JPH063474B2 - Signal analyzer - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a Fourier analysis device for signals, and more particularly to a signal analysis device suitable for analyzing acoustic signals such as noise.

[Background of the Invention]

Conventionally, there is a spectrum analyzer based on Fourier transform as a device for analyzing a signal. When this is used, the sampling frequency for the input signal and the total number of data can be set appropriately, so that analysis can be performed by changing the necessary frequency range and resolution. Further, it is widely used because a specific part of an input signal can be analyzed at a time over a predetermined frequency range.

However, in the case where the shape of the spectrum is comparatively examined in relation to the auditory sense such as the noise of the device, the analyzed spectrum shape and the actual feeling may not correspond. One of the reasons for this is that the signal analysis in auditory sense has a property close to signal processing by a large number of bandpass filters described later, not by a transform such as Fourier transform. Therefore, for example, in order to investigate the relationship between the noise spectrum of a device and the feeling of hearing,
It is necessary to perform calculation processing that incorporates some kind of auditory property in the Sourier-transformed data.

On the other hand, there is a conventional signal analyzer called an octave analyzer. This device is provided with a large number of bandpass filters, and usually, a mechanical scan is used to sequentially select each bandpass filter and record the amplitude value of the signal passing therethrough. Octave analyzer from 20HZ to 20kH
It is used in the audible range up to z, or before and after the audible range, and it is possible to roughly associate the spectral shape with the auditory sense. In other words, if the frequency axis is divided by 1/3 octave width, it will roughly coincide with the critical band in hearing. Also,
The perceptual loudness is approximately proportional to the sound pressure level (dB) in the range where the change is not large.

As described above, the octave analyzer has an advantage that it has a high correlation with hearing, but has a drawback that it has a low resolution. For example, the amplitude value obtained by analyzing 20 Hz to 20 kHz with a filter of 1 octave is 10, and the amplitude value obtained by the filter of 1/3 octave is 30. Another disadvantage of the mechanical scan octave analyzer is that it is not possible to analyze a specific portion of the signal for a relatively short time due to the time difference due to the scan. That is, only stationary signals can be applied.

By the way, it is possible to calculate a spectrum corresponding to 1/3 octave analysis based on the analysis result obtained by the Fourier transform. However, there is no known analyzer that calculates with arbitrary resolution.

[Object of the Invention]

An object of the present invention is to provide a signal analysis device that can obtain a spectrum corresponding to the spectrum obtained by the octave analysis method using a bandpass filter by Fourier transform.

[Outline of Invention]

Since this device targets acoustic signals such as noise, the overall equipment configuration is a microphone that receives sound waves, an amplifier, an interface for capturing analog signals, and a book that performs calculation processing on sampled signals. It comprises a processor of the invention and a display etc. for displaying the results.

Here, first, a calculation method for a signal performed by the present apparatus will be described, and then the configuration of the apparatus will be described by way of examples.

In the measurement and calculation method of this device, first, for the measurement signal, the total number of amplitude data on the time axis by the predetermined sampling frequency and sampling is determined, and the Fourier spectrum (amplitude value) is calculated by the discrete Fourier transform (DFT) calculation method. ) And frequency pairs.

Hereinafter, the principle of the present invention will be described with reference to the drawings. Figure 1 shows D
It is an example of the Fourier spectrum of the signal obtained by FT calculation. The signal shown in the example has a constant value regardless of frequency like white noise, and the maximum value is set to 1.0 by standardizing the amplitude value. The interval for each data is 500Hz. The frequency axis in Fig. 1 is displayed from 1 kHz to 10 kHz in 1 kHz units at equal intervals.

The frequency axis in FIG. 2 is logarithmic, but the spectrum shown above is the same as the spectrum in FIG.
The respective data of the Fourier spectrum are not arranged at equal intervals on the frequency axis, and the number of data becomes denser as the frequency becomes higher. It is assumed that three regions are provided on the logarithmized frequency axis. That is, 1.4 kHz to 2.
Region R ₁ of 3 kHz, a region R ₂ of 5.6KHz from 2.8 kHz, a region R ₃ of 11.2kHz from 5.6KHz. These regions are evenly spaced with respect to the logarithmic frequency axis, and correspond to so-called one octave frequency spacing.

