JP2018007126A - Signal compression/decompression method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To highly precisely compress/decompress a sound/vibration signal even if a computer having a computational resource enough to perform FET and DCT cannot be installed at a terminal performing a compression.SOLUTION: A signal compression/decompression method includes the steps of: generating a sampling time of z_1Δt, ..., z_KΔt (where 0=z_1<...<z_K<L, K<L) corresponding to such series z_1, ..., z_K that a pair of z_i and z_j satisfying p≡z_i -z_j(mod L) exists for all p satisfying 0≤p≤L for L of provision; sampling an input time signal at the sampling time to out put a compression signal; and decompressing an original input time signal on the basis of information on the compression signal and the sampling time and outputting a decompression signal.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a compression / decompression method for periodic signals such as sound, vibration, and pressure.

  There is an increasing need for remote maintenance related to products using elevators, factories, or motors, and the state of a machine is grasped by sensing with various sensors.

  Here, since the state of the machine often appears in sound, vibration, and pressure, it is important to understand the state of the machine by monitoring the sound, vibration, and pressure of the machine with various sensors such as a microphone and vibration sensor. Become.

  However, when there are many parts to be monitored, a large number of microphones and vibration sensors are installed, so it is necessary to communicate a large amount of data and sound and vibration signals input from them to the server. Have difficulty.

  There is Patent Document 1 as a method for communicating an acoustic / vibration signal even in such a situation.

  Patent Document 1 states that “a video receiving unit that receives an input signal input from an external peripheral device, a video encoder that receives a video signal output from the video signal unit and forms an image compression signal, and an output from the video signal unit. An audio encoder that receives an audio signal and forms a compressed audio signal, a first STC counter value generator that receives a 74.25 MHz video clock output from the video receiver and forms a first STC counter value, and a first STC counter value The first STC counter value generation unit generates a STC counter value by performing a counter operation of incrementing four times every 11 cycles of the video clock. Yes.

JP 2012-138826 A

  Patent Document 1 describes “an audio encoder that forms an audio compression signal”. A general audio encoder performs compression by performing Fast Fourier Transform (FFT) and Discrete Cosine Transform (DCT) and quantizing with a different number of quantization bits for each frequency. However, a computer having sufficient computing resources for performing FFT and DCT is required on the terminal to be compressed, and such computing resources cannot be installed in many cases.

  Therefore, even when a computer with sufficient computing resources to perform FFT or DCT cannot be installed on the terminal to be compressed, periodic signals such as sound, vibration, and pressure can be compressed and restored with high accuracy. Desired.

  In order to solve the above problems, for example, the configuration described in the claims is adopted.

  The present application includes a plurality of means for solving the above-mentioned problem. For example, p ≡ z_i-z_j (mod L) for all p satisfying 0 ≦ p ≦ L for the prescribed L Generating a sampling time of z_1Δt,…, z_KΔt corresponding to a sequence z_1,…, z_K (where 0 = z_1 <… <z_K <L, K <L) such that a pair of z_i and z_j exists Sampling the input time signal at the sampling time, and outputting the compressed signal; restoring the original input time signal based on the compressed signal and the sampling time information; A signal compression and decompression method including an output step.

According to the present invention, sound / vibration / pressure signals can be compressed / restored with high accuracy even when a computer having sufficient computing resources for performing FFT or DCT cannot be installed on the terminal to be compressed. it can.
Problems, configurations, and effects other than those described above will be clarified by the following description of embodiments.

The block diagram which shows the structure of a present Example. The block diagram which shows the structure of a present Example. The block diagram which shows the structure of a present Example. The processing flow of decompression | restoration sensing signal of a present Example.

  Hereinafter, examples will be described with reference to the drawings.

  FIG. 1 is a block diagram showing the configuration of this embodiment.

  The sampling time generation unit 102 determines and outputs a sampling time for converting an analog signal into a digital signal.

  In order to convert an analog signal into a digital signal, if the sampling time is equal, the interval is shorter than the interval 1 / (2f_max) corresponding to the frequency 2f_max that is twice the highest frequency component f_max included in the analog signal. Sampling is required. On the other hand, the sampling time generation unit 102 generates sampling time at certain non-uniform intervals. The sampling time includes an interval 1 / (2f_max) longer than the interval corresponding to the frequency 2f_max that is twice the highest frequency component f_max included in the analog signal, that is, the sampling time is thinned out. By sampling using the sampling time, there is an effect that it can be converted into a digital signal without losing all frequency components included in the analog signal.

