JPH0765929B2 - Spectrum analyzer - Google Patents

Description

The present invention relates to a spectrum analyzer for measuring the power spectrum of light or measuring the power spectrum of high frequency signals and acoustic signals.

[Background of the Invention] With the progress of semiconductor integrated circuit devices, fast Fourier transformers have become easy to put into practical use. For this reason, spectrum analyzers using fast Fourier transformers are in practical use.

"Problems to be Solved by the Invention" The analysis data obtained as a result of frequency analysis by the fast Fourier transform (hereinafter referred to as FFT) is intermittent data arranged at equal intervals with respect to the frequency axis.

In order to improve the resolution of the spectrum analyzer, the array pitch of analysis data may be made fine. However, in order to make the array pitch of the analysis data dense, it is possible to take in a large amount of data obtained by AD-converting the measurement signal over time and perform FFT on the time-series data generated over a relatively long time.

However, when this method is adopted, there are disadvantages that the capacity of the memory for capturing the time series data becomes large and that it takes time until the measurement result is obtained.

Therefore, conventionally, there has been considered a method of increasing the resolution by fetching time-series data sampled at a rough cycle in a memory having a limited capacity and performing FFT on the time-series data. This method is called a zoom method, and the coarser the sampling period of the data is, the more the amount of information on the time axis of the time series data stored in the memory is increased, and the resolution is improved.

However, even if this zoom method is adopted, there is a limit to the improvement in resolution. Even in the case of the zoom method, if the zoom ratio is increased to increase the resolution, it takes a long time to capture the data and the memory capacity must be increased.

When measuring the spectrum of light, the measurement result is displayed in the wavelength region with the wavelength λ on the horizontal axis. When the data obtained by frequency analysis by FFT is displayed in the wavelength region, there is a drawback that the resolution decreases as it goes to the long wavelength side. That is, the data subjected to frequency analysis by FFT exists at equal intervals with respect to the frequency F axis. Since this data is reciprocally converted into λ = 1 / F, the valve resolution decreases as the frequency F becomes lower, that is, the longer wavelength side. As an example 0.4μm ~ 1.6μ
When the wavelength range of m is displayed, the resolution ratio of the short wavelength side to the long wavelength side is 1:16. In other words, the resolution becomes 16 times worse on the long wavelength side.

This phenomenon is an unavoidable phenomenon when a method using frequency-analyzed data by Fourier transform is adopted.

The object of the present invention is to improve the resolution without increasing the data acquisition time and without increasing the memory capacity, and to obtain a resolution higher than the conventional limit value. Accordingly, it is an object of the present invention to provide a spectrum analyzer which can partially improve the resolution on the long wavelength side of data displayed in the wavelength region.

"Means for Solving Problems" In the present invention, A. multiplication means for multiplying a measured signal obtained by AD-converting an analog signal input according to a time series by a first window function called Hanning window, and B. this multiplication Fourier transform of the signal obtained from the means and frequency analysis, and fast Fourier transform means for obtaining the complex spectrum of the signal under measurement, and C. Calculation of the power spectrum by squaring the complex spectrum obtained by the fast Fourier transform means Means, and a part of the spectrum of the power spectrum obtained by the D. calculating means is multiplied by a second window function called minimum 4 term window, and the position of the window function is sequentially shifted with respect to the spectrum to obtain a plurality of power spectrum groups. Extraction means to be extracted and E. Power spectra existing in each group of power spectrum groups extracted by this extraction means Means for calculating the partial sum of F., F. storage means for storing the added value obtained by the addition means as an interpolated value between each spectrum of the power spectrum, and G. the interpolated value stored in this storage means for the power spectrum. And display means for displaying as.

[Operation] According to the configuration of the present invention, a partial sum is obtained by multiplying a part of the spectrum of the power spectrum by the second window function. Therefore, the partial sum is obtained by frequency analysis of the FFT at each frequency of the power spectrum. It becomes an interpolation value for interpolating between the analysis components. The resolution can be improved by this interpolation.

Here, in particular, in the present invention, the time series data is multiplied by a first window function called Hanning window, and further FFT is followed by a second window function called minimum 4 term window to obtain a partial sum of the power spectrum to obtain an interpolated value. Therefore, the power spectrum can be faithfully reproduced. The reason for this will be explained later using experimental results.

