JP2006145515A - Device for generating parametric time stretched pulse - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a device for generating a measuring input waveform and a reverse filter thereof used for measuring an accurate impulse response. <P>SOLUTION: In a method for measuring a discrete impulse response of a measuring object system having a continuous time with invariant linear time by use of an non-impulse optional waveform input signal to the system and the reverse filter of the input signal, convolution is executed by the reverse filter while keeping the linearity of an envelope by mutually relating amplitude characteristic, group delay characteristic and phase characteristic by numerical integration and numerical differentiation, and also while having having an optional power spectrum, whereby a time stretched pulse (TSP) capable of strictly reproducing an impulse response and the reverse filter thereof are generated. Compared with a sweep-out line of ASTSP in which frequency was linearly changed to time, the TSP in the present invention capable of freely design a change graph of sweep-out line generates a measuring input waveform considering unpreferable characteristics of the measuring object system and the waveform of the reverse filter thereof, and these are used for measurement, whereby further precise measurement of impulse response can be performed. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

The present invention relates to a method for measuring an impulse response performed to measure an unknown dynamic characteristic of a system, for example, an acoustic characteristic at each location of a music hall, and more particularly, a measurement used for measuring a highly accurate impulse response. The present invention relates to generation of an input waveform and its inverse filter.

As an impulse response digital measurement method, a time-extended pulse (OATSP) optimized so that the phase characteristic becomes a real number smoothly in the vicinity of half the sampling frequency (Nyquist frequency) shown in Patent Document 1 is used. A method has been proposed in which an impulse response is restored by performing linear convolution or cyclic convolution of an output from a system under measurement with an inverse filter of the input signal, as an input signal for measurement.
Further, Non-Patent Document 1 and the like have been devised as an attempt to change the sweep line (group delay characteristic) of the time extension pulse.
Also, in measurement using OATSP, the input waveform is often reproduced continuously, and the output from the system under test is averaged at a period in which the phases are completely matched, so that the input waveform is discriminated against the background noise. A technique called synchronous addition for enhancing the output from the related system under test is used in parallel.

In addition, since the impulse response is usually measured through a loudspeaker and a microphone, for example, when a conventional measurement method using TSP is used alone to measure the impulse response of a music hall, the frequency characteristics unique to the speaker and microphone are also measured. Only the impulse response as a result of the simultaneous convolution is obtained, and the pure impulse response of the music hall cannot be obtained. As a measure to avoid or reduce this problem, obtain the impulse response of the same speaker and microphone itself in an anechoic room, etc., and convolve the impulse response after measurement with a filter having this inverse characteristic. And a method of canceling the frequency characteristics of the microphone.
Patent 2725838 Proceedings of the Acoustical Society of Japan (September-October 1999, 433-434)

Since the OATSP sweep line is like a sine wave whose frequency changes linearly with time, it often has an important meaning in the system under measurement, and the time occupied by the low frequency that requires more accurate measurement. The ratio is small.
For example, the frequency band that humans use to judge timbres and pitches is up to about 5 KHz, and a higher frequency band is necessary to obtain a high-quality sound, but the content of perceived speech is This is a thin band.
However, in the conventional OATSP, for example, when the sampling frequency is 44.1 KHz, the Nyquist frequency, which is the upper limit of the effective frequency band, is 22.05 KHz. Therefore, the time ratio occupied by the band below 5 KHz is about a quarter. It is only about.
Since a large amount of time (in other words, energy) is used for high frequencies that are less important as human senses, low frequencies that are more important as human senses are relatively more susceptible to noise.
Also, in the natural environment, every object and air itself has a tendency to act as a low-pass filter for the sound source, so the spectrum of background noise is usually dominated by low frequencies. Therefore, a low frequency with a small time ratio is more susceptible to noise.
Further, the system under measurement usually includes undesirable nonlinear effects (distortion), and the spectrum of noise (distortion component) generated by the distortion is concentrated at a frequency that is an integral multiple of a TSP waveform that is regarded as a sine wave at a specific time. There is a tendency. Since the distortion component is generated with the input of the TSP, it is not suitable to reduce the influence even if the synchronous addition is used.
For this reason, for example, in measurement of a music hall with a very long reverberation time, the reverberation of the distortion component is mixed into the original impulse response component as shown in FIG.
This phenomenon itself is unavoidable, and moreover, since the original impulse response component and the distortion component are close in time, particularly at low frequencies, more components are mixed.
Furthermore, the spectrum of background noise in the measurement environment usually varies from measurement environment to measurement environment depending on the type of noise source and the degree of resonance.
In addition, in the measurement method combining the TSP and the inverse filter of the measurement medium, the relative amplification factor increases when compensating for the drop in power of the measurement medium, particularly near the reproduction frequency range limit. Existing noise is also amplified at the same time, and the S / N ratio is significantly reduced. Further, since the convolution for restoring the impulse response from the input of the TSP and the convolution by the inverse filter of the measurement medium are necessary, the amount of calculation is increased.