  The method for determining the sampling time is, for example, the following method.

First, let Z be the union of multiples of two prime numbers a and b, as shown in the following equation.
Z = {a, 2a, 3a,…} ∪ {b, 2b, 3b,…}
Then, zΔt (zεZ) is determined as a sampling time for a certain minimum interval Δt.

  The sampling time defined in this way is such that for every integer p that satisfies 0 ≤ p ≤ L for L = ab, there exists a pair of integer z_i and integer z_j such that p ≡ z_i-z_j (mod L) The timings of z_1Δt,..., Z_KΔt corresponding to the series z_1,..., Z_K (where 0 = z_1 <... <z_K <L, K <L). That is, since the sampling time interval includes all multiples Δt, 2Δt, 3Δt, 4Δt,..., It can be compressed without losing a wide frequency component.

  The sampling time determination method described above has an advantage in that the generation calculation cost is low and the adaptation to the required compression rate is easy. The latter merit is that the sampling time can be uniquely determined for the compression rate θ as follows.

That is, if two consecutive integers are a and b (= a + 1), a and b are always sparse.
At this time, the compression ratio θ = (a + b−1) / ab = 2a / (a × (a + 1)) = 2 / (a + 1).
Therefore, a can be determined from the compression rate θ by a = 2 / θ−1. From the determined a and b = a + 1, the sampling time is determined by the union of the multiple of a and the multiple of b described above.

  Another method for determining the sampling time is the following method using “circular sparse ruler”.

  For all integers p satisfying 0 ≤ p ≤ η for a specified integer η, a sequence z_1,…, z_K where there exists a pair of integers z_i and integers z_j where p ≡ z_i-z_j (modη) , 0 = z_1 <… <z_K <η, K <η), and any p satisfying 0 ≤ p ≤ η, excluding any z_k (1 ≤ k ≤ K) in the sequence If the pair of z_i and z_j with p ≡ z_i-z_j (modη) no longer exists, the sequence z_1, ..., z_K is called a "minimal sparse ruler" of length η.

  An empty η point that is not sampled is connected to the end point (ηth) of the “minimal sparse ruler” of length η, and connected to the start point (0th) of the “minimal sparse ruler” to make a circle. This is called a “circular sparse ruler” of length 2η. The “circular sparse ruler” having a length of 2η corresponds to sampling by repeating the pattern “z_1Δt,..., Z_KΔt” of the “minimal sparse ruler” with a period (2η + 1) Δt.

  Historically, “minimal sparse rulers” have been found for many natural numbers η. These “minimal sparse rulers” are listed as candidates, and the “circular sparse ruler” corresponding to each is determined by the above method. Further, the compression ratio θ = K / (2η + 1) is calculated for each “circular sparse ruler”. The “circular sparse ruler” corresponding to the compression rate θ closest to the required compression rate is selected as the sampling time to be used.

  The sampling time determination method described above is advantageous in that the generation calculation cost is low and the compression can be performed most efficiently with respect to the compression rate.

Another method for determining the sampling time is the following method using random sampling.
Under the specified compression ratio θ, randomly select θL out of all integers between 0 and less than L, and select the sequence z_1,…, z_K (where K = θL, z_1 <… <z_K <L , K <L). Then, for all integers p satisfying 0 ≦ p ≦ L, it is determined whether or not a condition that a pair of integer z_i and integer z_j of p≡z_i−z_j (mod L) exists is satisfied. If the condition is satisfied, z_1Δt,..., Z_KΔt is determined as the sampling time. The random selection is repeated again until the condition is satisfied.

  The above sampling time determination method has an advantage in that it can be easily adapted to the required compression rate. This merit is that the sampling time can be uniquely determined for the prescribed compression rate θ as described above.

Another method based on random sampling to determine the sampling time is as follows.
This method is effective when the frequency range important for grasping the state of the machine is known in advance. First, similarly to the above-described method, θL pieces are randomly selected from all integers of 0 or more and less than L under a specified compression ratio θ, and the sequence is z_1, ..., z_K (where K = θL, z_1 <... <z_K <L, K <L). Then, for all integers p satisfying 0 ≦ p ≦ L, it is determined whether or not a condition that a pair of integer z_i and integer z_j of p≡z_i−z_j (mod L) exists is satisfied.