The spectrum value asj at the center frequency of each region is defined by the following equation from the amplitude value of each Fourier spectrum in these regions.

Here, m is the first number and n is the last number of the Fourier spectrum amplitude values falling in the j region. Equation (1) of the sum of squares represents the energy sum obtained by adding the energy of the amplitude a _{i in} the frequency band. For example, in the R ₁ region, a _S1 is obtained from the amplitude values a ₁ , a ₂ , and a ₃ to obtain R ₁
The spectral value at the center frequency of 2 kHz is defined. Similarly, spectral values a _S2 and a _S3 of 4 kHz and 8 kHz are defined.

Figure 3 shows all Fourier spectrum amplitude values (total N / 2)
Sum of squares Is used as a reference value, and the response (meaning the relative level of the spectrum) defined by the following equation is represented.

The difference in each value expressed in the response (dB) in the figure is approximated by a straight line with a slope of 3db. This tendency is consistent with the result of octave analysis of white noise.

In the calculation method of the apparatus of the present invention, a sufficiently small section is provided on the logarithmic frequency axis, and a sufficient number of amplitude values is prepared so that a plurality of Fourier spectrum amplitude values are included in the section, and the resolution is set. It is intended to obtain a high octave analysis spectrum.

Also, the individual amplitude values of the Fourier spectrum obtained by the Fourier transform are relative values, and the original signal (on the time axis)
Is uncorrelated with the amplitude value of. Therefore, the amplitude value of the input signal (eg RMS value) from the finally obtained spectrum
One is to find the total sum A _F of the spectrum from each amplitude value in the Fourier spectrum by the following equation, That is, each amplitude value a _i of the Fourier spectrum is divided by A _F , that is, normalized. Here, N / 2 is the total number of Fourier spectra. On the other hand, for the input signal, the RMS value A _I of the sampled signal amplitude is obtained by the following equation.

The value of A _I is proportional to the value of A _F (A
_F ≡A _I). Here, N is the total number of sampled signal amplitude data. Thus, the input signal amplitude value can be known from the value of A _I , and the amplitude value of each spectrum can be known from the difference between A _F and each spectrum value in the finally displayed spectrum.

Next, as a second method, a ratio F is calculated by the following equation, and each amplitude value a _i of the Fourier spectrum is divided by F = A _I / A _F (6) F, and a _fi = a _i / F (7) a _If the above calculation is performed based on a _fi instead of _i , the amplitude of the input signal and the amplitude of the final spectrum can be related. That is, when the input signal amplitude is small, the spectrum amplitude is small as a whole, and when the input signal amplitude is large, the spectrum amplitude is large as a whole.

Next, when obtaining the octave analysis spectrum,
The size of the frequency axis section is determined in advance and calculated. However, as a result of looking at the spectrum, when it becomes necessary to improve the resolution in a certain frequency range and investigate the spectral structure, it is necessary to appropriately change the size of the frequency section to obtain the spectrum. The apparatus of the present invention provides a calculation method that enables this.

Example of Invention

Embodiments of the present invention will be described below with reference to the drawings. FIG. 4 is a schematic block diagram of the signal analyzer of the present invention. In the figure, 1 is called an anechoic chamber, an anechoic box or a soundproof room, in which the measuring object T is placed. The anechoic chamber 1 is provided to eliminate external noise as much as possible. Microphone 2
Thus, the acoustic signal generated by the measuring object T is detected. The detected signal is microphone amplifier 3, measurement amplifier 4
Then, the signal is amplified to a predetermined amplitude and input to the interface 5. The interface 5 samples the analog signal at a predetermined sampling frequency and converts it into a digital signal. The digitized signal is processed by the device a of the present invention, and the result is displayed on the graphic display 11 or the XY plotter 16.

Next, the device a of the present invention will be described with reference to FIG. In the figure, an analog signal is digitized by an interface 5 and then temporarily stored in a random access memory (RAM) 6. The signal read from the RAM 6 is Fourier-transformed by the DFT processor 7 which performs the discrete Fourier transform (DFT) calculation. These are read-only memories
Sequentially according to the program recorded in (ROM) 15. Sampling frequency at interface 5,
Control panel 12
, And the information is transmitted by the program in ROM15. The same applies to the calculation conditions in the DFT processor 7.