In a method for measuring a discrete impulse response of a system under test using an arbitrary non-impulse waveform input signal and an inverse filter of the input signal with respect to the system under measurement having a linear time invariant continuous time, amplitude characteristics and group delay characteristics By associating the phase characteristics with numerical integration and numerical differentiation, the impulse response can be accurately reproduced by performing convolution with the inverse filter while maintaining the linearity of the envelope while having an arbitrary power spectrum. A device that generates a time-extended pulse (TSP) and its inverse filter waveform.
In the above measurement method, a time-extended pulse (TSP) having a time-frequency graph as a sweep line that passes through a frequency 0 at an initial time, increases monotonically, and is represented by a function of frequency using a continuous arbitrary time as a parameter. A device for generating an input signal and an inverse filter waveform that can accurately reproduce an impulse response by performing convolution with the waveform of the inverse filter generated at the same time as the input signal.
In the above measurement method, the TSP signal whose group delay characteristic and amplitude characteristic are corrected based on the impulse response B prepared at a time different from the measurement time is used as the input signal of the system under test, and is simultaneously generated. A device for generating the input signal and the signal used for convolution, which can restore the impulse response obtained by removing the frequency characteristic of B from the measured system by convolving the output signal from the measured system with the filtered signal.
And an apparatus for synthesizing a plurality of arbitrarily designed group delay characteristics by multiplication of amplitude characteristic levels in the above TSP generation processing.
In the TSP generation process, the TSP power spectrum is changed so as to have an equivalent characteristic based on the background noise power spectrum measured in advance at the measurement location.

Compared with the OATSP sweep line whose frequency has changed linearly with respect to time, the TSP according to the present invention, which can freely design the sweep line change graph, takes into account the undesirable characteristics of the system under measurement. A more accurate impulse response can be measured by generating a measurement input waveform and a waveform of its inverse filter and using them. For example, in a system under measurement having distortion, as shown in FIG. 3, in the low frequency band, mixing of distortion components can be suppressed to a minimum, and the strict restoration capability of the impulse response is maintained.
Furthermore, after restoring the impulse response of the system under test including the measurement medium, the correction amount for each frequency band is averaged by changing the power spectrum of the TSP, compared to the case where the inverse filter of the measurement medium is convoluted. A decrease in the S / N ratio can be suppressed.
In addition, since the inverse filter characteristic of the measurement medium is incorporated in a filter that restores an impulse from TSP, the number of convolutions after measurement can be reduced from two to one.
Furthermore, by combining the group delay characteristics and amplitude characteristics of the arbitrarily designed TSP and the above inverse filter characteristics, it can be used together with the TSP design method considering the influence of background noise and distortion.
Furthermore, by changing the power spectrum of the TSP so as to have the same characteristics based on the background noise measured in advance, it is possible to design an optimum TSP for the background noise.