Only sequences [z_1,..., Z_K] that satisfy this condition are stored in the sequence set U. Then, the random selection is repeated again until the number of elements of U becomes equal to or more than the prescribed ζ.
Now, an important frequency range is given by a set of frequencies F. For all elements f of the set F, q of the following expression corresponding to each f is calculated.

  Next, a set P having all q as elements is generated. Next, for each element u = [z_1,..., Z_K] of U, the number c_u of the combinations of i and j such that p≡z_i−z_j (mod L) is included in the set P is counted. Finally, u = [z_1,..., Z_K] that maximizes c_u is selected, and z_1Δt,..., Z_KΔt are determined as sampling times.

  The sampling time determination method described above has advantages in that it can be easily adapted to the required compression rate and that the restoration accuracy for important frequencies can be improved.

  The sampling time generation unit 102 uses hΔT, which is a specified integer h times larger than a specified frame shift ΔT, as a cycle, and prepares only sampling patterns for the cycle hΔT. A sampling unit 101 to be described later repeats the sampling pattern every period hΔT. As a result, there are at most h decimation matrices A described later, and there are at most h observation matrices B corresponding to A. Therefore, h patterns B are calculated in advance and stored in the memory. Thus, the compressed sensing signal restoration unit 103 described later has an advantage that the compressed sensing signal restoration can be performed at high speed.

  The sampling unit 101 receives the analog signal received from the microphone, vibration sensor (acceleration sensor or angular velocity sensor) or pressure sensor, and the sampling time received from the sampling time generation unit 102, and the analog signal is temporally according to the sampling time. Outputs signals after decimation and decimation.

  Since the sampling unit 101 compresses the signal by thinning out, it is not necessary to perform FFT or DCT on the terminal side to be compressed. Therefore, there is an advantage that sound / vibration signals can be compressed with high accuracy even when a computer having sufficient computing resources for performing FFT or DCT cannot be installed on the terminal to be compressed.

  The compressed sensing signal restoration unit 103 receives the decimation signal received from the sampling unit 101 and the sampling time received from the sampling time generation unit 102 as input, and calculates and outputs a restoration signal.

  For each time corresponding to the frame shift ΔT, the compressed sensing signal restoration unit 103 extracts only the K-thinned signal sampled during the time corresponding to the frame size T, and uses the extracted dethinned signal as an input. Calculate the restoration signal of frame size T. Here, the frame size T is an integer that satisfies the condition that it is not less than the period hΔT of the sampling pattern described above.

The compressed sensing signal restoration procedure of the compressed sensing signal restoration unit 103 will be described.
y is the time value y (1), ..., y (T) of the signal before decimation, and z is the time value z (1), ..., z (K ) Are arranged in a vertical vector, x is a frequency domain signal obtained by performing linear transformation such as FFT, DCT or Gabor matrix transformation on the signal before decimation, D is a T × T inverse FFT matrix or inverse DCT matrix or 2T × A dictionary matrix such as an inverse Gabor matrix of T, and A is a decimation matrix of K × T. Each element of D is an inverse FFT coefficient, a DCT coefficient, or a Gabor coefficient. If the i-th row and j-th column of A is 1, it means that the j-th sampling is performed at time iΔt. That is, A is a matrix in which only one element in each row is 1 and the other elements are 0. At this time, the observation model equation is as follows.

  Therefore, the compressed sensing signal restoration unit 103 solves the underdetermined simultaneous equations in order to estimate the unknown x from the known z and the known B. Specifically, a known method such as L1 norm minimization or orthogonal matching pursuit (OMP) using alternating direction method of multipliers (ADMM) can be used. However, if the compression ratio θ = K / T is too small to satisfy the restricted isometry property, an error may occur in the restored signal.

  In the following, a compressed sensing signal restoration processing flow is disclosed in which signal restoration is possible even when the compression rate θ = K / T is so small that the restriction isometric property is not satisfied.

  FIG. 4 is a processing flow of compressed sensing signal restoration according to this embodiment.

  First, the compressed sensing signal restoration unit 103 stores z in the residual vector r as an initialization process in S401, and further sets the support set S as an empty set.

  Next, the compressed sensing signal restoration unit 103 calculates j in the following equation as the atom selection in S402.