The converter 7'calculates the result of the Fourier transform, and then the Fourier amplitude value is stored in the RAM8. Each of the series of amplitude values has its own frequency, but these are specified by the ROM 13 which records the address of the frequency axis, and here two sets of data of the Fourier amplitude value and the frequency are recorded in the RAM 8. The frequencies here follow the conditions specified by the control panel 12. Next, arithmetic unit
According to 9, the value of the octave analysis spectrum is calculated using the amplitude value and the frequency recorded in the RAM 8. If the calculation conditions in the arithmetic unit 9 are designated in advance on the control panel 12, the information is transmitted to the program in the ROM 15, and the arithmetic unit 9 is controlled by this. The spectrum value obtained as a result of the calculation is processed by the computing unit 9'and then combined with the frequency in the ROM 14 to temporarily convert it to R
After being stored in AM10, it is displayed on the display 11.

Next, the contents of calculation in each of the above steps will be described. First, the analog signal sampling conditions in the interface 5 will be described. Sampling frequency is 2
It is 0.48 kHz, and the total number of data is 4096. As a result, the acoustic signal generated by the measuring object is recorded for 0.2 seconds.

When the recording is finished, the calculation is started, but the contents of the calculation using the flowchart of FIG. 6 will be described. In the figure, in the step, a parameter m _{O in the} frequency section and an upper limit F _H and a lower limit F _L of the frequency range are determined. The parameter m _O will be described later, but in this embodiment, m _O = 1/20 and F _H = 10.
240H _Z, a _{F L} = 200H _Z. In the flow chart shown in the figure, the step is the starting point of the calculation, but in reality, it is continuously executed from the recording of the above-mentioned signal. The calculation from the next step to step is the DF in FIG.
The calculation contents in the T processor 7 are shown.

In the step, discrete Fourier transform as shown in the following equation is performed on 4096 pieces of data.

Here, x (n) is amplitude value data on the time axis, which is taken in by the interface of FIG. 5 and recorded in the RAM 6. N is the total number of data. The second term on the right-hand side is a weighting function called Hanning Operation.
Here, since the odd term in B (K) is calculated so as to represent a real number and the even term is expressed as an imaginary number, the Fourier spectrum (amplitude value) is obtained by the following equation.

This is the step calculation. Since N is 4096,
The total number of a _i is 2048. Also the sampling frequency
From 20.48kHz, the upper limit of frequency of Fourier spectrum is 10
It becomes 240Hz. Therefore, one amplitude value is arranged at intervals of 5 Hz.

Next, in step, the sum of the Fourier spectra a _j is calculated using the equation (4) to obtain A _F. In the next step, the RAS value of the input signal is calculated to obtain A ₁ . Here, A _F and A _I in the sense that in which both represent the energy of the signal, but the same as the original, A _F is a relative value based on the Fourier spectrum. Therefore, in the step, instead of A _F , the RMS value A _I of the input signal
Is displayed. The calculation from step to is performed in the arithmetic unit 7'of FIG. 5, and the result is recorded in the RAM 8.

In the step, the octave analysis spectrum a _si is derived from the 2048 Fourier spectra. This calculation is performed by the arithmetic unit 9, the details of which will be described later.

Next, in step, the octave analysis spectrum a _si is standardized by A _F. Then, the relative level L _i is obtained by the equation (3). That is, when A _{F is set} to 0 dB, each spectrum value is set to a relative level (d
B). This calculation is performed in the arithmetic unit 9 '. The step is a graphic program which displays the octave analysis spectrum on an XY blotter or graphic display as shown in FIG. Step when display ends In step 1, the resolution is changed and calculation is performed to determine whether or not to display. If it is not necessary, an instruction to that effect ends the calculation. If so, support it and step At, the upper limit F _H of the frequency range, the lower limit F _L , and the parameter m _{O of the} frequency section are input from the control panel.
At the starting point of calculation, m _O = 1/20, F _H ＝ 10240Hz, F
_{Although L} = 200 Hz, for example, m = 1/30, F _H = 10240
Hz, it is to enter F L ₌ 1000 Hz.

Next, the method of calculating the octave analysis spectrum will be described with reference to FIG. In the steps shown, an initial value for the frequency bandwidth is defined. f ₀ is the center frequency of the bandwidth, f ₁ is the lower limit frequency, and f _{2 is} the frequency. These frequencies have the following relationship.