Conventional TSP (time-extended pulse) is a technique for dispersing impulse energy on the time axis by changing the phase of each spectrum constituting the impulse in proportion to the square of the frequency. The inverse filter is obtained by reversing the TSP itself on the time axis.
The reason why the phase is changed in proportion to the square of the frequency is that the group delay characteristic is defined as a frequency derivative of the phase characteristic, and thus the group delay characteristic is actually changed linearly with respect to the frequency. It will be a thing.
Here, consider the definition of a time-stretching pulse in which the power spectrum is not flat while maintaining the linearity of the envelope.
If a certain band has a larger power than other bands, the envelope of the band becomes higher if the group delay graph remains a straight line, and the linearity cannot be maintained.
For this reason, in a band having relatively large power, it is necessary to increase the slope of the group delay graph (that is, increase the delay amount per unit frequency) in order to distribute the power over a longer time width.
It can be seen that the power is represented by the square of the amplitude, and the group delay characteristic is intuitively the frequency integral of the power spectrum.
Further, since the group delay characteristic is defined as the frequency derivative of the phase characteristic, the design expression H () in the frequency domain of the time-extended pulse to be defined here is expressed as a function A () representing the amplitude characteristic. The starting point can be expressed by the following equation.

Number 1

F (k) = Σ (A (k) ^ 2) (0 ≦ k ≦ 1)
* Σ (sigma) represents integration * ^ represents power

Number 2

      S (k) = ΣF (k) (0 ≦ k ≦ 1)

Number 3

h (k) = exp (−S (k) Q) (0 ≦ k ≦ 1)
* Exp (x) = cos (x) -jsin (x)
H (k) = h (k) A (k) (0 ≦ k ≦ 1)
H (k) = C (h (2-k)) A (2-k) (1 ≦ k <2)
* C () represents a complex conjugate * Q is a normalization constant F () is a function representing a group delay with respect to frequency, and S () is a function representing a phase rotation amount.
k is a parameter representing a frequency. When k = 0, it represents 0 Hz, and when k = 1, it represents a Nyquist frequency. In the formal definition of the conventional OATSP, the TSP sweep line is a straight line starting from a high frequency and descending to a low frequency. If this is used for the input waveform, the measured system has distortion as shown in FIG. The component appears on the main component side of the impulse response. Therefore, the TSP for the input waveform in the present invention inverts the sign of the phase so that the TSP sweep line draws an ascending curve.
h () is the result of the phase rotation, and this is multiplied by the amplitude characteristic A () to obtain H ().
When 0 is included in the value of A (), an inverse filter cannot be obtained. For this reason, if A (k)> 0 in the range of at least (0 ≦ k ≦ 1), the graph of F () increases monotonously and becomes the maximum group delay amount when F (1).

When H () is inverse Fourier transformed and expanded to the real-time domain, all energy is converted to real numbers, so H (1) is a real number, and H (k) and H (2-k) are complex. It is necessary to satisfy the conditions for conjugation.
By preparing a constant Q and making S (1) Q an integral multiple of π, h (1) can be made a real number, and H (1) multiplied by the amplitude of the real value can also be a real number.

Number 4

Q = πN / S (1)
* N is an arbitrary natural number

However, the group delay amount from the direct current to the Nyquist frequency, that is, F (1) representing the total length of the TSP naturally changes according to the shape of A (), so that it is necessary to normalize F (1) as well. Therefore, the definition of Q is corrected as follows.

Number 5

Q = π · Int (n · S (1) / F (1)) / S (1)
* Int represents fractional truncation * n represents an arbitrary real number When n = 0, the TSP has an impulse-like waveform, and when n = 1, the TSP Nyquist frequency component and DC component wrap around in time. In general, n is determined from the range (0 <n <1).
The target TSP waveform can be obtained by inverse Fourier transforming H ().
The inverse filter design formula may be obtained by inverting the sign of the phase and taking the inverse of the amplitude characteristic.