  Where E is the size of the column of B, and b_j is the jth column vector of B.

  Next, the compressed sensing signal restoration unit 103 adds j to the support set S as a support update in S403.

  Next, the compressed sensing signal restoration unit 103 calculates x in the following equation as the solution update in S404.

However, B_S is a matrix obtained by extracting only the columns of numbers included in the support set S from B,

And σ_e ^ 2 is the sample variance of r,

Σ (x (j)) ^ 2 is the sample variance of the frequency component x (j) corresponding to the number j.

  σ_e ^ 2 may be stored in advance as a set value, or the sample variance of r estimated up to the previous frame may be used. Similarly, σ (x (j)) ^ 2 may be held in advance as a set value, or the sample variance of x (j) estimated up to the previous frame may be used.

  The compressed sensing signal restoration method of the present embodiment is such that the power for each frequency of the signal before thinning follows a zero mean Gaussian distribution of the standard deviation corresponding to that frequency, and the power for each frequency of the restoration error is the frequency. Since it is possible to reduce the candidates for the solution of the underdetermined simultaneous equations by assuming that the standard deviation corresponding to 0 has a zero mean Gaussian distribution, the signal can be restored when the compression rate θ is small.

  As described above, the sampling time generation unit 102 sets hΔT, which is a specified constant h times larger than the specified frame shift ΔT, as a cycle, and prepares only sampling patterns for the cycle hΔT. The sampling unit 101 sets the sampling pattern as a cycle. Repeat every hΔT. Therefore, there are at most h thinning matrices A. Therefore, there are at most h observation matrices B corresponding to A. Therefore, the compressed sensing signal restoration unit 103 has an effect that the compressed sensing signal restoration can be executed at a high speed by calculating h types of B in advance and storing them in the memory.

  The restored signal y is calculated by restoring the signal before thinning out from the estimated x by the following equation.

  Finally, the final waveform is output by superimposing and adding the restoration signal y calculated in each frame in terms of time.

  The present embodiment discloses an embodiment in which a signal of a plurality of channels is encoded by a single channel A / D converter without using a plurality of channels of A / D converters. The present embodiment has an effect that signals of a plurality of channels can be collected without a multi-channel A / D converter.

  FIG. 2 is a block diagram showing the configuration of this embodiment.

The sampling time generation unit 202 determines and outputs a sampling time for converting an analog signal to a digital signal. However, the sampling time generation unit 202 determines a sampling time such that each channel does not overlap. Specifically, it is determined by the following method.
First, as in the first embodiment, for only one channel, for all p satisfying 0 ≦ p ≦ L with respect to the specified L, a pair of z_i and z_j such that p≡z_i−z_j (mod L) , Z_K (where 0 = z_1 <... <z_K <L, K <L) corresponding to the sequence z_1,. Specifically, it may be the sampling time determined by the union of the multiples of the relatively prime numbers a and b described in the first embodiment, or the sampling time determined by the “circular sparse ruler” described in the first embodiment. There may be a sampling time determined by the random sampling described in the first embodiment. There are L types in which the sampling time is shifted. M of these L candidates are assigned to M channels.

  That is, among the (LM) combinations, the overlapping number of sampling times of each channel is evaluated, and the combination having the smallest overlapping number is found. For the overlapping sampling time, the sampling time is deleted so as not to sample the time in any channel. Through the above processing, a sampling time is determined so that each channel does not overlap and output.

  The sampling units 2011 to 201M receive the analog signal received from the microphone, vibration sensor (acceleration sensor or angular velocity sensor) or pressure sensor, and the sampling time of each channel received from the sampling time generation unit 202, and the analog signal is sampled. Decimate in time according to time and output a signal after decimation.

Sampling units 2011-201M are realized by, for example, an M-channel multiplexer circuit. Based on the sampling time of each channel received from the sampling time generation unit 202, the multiplexer selects the m-th channel signal at the time for sampling the m-th channel and outputs it as a thinned signal.
Since the sampling units 2011 to 201M can be realized by a multiplexer circuit, it is not necessary to perform FFT or DCT on the terminal to be compressed. Therefore, there is an effect that it is possible to compress sound / vibration signals with high accuracy even when a computer having sufficient calculation resources for performing FFT or DCT cannot be installed on the terminal to be compressed.

