JP2644490B2 - Digital frequency analyzer - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a digital frequency analyzer, and more particularly to a digital frequency analyzer capable of accurately determining a maximum intensity without being affected by resolution.

[Conventional technology]

FIG. 4 is a block diagram showing a conventional digital frequency analyzer.

An A / D converter 2 for digitizing the analog signal is connected to the sensor 1 for detecting data.
A multiplier 4 is connected to the output of the A / D converter 2 and the output of the window function generator 3, and the multiplier 4 is connected to a Fourier converter 5. The window function generator 3 is for removing a temporal discontinuity of an analysis signal (for example, for example, “manual utilizing FFT analyzer”).
(Edited by Kenichi Kido, published by Japan Management Association, pages 15 to 17).

The data detected by the sensor 1 is transmitted to the A / D converter 2
Is applied to the multiplier 4 and multiplied by the output of the window function generator 3. The result of the multiplication by the multiplier 4 is decomposed into frequency components by the Fourier transformer 5.

This type of digital frequency analyzer outputs a frequency analysis result at a certain fixed frequency interval (Δf = frequency resolution) because data is discretized during signal processing.

The frequency resolution (Δf) is determined by the number N of data taken from the sensor 1 and the time interval Δt at which the data is taken.
The relationship is as follows.

The maximum frequency that can be analyzed is determined by the sampling theorem, and is expressed by the following equation.

Normally, the number of samples N is 512 to 1 in terms of calculation speed.
024 points are used. For this reason, the frequency resolution Δf can be obtained by the following equation obtained by modifying the equations (1) and (2). Δf in this case, to a number of about 1/1000 of f _max.

FIGS. 5A and 5B are signal strength characteristic diagrams for explaining the frequency analysis processing.

As shown in FIG. 5 (a), the frequency is 4 Hz and the signal strength is 1
When a 00% sine wave is input to a digital frequency analyzer of Δf = 1 Hz, this signal is discretized by the A / D converter 2 in FIG.
Is converted into frequency data. FIG. 5B shows the result. In this case, the signal strength at 4 Hz is 100%, and the signal strength of the input signal is measured with an error of 0%.

When processing various analog data (for example, noise and vibration of a rotating machine, sound, etc.) and controlling and monitoring a boiler, etc., the data is processed on the time axis, the data is subjected to Fourier transform, and the frequency spectrum is converted. The analysis is often done. Then, from the viewpoint of ease of signal processing, it is desirable to perform signal processing after converting analog data into digital from the viewpoint of noise, S / N ratio, signal processing error, and the like.

[Problems to be solved by the invention]

However, for the conventional digital frequency analyzer,
Since the Fourier transformer has a digital configuration, its output is discrete (the discrete frequency is an integral multiple of Δf),
There is a problem that the amplitude value of the input frequency cannot be measured to an accurate value.

That is, when a sine wave (4.5 Hz, signal intensity 100%) as shown in FIG. 6A is converted into frequency data by the configuration of FIG. 4, the result becomes as shown in FIG. 6B. As is clear from FIG. 6 (b), since the output is discretized, the frequency is 4.5 Hz and is not output but becomes 4 Hz and 5 Hz. In other words, only the signal strength (50% to 60%) of the part other than the peak value of the input 4.5 Hz frequency is output.

As described above, conventionally, when the input frequency is other than an integral multiple of the frequency resolution Δf, the amplitude value of the input frequency cannot be accurately obtained. The frequency actually handled is
It hardly becomes an integral multiple, and therefore, it cannot be expected that the amplitude value is accurately obtained.

SUMMARY OF THE INVENTION An object of the present invention has been made in view of the above circumstances of the prior art, and has been made in consideration of a digital frequency analysis capable of accurately determining an amplitude value of an input frequency even when the input frequency is other than an integer multiple of the frequency resolution. It is to provide a device.

[Means for solving the problem]

In order to solve the above problems, the present invention provides a window function generator for generating a window function for removing a temporal discontinuity of an analysis signal, a sine wave generator for generating a sine wave, and the window function generator. Adder that adds the output signal of the sine wave generator and the output signal of the sine wave generator, a multiplier that multiplies the output signal of the adder with the digitized measurement signal, and performs a Fourier transform on the output signal of the multiplier to obtain a frequency component. And a Fourier transformer for decomposing the data into four components.

[Action]

By adding the output of the sine wave generator to the output of the window function generator, the input frequency f is distorted, and a frequency f 'obtained by adding a frequency component lower by a frequency resolution Δf to the input frequency f is obtained. . As a result, the width of the peak frequency of the input frequency becomes wider than Δf.
The amplitude value of the input frequency can be accurately measured even if it is not an integer multiple of.

〔Example〕

 Hereinafter, an embodiment of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram showing an embodiment of the present invention.
2 (a), (b) and (c) are characteristic diagrams for explaining the analysis processing.

In FIG. 1, the same elements as those in FIG. 4 are denoted by the same reference numerals, and duplicate description will be omitted. However, the adder 6 connected to the input terminal of the multiplier 4 and the adder 6 connected to the adder 6 A sine wave generator 7 is provided.

The output of the window function generator 3 in addition to the output of the sine wave generator 7 is input to the adder 6. The adder 6 and the window function generator 3 extend the width of the maximum amplitude value of the frequency of the input signal by the frequency resolution Δf.