Equation 6

hi (k) = exp (S (k) Q) (0 ≦ k ≦ 1)
Hi (k) = hi (k) / A (k) (0 ≦ k ≦ 1)
Hi (k) = C (hi (2-k)) / A (2-k) (1 ≦ k <2)

An inverse filter waveform of the target TSP (hereinafter referred to as inverse TSP) is obtained by performing inverse Fourier transform on Hi ().
The above design formula can be rewritten starting from F ().

Number 7

A (k) = sqrt (F ′ (k))
* '(Apostrophe) represents differentiation * sqrt () represents the square root The subsequent formulas are the same as when A () is used as the starting point, and will be omitted.
F () must be a strictly monotonically increasing function (slope always exceeds 0) due to the constraint of A (k)> 0.

As a TSP design policy, A () is used as the starting point when designing based on the power spectrum, and F () is used as the starting point when designing based on the shape of the sweep line (frequency-group delay graph). Design becomes easy.

Here, TSP design means based on the shape of the sweep line (frequency-group delay graph) will be specifically described.
First, a function f (t) of time with respect to frequency is defined. f (t) is a function that uses the time t as a parameter and outputs the frequency k in order to facilitate the design of the TSP sweep line.
The change range of t is 0 ≦ t ≦ 1, and the frequency changes from 0 Hz to the Nyquist frequency within this range. That is, the value of k at t = 1 is the Nyquist frequency.

Number 8

k = f (t)
Since the sweep line of the TSP has a frequency range from 0 Hz to the Nyquist frequency, f (t) needs to pass through 0 Hz.
Further, since the sweep line is the result of the group delay graph for each frequency, the same frequency cannot exist at different times in the TSP waveform for one period. For this reason, f (t) needs to increase monotonously.
Also, since TSP needs to include all frequencies, f (t) must be continuous.

Next, an inverse function F (k) of f (t) is obtained so that the function parameter is a frequency. Also, normalization is performed so that the value of f (1) corresponds to the Nyquist frequency (k = 1). Here, the change range of t and k is reversed, and 0 ≦ k ≦ 1.

Number 9

t = F (k) where F (x) = Inv (f (x) / f (1))
* Since Inv () monotonically increases f (t) representing an operation for obtaining an inverse function, F (k) that is the inverse function also monotonously increases. Thereafter, the amplitude characteristic A (k) is obtained by performing the transformation represented by Equation 7, and the TSP and inverse TSP are designed in the frequency domain by performing the transformation represented by Equation 2, Equation 3, Equation 5, and Equation 6. An expression can be obtained.

However, when f (k) has a sharp incremental change (for example, when f (t) is a function combining arbitrary line segments, etc.), the inverse function F (k) also has a similar incremental change. A point that is not smooth occurs in the amplitude characteristic A (k) corresponding to the differential function of (k), and when developed in the time domain, it appears as an oscillation-like spectrum in the vicinity of the frequency where the increment changes. (FIG. 4) When the system under test is completed within the software of a computer, for example, the oscillation-like spectrum can be canceled out by an inverse filter. There is not a little distortion through the target element. However, the oscillation-like spectrum is fragile due to cross modulation and standing waves in a measurement system having distortion.
For this reason, a function L () representing a low-pass filter is prepared as necessary, and F (k) is defined as follows.

Number 10

      t = F (k) where F (x) = L (Inv (f (x) / f (1)))

In a normal TSP design, since it is desired to give a longer measurement time to a low frequency, f (t) is often a high-order expression or an exponential function of t.
However, these equations have a slope of 0 or a value close to 0 near 0 Hz. For this reason, A (k), which is a derivative of the inverse function of f (t), has a pole near 0 Hz, and the envelope is disturbed. One solution to this problem is to provide a linear term of t having a small coefficient in f (t) to prevent the slope from becoming zero.