  The single channel A / D conversion unit 204 performs A / D conversion on a single channel signal on which signals after decimation on each channel are superimposed, and outputs a transmission signal.

  The distribution unit 205 inputs the transmission signal received from the single channel A / D conversion unit 204 and the sampling time received from the sampling time generation unit 202, and extracts only the sampling time value of each channel from the transmission signal. The signal after distribution for each channel is output.

  The compressed sensing signal restoration units 2031 to 203M receive the decimation signal received from the distribution unit 205 and the sampling time received from the sampling time generation unit 202, and calculate and output a restoration signal.

  As in the first embodiment, the compressed sensing signal restoration units 2031 to 203M extract only the signals after decimation at K points sampled during the time corresponding to the frame size T for each time corresponding to the frame shift ΔT. A restoration signal of frame size T is calculated using the extracted post-thinning signal as an input. Here, the frame size T is an integer that satisfies the condition that it is not less than the period hΔT of the sampling pattern described above.

The compressed sensing signal restoration procedure of the compressed sensing signal restoration units 2031 to 203M will be described.
y_m is the time value y_m (1), ..., y_m (T) of the signal of the mth channel signal before decimation, z_m is the value of each time z_m ( 1), ..., z_m (K) arranged in a vertical vector, x_m is a frequency domain signal obtained by performing linear transformation such as FFT, DCT or Gabor matrix transformation on the m-th channel signal before decimation, and D is T × A dictionary matrix such as an inverse FFT matrix or inverse DCT matrix of T or an inverse Gabor matrix of 2T × T, A_m is a K × T decimation matrix of the m-th channel. Each element of D is an inverse FFT coefficient, a DCT coefficient, or a Gabor coefficient. If the i-th row and j-th column of A_m is 1, it means that the j-th sampling is performed at the m-th channel at time iΔt. As described above, since the sampling time is determined so that each channel does not overlap, A_m has only 1 element corresponding to one set of i and m for all j, and other than that The element is 0. At this time, the observation model equation is as follows.

Therefore, the compressed sensing signal restoration units 2031 to 203M solve the underdetermined simultaneous equations in order to estimate the unknown x_m from the known z_m and the known B_m. The compressed sensing signal restoration of the present embodiment uses the property that the power of each frequency has a high correlation among a plurality of channels, and performs restoration with higher accuracy than that of the first embodiment.

The compressed sensing signal restoration processing flow of this embodiment will be described with reference to FIG. 4 as in the first embodiment.
First, the compressed sensing signal restoration units 2031 to 203M store z_m in the residual vector r_m as an initialization process in S401, and set the support set S as an empty set.

Next, the compressed sensing signal restoration units 2031 to 203M calculate j in the following equation as the atom selection in S402.

  Here, E is the size of the B_m column, and b_m, j is the jth column vector of B_m.

  Next, the compressed sensing signal restoration unit 103 adds j to the support set S as a support update in S403.

  Next, the compressed sensing signal restoration unit 103 calculates x_m of the following equation as the solution update in S404.

However, B_m, S is a matrix in which only the column of the number included in the support set S is extracted from B_m,

And σ_e ^ 2 is the sample variance of r_m,

Σ (x_m (j)) ^ 2 is the sample variance of the frequency component x_m (j) corresponding to the number j.

  σ_e ^ 2 may be stored in advance as a set value, or the sample variance of r_m estimated up to the previous frame may be used. Similarly, σ (x_m (j)) ^ 2 may be held in advance as a set value, or the sample variance of x_m (j) estimated up to the previous frame may be used.

The compressed sensing signal restoration method of the present embodiment is a generalization of the compressed sensing signal restoration method of the first embodiment for multiple channels, taking advantage of the fact that the power of each frequency has a high correlation between multiple channels. There is an effect that restoration can be performed with higher accuracy than in the first embodiment.
The restored signal y_m is calculated by restoring the signal before thinning out from the estimated x_m according to the following equation.

  Finally, a final waveform is output by superimposing and adding the restoration signal y_m calculated in each frame in terms of time.

  In the present embodiment, an embodiment in which a compression rate higher than that in the first embodiment is obtained will be disclosed.

  FIG. 3 is a block diagram showing the configuration of the present embodiment.

  The sampling time generation unit 303 determines and outputs a sampling time for converting an analog signal to a digital signal. The method for determining the sampling time may be the same as in the first embodiment.