[Embodiment] FIG. 1 shows an embodiment of the present invention. In FIG.
11 is an optical interferometer, 5 is a light receiver, and 12 is a spectrum analyzer. In other words, this example shows the case of measuring the spectrum of light. The spectrum analyzer 12 includes an amplifier 6 that amplifies an electric signal output from the light receiver 5, an analog filter 13 provided at a subsequent stage, an AD converter 7, a magnification change switch 14, a magnification conversion circuit 15, a buffer memory 16, and a micro. It comprises a computer 17, a fast Fourier transform circuit 18, a main memory 19, and a display 9.

The magnification change switch 14 is switched to the state without magnification change by selecting the contact A, and is changed to the state with magnification change by selecting the contact B.

The magnification changing circuit 15 includes digital frequency converters 15A and 15B,
It is composed of digital filters 15C and 15D and resampling switches 15E and 15F.

In the digital frequency converters 15A and 15B, the analysis center frequency f ₀
Cos2π f ₀ n Δt and sin
Multiply by 2πf ₀ n Δt.

The digital filters 15C and 15D are provided for removing unnecessary wave components generated by frequency shift by the digital frequency converter and frequency components not analyzed, and the signal from which such unnecessary wave components are removed is resampled by the resampling switch 15
It is resampled at E and 15F and taken into the buffer memory 16. Magnification is mainly resampling switches 15E and 15F
It is determined by the resampling period (thinning rate).

In other words, if the capacity of the buffer memory 16 is 1024 points, for example, and if the data taken in the memory of 1024 points over the time period T at each cycle t is set to the scaling factor "1",
When the same signal is taken in every 2t period and 2T time, the magnification becomes "2".

By changing this magnification, the frequency spectrum displayed on the display 9 can be magnified and displayed at an arbitrary magnification,
The resolution can be increased by that magnification. By improving the resolution, it becomes possible to display a spectral display that was previously invisible.

As a practical example, a model that can increase the magnification from 2 times to 256 times is in practical use.

The factor that determines the magnification is the resampling period (thinning-out ratio) of the resampling switches 15E and 15F, and the center frequency when expanding is the center frequency set by the digital frequency converters 15A and 15B.

The data taken in the buffer memory 16 is sent to the fast Fourier transform circuit 18, Fourier transformed and stored in the main memory 19, and the frequency spectrum is displayed on the display 9. Further, the spectrum stored in the main memory 19 can be displayed as a spectrum in the wavelength region by reciprocal conversion.

In the present invention, the above-mentioned general-purpose spectrum analyzer is obtained from the multiplication means 17A for multiplying the time series data taken in the buffer memory 16 by a window function called Hanning Window, and the fast Fourier transform circuit 18. A calculating means 17B for obtaining the sum of squares of the complex spectrum and converting it to a power spectrum, and a second part called a minimum 4-term window in a part of the power spectrum.
Extraction means 17C for multiplying the window function and sequentially shifting to the position of the second window function with respect to the spectrum to extract a plurality of power spectrum groups, and power existing in each group of the power spectrum groups extracted by the extraction means 17C. The addition means 17D for calculating the partial sum of the spectrum is newly provided.

Each of these means 17A, 17B, 17C, 17D is a microcomputer 1
7, and the partial addition value obtained by the addition means 17D is stored in the main memory 19 as an interpolation value between each spectrum of the power spectrum. The interpolated value stored in the main memory 19 is displayed on the display 9 to display a high resolution spectrum.

The Hanning window has a frequency characteristic as shown in FIG. 2, for example, and the minimum 4-term window has a frequency characteristic as shown in FIG.

In order to obtain sufficient resolution, in the case of Hanning window, it is possible to obtain good results by using the horizontal axis L _{f up} to 16 frequency decomposition widths for multiplication.

Also, in the case of the minimum 4-term window, it is possible to obtain a good result by obtaining the partial sum by using the horizontal axis L _{f up} to the 4 frequency resolution width.

The window function shown in FIGS. 2 and 3 shows only the upper half from the center. Actually, it uses a vertically symmetrical characteristic.

The data AD-converted by the AD converter 7 and taken into the buffer memory 16 is a time domain signal. The microcomputer 17 reads this time domain signal, and the first window function multiplication means 17A multiplies the signal by the Hanning window.