Equation 11

f (t) = fo (t) + αt
* Fo () is a monotonically increasing function with a slope of 0 * α is a small constant

When f (t) is an exponential function of t, a sufficient TSP length may not be obtained unless low-frequency wraparound is allowed. For this reason, an arbitrary roll-off function R (k) is prepared as necessary to suppress the amplitude of the band where the wraparound occurs.

Number 12

      A (k) = sqrt (F ′ (k)) R (k)

The above is the description of the TSP design means based on the shape of the sweep line.
Next, design means based on the TSP power spectrum will be described. When using a typical TSP, such as measuring the impulse response of a music hall using a speaker and a microphone, it is important to pay special attention to the power spectrum in terms of the frequency characteristics of the speaker and microphone (so-called sound habit). And the power spectrum of background noise. First, the former will be described.

When the TSP signal is convoluted with the inverse TSP for the definition of the design formula in the frequency domain of the TSP and the inverse TSP expressed by the mathematical expressions 1 to 7, it is not a pure impulse signal but an inverse filter of an arbitrary signal. Attempt to transform so that the impulse response with the following characteristics is restored.
In the following, an arbitrary signal to be subjected to inverse filter restoration by convolution is referred to as a correction signal.

First, the correction signal is Fourier-transformed to obtain amplitude characteristics and phase characteristics.

Equation 13

Aa (k) = sqrt (Ra (k) .Re ^ 2 + Ra (k) .Im ^ 2)
(0 ≦ k ≦ 1)

Number 14

Pa (k) = atan (Ra (k) .Im / Ra (k) .Re)
(0 ≦ k ≦ 1)
* Atan () represents an arctangent, Ra represents a complex signal after Fourier transformation of the correction signal, Re represents a real part, and Im represents a real number of an imaginary part.
Aa () is the amplitude characteristic of the correction signal, and Pa () is the phase characteristic. k is a parameter representing the frequency. When 0, the direct current is 2 and when it is 2, the sampling frequency is represented. The range of k used for TSP processing is from DC to the Nyquist frequency.

The group delay characteristic of TSP is processed based on Aa (). However, the impulse response of a normal speaker or microphone has a sharp undulation in the amplitude characteristics, and the average value of the amplitude tends to attenuate as a whole near the reproduction limit region.
When the amplitude characteristic of the TSP has a sharp undulation, an oscillation-like spectrum is generated and is vulnerable to distortion generated during measurement. Further, when the attenuation near the reproduction limit region is significant, a large amount of time is allocated to the band in the entire length of the TSP signal, and conversely, the S / N ratio in the central reproduction region is lowered.
In order to avoid this problem, the minimum value of the amplitude of Aa () is limited and the amplitude is averaged.

Number 15

Ea (k) = Avg (Lmin (Aa (k))) (0 ≦ k ≦ 1)
* Lmin () represents an operation for limiting the minimum value * Avg () represents an operation for obtaining a moving average value. An operation for obtaining a moving average value uses a weighted moving average by a window function to obtain a smoother curve. .

Next, the reciprocal of Ea (k) is taken to obtain the amplitude characteristic A1 () for TSP correction.

Equation 16

      A1 (k) = 1 / Ea (k) (0 ≦ k ≦ 1)

Further, since the amplitude characteristic is limited and averaged in Equation 7, it is necessary to incorporate the difference between Aa () and Ea () into the amplitude characteristic of the inverse TSP. The value Fa () is obtained by the following equation.

Equation 17

Fa (k) = Aa (k) / Ea (k) (0 ≦ k ≦ 1)
In inverse TSP, problems such as bias due to the frequency band of the S / N ratio and oscillation-like spectrum occur, so the same operation as Aa () is performed to obtain amplitude characteristic A2 () for inverse TSP correction.

Number 18

A2 (k) = 1 / Avg2 (Lmin2 (Fa (k))) (0 ≦ k ≦ 1)
* Lmin2 () represents an operation for limiting the minimum value. * Avg2 () represents an operation for obtaining a moving average value.