▲ f ² ₀ ▼ = f ₁ · f ₂ , f ₀ = 2 ^m0 · f ₁
(10) m ₀ is a parameter that determines the bandwidth, and is 1 in this embodiment.
/ 20. That is 1/10 on-turbed width. f ₀ = F
_{If L} is used, the frequencies f ₁ and f ₂ are derived from the equation (10). For example, if the frequency f ₀ is 200 Hz, then f ₁ = 186.6 Hz, f ₂
= 214.4Hz. In the step, a _K (K = m, m +) existing between frequencies f ₁ and f ₂ among the Fourier spectra a _j (i = 1,2 ..., N / 20) calculated in advance is used.
Select 1, ... n). It is necessary to include at least one a _K in the band, and the frequency f _{0 of the} initial value cannot be set too low. In step, the sum of squares a _sj is calculated based on the selected a _K. In the step, a _sj is defined as a spectrum value of f ₀ and fos is a frequency of asj. In the step, based on the frequency f ₁ newly defined as f ₁ = f ₂ , the frequencies f ₀ and f
Calculate ₂ . Next, the data number j is increased by 1, and the frequency f ₂
If is less than or equal to F _H , the above calculation is repeated. Frequency f
_{When 2} becomes F _H or more, the calculation is ended and the process moves to the next calculation stage.

In the above example, 57 spectral values would be defined between 200Hz and 10240.0Hz.

In the above embodiment, the value of each spectrum is standardized by the sum A _F of the octave analysis spectrum. Therefore, since A _{F is set} to 0 dB in any case, it is possible to easily compare the generation of different measurement objects with each other in terms of spectrum shape and level difference.

As another example, as described in the principle of the present invention, the formula
By determining the spectrum value using (6) and (7), it is possible to obtain a spectrum in which the spectrum amplitude changes depending on the RMS value of the input signal.

EFFECTS OF THE INVENTION According to the present invention, it is possible to obtain an octave analysis spectrum without a time delay based on the calculation of discrete Fourier transform. Therefore, when investigating the spectral shape in relation to the sense of hearing such as noise, it is possible to easily obtain a spectrum having a resolution higher than that of the generally used 1/3 octave, for example, 1/10 octave. . As a result, it becomes easy to elucidate the relationship between the spectral structure and its cause.

[Brief description of drawings]

1, 2 and 3 are diagrams for explaining the relationship between Fourier analysis and octave analysis, Fig. 4 is the overall equipment configuration diagram, Fig. 5 is a circuit block diagram for performing analytical calculation, and Fig. 6 is FIG. 7 is a flow chart showing the contents of the analytical calculation, FIG. 7 is a characteristic diagram of a display example of the results, and FIG. 8 is a flowchart of the calculation for obtaining the octave analysis spectrum from the result of the Fourier transform. 5 ... Interface, 6, 8, 10 ... RAM 7 ... DFT processor, 7 ', 9, 9' ... Arithmetic unit 11 ... Display 12 ... Control panel 13, 14, 15 ... ROM

Claims (1)

[Claims] 1. A signal analyzing apparatus for obtaining an octave analysis spectrum by analyzing an acoustic signal such as noise as an analysis target. Sampling for obtaining amplitude data by sampling the analog acoustic signal as an analysis target at a predetermined cycle. means
(5), a storage means (6) for storing the plurality of amplitude data obtained by the sampling means, and a plurality of amplitude data stored in the storage means, and a Fourier transform is performed on the amplitude data. By performing, as a Fourier spectrum, a Fourier transform means (7) for obtaining an amplitude value corresponding to each frequency, and a desired frequency range within the frequency range covering the entire Fourier spectrum, on a logarithmic frequency axis. On the other hand, it is divided into a plurality of frequency sections so as to have substantially equal intervals, and from among the amplitude values respectively corresponding to the respective frequencies obtained by the Fourier transform means, for each frequency section obtained by the division, the The amplitude value corresponding to each frequency belonging to the frequency section is selected, the sum of squares of the selected amplitude values is calculated, and the octave component is calculated. Signal analysis apparatus characterized by comprising comprises an arithmetic unit for outputting a spectrum (9), the.