The multiplication result is sent to the fast Fourier transform circuit 18, and FFT is performed. The data FFTed by the fast Fourier transform circuit 18 is R
It is a complex spectrum represented by _e (f) + jI _m (f). If the partial sum is calculated directly from the complex spectrum, the real part R _e (f) and the imaginary part jI _m (f) must be calculated separately, which results in a disadvantage that the amount of calculation increases. Therefore, in the present invention, the sum of squares of the complex spectrum, that is, the power spectrum P _w = R _e ² + I _m ² is obtained by the calculating means 17B and the partial sum is obtained using the power spectrum P _w . As a result, the amount of calculation can be reduced to 1/2 and the processing time can be halved compared with the case of obtaining the partial sum of the complex spectrum.

Analysis data converted to power spectrum is the extraction method
Multiply a part of the spectrum by the second window function by 17C,
A plurality of power spectrum groups are extracted by sequentially shifting the position of the second window function with respect to the spectrum, and the sum of the extracted power spectrum groups is obtained by the adding means 17D to calculate a partial sum. The extraction operation and the operation for obtaining the partial sum are generally called convolution.

The state of the extracting operation and the operation of obtaining the partial sum will be described with reference to FIG. FIG. 4A shows the power spectrum calculated by the calculating means 17B. P ₁ , P ₂ , P _3, ... P ₁₀ represent respective power spectra. The power spectra P _{1 to} P ₁₀ are arranged at equal intervals with respect to the frequency F. This shows that frequency analysis was performed by FFT.

4B to 4I show the state of the extracting operation. The triangle 21 shown in B to I is similar to the characteristic of the second window function. The second window function is multiplied by part of the power spectrum and extracted. The example of FIG. 4 illustrates a state in which the power spectra P ₅ and P ₆ are interpolated by convolution. Further, in this example, a case is shown in which each spectrum is divided into seven equal parts, and each of the seven equal parts is interpolated.

Further, the characteristic 21 of the second window function uses up to 4 frequency resolution width in the characteristic of the minimum 4-term window function shown in FIG. Therefore, 4 from the center of characteristic 21 up and down
The spectrum of the book is extracted, and up to 9 spectra are extracted together with the spectrum of the center.

In FIG. 4B, four spectra P _{1 to} P ₄ and P _{6 to} P ₉ are extracted above and below the spectrum P ₅ as a center, and these spectra are extracted.
It shows a state in which P _{1 to} P ₄ and P _{6 to} P ₉ and the central spectrum P ₅ are multiplied by the characteristic 21 of the second window function and extracted. The power spectrum group extracted in FIG. 4B is added by the addition means 17D, and the added value n ₁ is written in the main memory 19 as a value corresponding to the power spectrum P ₅ as shown in FIG. 4J.

In FIG. 4C, the position of the second window function is shifted by one interpolation width T,
Spectrum P _2, P ₃ are included in the scope of the characteristic 21 at that position, P ₄
… Shows the state where P ₉ is multiplied by characteristic 21 and extracted. The extracted spectrum group is added by the addition means 17D, and the added value n ₂
In the main memory as an interpolated value for the interval adjacent to spectrum P _5.
Remember in 19.

In FIG. 4E, the position of the characteristic 21 of the second window function is further expanded by one interpolation width T
The spectrum included in characteristic 21 at that position
Multiplied by the characteristic 21 P ₂ to P ₉ shows a state in which the excised.

Similarly, while shifting the characteristic 21 of the second window function by one interpolation width T, the spectrum included in the characteristic 21 in each state
Excised by multiplying the characteristic 21 P ₂ to P _9, the excised spectrum groups are added in the addition unit 17D, while the spectrum P ₅ and P ₆ to n ₂ ~n ₈ in addition value n ₁ ~n ₈ , And n ₁ is the spectrum P ₅
Is stored in the main memory 19 as the value of. This interpolation operation is performed between all the spectra P ₁ -P ₂ , P ₂ -P ₃ , P ₃ -P ₄ , P ₄ -P ₅ ..., and the interpolated values obtained between them are stored in the main memory 19. Remember.

By displaying the data including the interpolated value stored in the main memory 19 on the display 9, the spectral information that has been present only intermittently is replenished, so that the resolution is improved. In the example of FIG. 4, the resolution is increased to 8 times the original power spectrum. Therefore, if the power spectrum shown in FIG. 4A is raised to the limit of the device by the zoom method,
From that limit, the resolution can be further increased eight times.