Next, Ap () representing the amplitude characteristic of TSP and An () representing the amplitude characteristic of inverse TSP are obtained as follows.

Number 19

      Ap (k) = A1 (k) A (k) (0 ≦ k ≦ 1)

Number 20

      An (k) = A2 (k) / A (k) (0 ≦ k ≦ 1)

Then, S () representing the group delay characteristics of TSP and inverse TSP is modified as follows to obtain S2 ().

Number 21

S2 (k) = Σ (Σ (F ′ (k) Ad ′ (k))) (0 ≦ k ≦ 1)
However, Ad (k) = Σ (A1 (k) ^ 2)
Formula 21 represents an operation of multiplying values obtained by differentiating F () and Ad (), which are functions representing group delay characteristics with respect to frequencies, and integrating the result twice.
After all, it is the result of multiplying two power spectra.

Number 22

      S2 (k) = Σ (Σ (Ap (k) ^ 2)) (0 ≦ k ≦ 1)

Finally, the equations obtained so far are integrated to obtain design equations in the frequency domain of TSP and inverse TSP here.

Equation 23

h (k) = exp (−S2 (k) Q) (0 ≦ k ≦ 1)
H (k) = h (k) Ap (k) (0 ≦ k ≦ 1)
H (k) = C (h (2-k)) Ap (2-k) (1 ≦ k <2)
Q = π · Int (n · S2 (1) / S2 ′ (1)) / S2 (1)

Number 24

hi (k) = exp (S2 (k) Q-Pa (k) (0 ≦ k ≦ 1)
Hi (k) = hi (k) An (k) (0 ≦ k ≦ 1)
Hi (k) = C (hi (2-k)) An (2-k) (1 ≦ k <2)
Equation 23 is a design equation in the frequency domain of TSP, and Equation 24 is a design equation in the frequency domain of inverse TSP, and these are expanded into real-time signals by inverse Fourier transform.
In Formula 24, the filter characteristic for aligning the phase is included by subtracting the phase characteristic Pa () of the correction signal.

By the way, the frequency characteristics of measuring media such as speakers and microphones usually vary greatly depending on various conditions such as distance and angle, floor material to be installed, temperature, and humidity. Filter characteristics cannot often be assumed.
Therefore, the inverse filter characteristic of the correction signal is not included on the inverse TSP side, and the inverse filter can be applied as a case-by-case correspondence after measuring the impulse response.
In this case, Equation 24 is redefined as:

Number 25

hi (k) = exp (S2 (k) Q) (0 ≦ k ≦ 1)
Hi (k) = hi (k) / Ap (k) (0 ≦ k ≦ 1)
Hi (k) = C (hi (2-k)) / Ap (2-k) (1 ≦ k <2)

Next, TSP design means based on the power spectrum of background noise will be described.
A frequency characteristic of background noise can be obtained by extracting a result obtained by sampling for a certain period of time at a relatively low noise timing in a measurement environment, applying an arbitrary time window, and performing Fourier transform. If the amplitude characteristic is obtained from this and expressed as A () in Formula 1, it is considered that a TSP and an inverse TSP having the same power spectrum as the background noise can be designed.
However, background noise in the natural environment tends to concentrate in the low frequency band, and it is not uncommon for the difference between the average amplitudes near DC and Nyquist frequencies to exceed 1000 times (60 dB) in a general measurement environment. .
If a TSP with the same power spectrum is generated, the measurement time ratio near the DC and the Nyquist frequency exceeds 1 million times, and the component close to the DC accounts for most of the measurement time. The measurement time is very short, resulting in an impulse-like waveform. Improving the signal-to-noise ratio in the low frequency band is an important issue, but if such an extreme difference occurs, it is likely to be affected by non-linearity during measurement, and the measurement error will increase. .
Therefore, an operation for limiting the maximum value of the amplitude characteristic obtained from the background noise is performed to obtain the following expression.