  Band division filter sections 3011 to 301 N divide the input signal into N bands and output the band-divided signal. Each is a band-pass filter and may be constituted by an appropriate IIR filter or FIR filter.

  The sampling units 3021 to 302N receive the N band-divided signals received from the band division filter unit and the sampling time received from the sampling time generation unit 303, and temporally decimate the band-divided signals according to the sampling time. The signal after thinning is output.

  The quantization units 3041 to 304N receive the N decimation signals received from the sampling unit and output N post-quantization signals. However, an appropriate number of quantization bits is used depending on each of N bands.

  The configuration of the present embodiment has the following effects. The number of quantization bits required for each frequency band differs depending on the auditory characteristics. Therefore, since the number of quantization bits in the frequency band where hearing is not sensitive to quantization errors can be reduced, the compression ratio can be improved. Also, the number of quantization bits required for each frequency band differs depending on the effectiveness for machine diagnosis. Therefore, since the number of quantization bits in a frequency band with low effectiveness for machine diagnosis can be reduced, the compression rate can be improved.

  The compressed sensing signal restoration units 3051 to 305N use the quantized signal received from the quantization unit and the sampling time received from the sampling time generation unit 303 as inputs, and calculate and output a restored subband signal. The method for calculating the restoration signal may be the same as in the first embodiment.

  The bandpass filter units 3061 to 306N receive the restored subband signals received from the compressed sensing signal restoration unit, output N post-bandpass signals, superimpose them, calculate the restored signals, and output them. Each of the bandpass filter units is a bandpass filter, and may be configured by an appropriate IIR filter or FIR filter.

  In addition, this invention is not limited to an above-described Example, Various modifications are included. For example, the above-described embodiments have been described in detail for easy understanding of the present invention, and are not necessarily limited to those having all the configurations described. Further, a part of the configuration of one embodiment can be replaced with the configuration of another embodiment, and the configuration of another embodiment can be added to the configuration of one embodiment. Further, it is possible to add, delete, and replace other configurations for a part of the configuration of each embodiment.

  Each of the above-described configurations, functions, processing units, processing means, and the like may be realized by hardware by designing a part or all of them with, for example, an integrated circuit. Each of the above-described configurations, functions, and the like may be realized by software by interpreting and executing a program that realizes each function by the processor. Information such as programs, tables, and files for realizing each function can be stored in a recording device such as a memory, a hard disk, or an SSD (Solid State Drive), or a recording medium such as an IC card, an SD card, or a DVD.

  Further, the control lines and information lines indicate what is considered necessary for the explanation, and not all the control lines and information lines on the product are necessarily shown. Actually, it may be considered that almost all the components are connected to each other.

101 ... Sampling unit, 102 ... Sampling time generation unit, 103 ... Compressed sensing signal restoration unit,

Claims (3)

A method for compressing and decompressing signals,
For all p satisfying 0 ≤ p ≤ L with respect to the specified L, a sequence z_1,…, z_K (where 0 = z_1 <…) where z ≡ z_i-z_j (mod L) and a pair of z_i and z_j exist generating a sampling time of z_1Δt, ..., z_KΔt corresponding to <z_K <L, K <L);
Sampling the input time signal at the sampling time and outputting a signal after thinning;
Reconstructing the original input time signal based on the thinned signal and the sampling time, and outputting the restored signal,
Signal compression and decompression methods A signal compression and decompression method according to claim 1,
The input time signal is a plurality of channels,
Generating a multi-channel sampling time, which is a set of sampling times without temporal overlap between channels, based on the sampling time corresponding to each channel;
Sampling the input multi-channel time signal at the multi-channel sampling time, and outputting a signal after decimation;
Reconstructing the original time signal of the plurality of channels based on the post-decimation signal and the information of the plurality of channel sampling times, and outputting a restoration signal,
Signal compression and decompression methods A signal compression and decompression method according to claim 1,
Dividing the input time signal into a plurality of bands and outputting a band-divided signal;
Sampling the band-divided signal of each band at the sampling time and outputting a signal after decimation;
Quantizing the decimation signal of each band and outputting a quantized signal;
Restoring the post-band division signal based on the quantized signal and the sampling time information of each band and outputting the restored sub-band signal;
A step of restoring the original input time signal by adding the sub-band signal after restoration of each band by a band pass filter, and outputting the restored signal,
Signal compression and decompression methods

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