FIG. 5 shows an example of the spectrum displayed in the frequency domain. The spectrum of FIG. 5 shows the result of the display according to the invention.

On the other hand, FIGS. 6 and 7 show examples of displaying the power spectrum obtained when the first window function and the second window function are different from those in this application.

That is, the example of FIG. 6 shows a case where a minimum 4-term window is used for the first window function and the second window function. In the case of FIG. 6, it is difficult to distinguish the unnecessary spectrum from the necessary spectrum in the sideband portion 23 of the necessary spectrum 22, and the spectrum 22 necessary for this is displayed thicker, which is different from the characteristic of the original spectrum. Results are displayed.

The example of FIG. 7 shows the case where Hanning window is used as the first and second window functions.

As described above, when the Hanning window is used as the first and second window functions, there is a disadvantage that unnecessary sidebands are generated above and below the main spectrum 22 and the accuracy is deteriorated.

On the other hand, FIGS. 8 and 9 show spectra displayed in the wavelength region by inversely converting the interpolation values stored in the main memory 19. FIG. 8 shows the display result obtained by the present invention, in which the spectrums at each wavelength are accurately separated and displayed.

On the other hand, FIG. 9 shows a display result obtained by the conventional technique. As is apparent from FIG. 9, according to the conventional spectrum analyzer, the spectrum of each wavelength cannot be completely separated and displayed because of its low resolution.

[Advantages of the Invention] As described above, according to the present invention, it is possible to obtain a high resolution that cannot be obtained by the conventional technique. In particular, as a method for that purpose, the processing time is short because the capacity of the memory is not increased, the necessary data is not interpolated, and only the necessary data is interpolated and obtained. Therefore, the time until the display result is displayed can be shortened and a spectrum analyzer with high speed and high resolution can be obtained.

Further, when measuring each wavelength component of light, the resolutions on the short wavelength side and the long wavelength side can be made uniform by making the convolution magnification different between the long wavelength side and the short wavelength side of the measurement region.

[Brief description of drawings]

FIG. 1 is a block diagram for explaining an embodiment of the present invention, and FIGS. 2 and 3 are graphs for explaining the characteristics of the first window function and the second window function used in the present invention. FIG. 4 is a diagram for explaining the operation of obtaining the extraction and the partial sum used in the present invention, FIG. 5 is a graph showing the power spectrum displayed in the frequency domain obtained by the present invention, and FIGS. 6 and 7 are FIG. 8 is a graph showing a power spectrum obtained when the first window function and the second window function are different from those of the present invention, and FIG. 8 shows the power spectrum obtained by the present invention shown in FIG. FIG. 9 is a graph showing an example of displaying a spectrum, and FIG. 9 is a graph showing an example of displaying a spectrum in a wavelength region by a conventional technique. 9: Display, 12: Spectrum analyzer, 17: Microcomputer, 17A: Multiplying means, 17B: Arithmetic means, 17C: Extracting means, 17D: Adding means, 18: Fast Fourier Transform, 19: Main memory.

Front page continuation (72) Inventor Shinichi Watanabe 1-32-1, Asahi-cho, Nerima-ku, Tokyo Within Advantest Co., Ltd. (56) References JP-A-61-65171 (JP, A)

Claims (1)

[Claims] 1. A. Multiplying means for multiplying a signal to be measured input according to a time series by a first window function, and B. A signal obtained from this multiplying means is subjected to Fourier transform for frequency analysis to obtain a complex of the signal to be measured. Fast Fourier transform means for obtaining the spectrum, C. computing means for obtaining the sum of squares of the complex spectrum obtained from the fast Fourier transform means and converting it into a power spectrum, D. a part of the spectrum of this power spectrum
Extraction means for multiplying the window function and sequentially shifting the position of the second window function with respect to the position of the spectrum to extract a plurality of power spectrum groups, and E. Existence in each group of the power spectrum groups extracted by this extraction means F. Addition means for calculating the partial sum of the power spectrum, F. Storage means for storing the added value obtained by the addition means as an interpolated value between each spectrum of the power spectrum, G. Interpolation stored in this storage means A spectrum analyzer consisting of a display means for displaying values as a power spectrum.