In this embodiment, the function output from the window function generator 3 is a Hanning function represented by (4).

x (t) = (1−cos (2πt / Δt · N) (4) Further, the function output from the sine wave generator 7 is represented by equation (5).

y (t) = sin (2πt / Δt · N) (5) Next, the reason why the frequency width of the input signal is widened by using the sine wave generator 7 and the adder 6 will be described in detail. .

First, it is assumed that a sine wave represented by sin (2πft) is input to the sensor 1. This input signal is A / D converter 2
The signal becomes sin (2πft / Δt · N) by being converted from an analog to a digital amount of N at time intervals Δt. That is, when sampling is performed at the time interval Δt, the data is discretized, and therefore, the deformation process of the equation cannot be evaluated by the general wave equation. The minimum frequency at which the N pieces of data sampled at the time interval Δt is discretized, and this frequency is used as a reference to represent other frequencies. Therefore, the originally discretized frequency is a dimensionless number. Sin for continuous
(2πft), but in the case of discretization, it becomes sin (2πfn), and since n = (t / Δt · N), sin (2πft / Δt ·
N).

Next, the window function (1-cos (2πt / Δt)
.N)) and sin (2πt / Δt · N). The multiplication process and the result are shown below by mathematical expressions.

As described above, the output signal from the sine wave generator 7 is sin
(2πt / Δt · N) and the output signal from the window function generator 3 is (1−cos (2πt / Δt · N)), so the signal output from the adder 6 is sin (2πt / Δt · N). N)
+ (1−cos (2πt / Δt · N)).

The output signal from the A / D converter 2 is sin (2πft / Δt ·
N), the output signal and the output signal from the adder 6 are multiplied by a multiplier to obtain the following equation.

sin (2πft / Δt · N) {sin (2πt / Δt · N) + (1−cos (2πt / Δt · N))} Here, when 2π / Δt · N is ω, Here, if we return ω, And the components of the input frequency f and the input frequency f-1 are output. The two frequencies f and (f-1) have a wide spectrum as shown in FIG. 2 (c).

FIG. 2A shows the input frequency sin (2πf ₁ t / Δt · N).
Shows the waveform, FIG. 2 (b) shows a waveform of a frequency sin generated by the multiplier _{4 (2π (f 1 -1)} t / Δt · N + π / 4) ( however, (f ₁ -1 ) = F _{2. The} frequency
sin (2πf ₁ t / Δt · N), sin (2π (f ₁ −1) t / Δt
N + π / 4) both represent the frequency of the discretized wave. 3 (a) to 3 (d) show output waveforms when the frequency of equation (6) is input to the Fourier transformer 5.
FIG. 3A shows an input waveform centered at 4.5 Hz, and FIG. 3B shows a corresponding Fourier transform output. Also,
(C) is an input waveform centered at 5 Hz, and the corresponding Fourier transform output is (d).

As is apparent from FIGS. 3A to 3D, since the width of the input signal is wide, even if the frequency is discretized,
The signal strength can be determined accurately. That is, when the frequency is discretized, the signal strength of the frequency other than the discretized frequency cannot be accurately obtained. However, as in the present invention, the input signal is measured by the sine wave generator so that the input frequency can be measured at the discretized frequency. , The signal strength can be accurately obtained because it is within the calculation range of discretization.

It should be noted that even if the peak of the signal strength is accurately obtained, the entire shape of the frequency spectrum may not be accurately obtained because the width of the input signal is widened. In this case,
A switch is provided at the output of the sine wave generator 3 and the output is turned on.
/ OFF should be enabled. By turning off the switch when measuring the shape of the entire frequency spectrum,
Unnecessarily widening of the width of the input signal can be prevented.

Further, in the above embodiment, the Hanning function is used as the window function. However, other window functions, for example, a Hamming, a triangular window, a Brackman window, a 3-sigma Gaussian window, and the like can be used.

Further, a window function generator, a multiplier, a Fourier transformer, an adder, a sine wave generator, and the like can be configured by software.

〔The invention's effect〕

As described above, according to the present invention, a sine wave generator is provided, the output of the sine wave generator is added to the output of the window function generator, and the added value is multiplied by the output of the A / D converter. The signal strength can be accurately measured without being affected by the resolution.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an embodiment of the present invention, FIGS. 2 (a), (b) and (c) are characteristic diagrams for explaining the analysis processing of the present invention, and FIGS. 3 (a) to 3 (d). ) Is a characteristic diagram showing an analysis result of a frequency other than an integer multiple, FIG. 4 is a block diagram showing a conventional digital frequency analysis device, and FIGS. 5A and 5B explain conventional frequency analysis processing. Signal strength characteristic diagram, 6th
FIGS. 7A and 7B are signal strength characteristic diagrams for explaining a conventional frequency analysis process other than an integral multiple. 1 ... Sensor, 2 ... A / D converter, 3 ... Window function generator, 4 ... Multiplier, 5 ... Fourier transformer, 6 ...
Adder, 7 ... Sine wave generator.

Claims (1)

(57) [Claims] 1. A window function generator for generating a window function for removing a temporal discontinuity of an analysis signal, a sine wave generator for generating a sine wave, an output signal of the window function generator and a sine wave generation An adder for adding the output signal of the adder, a multiplier for multiplying the output signal of the adder by the digitized measurement signal, and a Fourier transformer for performing a Fourier transform on the output signal of the multiplier to decompose it into frequency components. A digital frequency analysis device comprising: