calculating means for calculating the coefficient group of the above, coefficient storing means for storing the calculated coefficient group, the stored region width, the number of the stored window functions, and the stored two. A window function group generating means for generating a window function group for multi-superposition using each power coefficient group of the order polynomial group, the filter having a given frequency characteristic Deployment device of the filter function, characterized by decomposing a number in window function group of a certain size. 4. Frequency characteristic storage means for storing a frequency characteristic function of the filter; number-of-stages storage means for storing the number of window functions when the frequency characteristic function is represented by a large number of convolutions of a group of window functions; A size storage means for storing the size of the range as the size of the window function when approximated to take a value of zero outside the range; a zero area storage means for storing a variable indicating the degree of the approximation; An area width calculation unit that determines an area width from the stored variable indicating the degree of approximation, the size of the stored window function, and the number of the window functions, and an area width storage unit that stores the determined area width Using the stored region width and the stored number of window functions, a wave function group of a harmonic oscillator is determined, and a frequency characteristic function of the filter is defined as A wave function expansion means for calculating an expansion coefficient when the function group is expanded as a basis, an expansion coefficient storage means for storing the calculated expansion coefficient group, and a function for storing the stored expansion coefficient group and the stored approximation. From the variable indicating the degree and the magnitude of the stored window function, a part that is a polynomial about the square of the angular frequency in the frequency characteristic function determined by them is calculated by multiplying a quadratic polynomial group about the square of the angular frequency. A coefficient calculating means for expanding and calculating a power coefficient group, a coefficient storing means for storing the calculated power coefficient group, a variable indicating the stored degree of approximation, and the stored window function And generating the window function group for multi-superposition using the magnitude of, the stored number of window functions, and the stored coefficient group of each power of the quadratic polynomial group. Comprising the Indo function group generating means, deployment device of the filter function, characterized by decomposing the filter function to window function group of a certain size with the given frequency characteristic.