Number 26

Am (k) = Lmax (Ab (k)) (0 ≦ k ≦ 1)
* Ab () represents the amplitude characteristics of background noise * Lmax () represents an operation to limit the maximum value, where Am () originally contains a sudden change in Ab () or the maximum value. Since a sharp change occurs due to the limiting operation, if it is converted into TSP as it is, an oscillation-like spectrum is generated. Therefore, Am () is averaged to be Ac ().

Number 27

Ac (k) = Avg3 (Am (k)) (0 ≦ k ≦ 1)
* Avg3 () represents the operation for obtaining the moving average value.

Here, Ac () can be multiplied by another amplitude correction as shown in Equation 19.

Number 28

AC (k) = Ac (k) Ax (k)
* After Ax () is an arbitrary amplitude characteristic, a design formula in the frequency domain of TSP and inverse TSP can be obtained by performing the conversion shown in Formula 1, Formula 2, Formula 3, Formula 5, and Formula 6. .

FIG. 1 shows a block diagram of a TSP and inverse TSP generation flow in the present invention.
In addition, since this invention is implement | achieved in a computer system, it is necessary to reproduce the conversion procedure shown by said numerical formula with an algorithm.
First, the conversion to the inverse function shown in Equation 9 is performed. By using the bisection method, t at which t−f (t) becomes 0 is obtained one by one using 0 ≦ t ≦ 1, and this is stored in the memory. This is realized. Since f (t) passes through the origin 0 and increases monotonously, the start value A in the bisection method is set to t or 0 obtained previously, and the end value B starts from the start value A with respect to the current value. It is obtained by repeating any operation that always increases.

For integration and differentiation, any numerical integration and numerical differentiation algorithm can be used. As a simple example, the integral is the sum of the values previously determined for each function. The derivative is obtained as a difference from the previous value.
In addition, exp () is provided with memory buffers for real numbers and imaginary numbers, respectively, and is calculated and stored according to the definition using built-in functions sin () and cos ().

It is the figure which showed the production | generation flow of TSP and reverse TSP in this invention. It is the figure which showed a mode that a distortion component mixes in the main component of an impulse response when OATSP is used. It is the figure which showed how the phenomenon in which a distortion component mixes into the main component of an impulse response is reduced when TSP in this invention is used. It is the figure which showed the mode of the oscillation-like spectrum which arises when the increment of f (t) changes to rapid increase.

Claims (5)

  In a method for measuring a discrete impulse response of a system under test using a non-impulse arbitrary waveform input signal and an inverse filter of the input signal with respect to the system under test having a linear time invariant continuous time, amplitude characteristics and group delay characteristics By associating the phase characteristics with numerical integration and numerical differentiation, the impulse response can be accurately reproduced by performing convolution with its inverse filter while maintaining the linearity of the envelope while maintaining the linearity of the envelope A device that generates a time-extended pulse (TSP) and its inverse filter waveform.   In the above measurement method, the time-extended pulse (TSP) having a time-frequency graph as a sweep line that passes through the frequency 0 at the initial time, increases monotonically, and is expressed by a function of frequency with a continuous arbitrary time as a parameter. A device for generating an input signal and an inverse filter waveform that can accurately reproduce an impulse response by performing convolution with the waveform of an inverse filter generated at the same time as an input signal.   In the above measurement method, the TSP signal whose group delay characteristic and amplitude characteristic are corrected based on the impulse response B prepared at a time different from the measurement time is used as the input signal of the system to be measured, but simultaneously generated. A device for generating the input signal and the signal used for convolution, which can restore the impulse response obtained by removing the frequency characteristic of B from the measured system by convolving the output signal from the measured system with the filtered signal.   2. An apparatus for synthesizing a plurality of arbitrarily designed group delay characteristics by multiplication of amplitude characteristic levels in the TSP generation processing according to claim 1.   In the TSP generation processing, the TSP power spectrum is changed so as to have an equivalent characteristic based on the power spectrum of background noise measured in advance at the measurement location.

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