CN113092850A - Time-frequency spectrum analysis method and system for simplifying S transformation - Google Patents

Time-frequency spectrum analysis method and system for simplifying S transformation Download PDF

Info

Publication number
CN113092850A
CN113092850A CN202110408929.8A CN202110408929A CN113092850A CN 113092850 A CN113092850 A CN 113092850A CN 202110408929 A CN202110408929 A CN 202110408929A CN 113092850 A CN113092850 A CN 113092850A
Authority
CN
China
Prior art keywords
frequency
time
signal
frequency spectrum
simplified
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202110408929.8A
Other languages
Chinese (zh)
Other versions
CN113092850B (en
Inventor
李建闽
张旭辉
曹远远
林海军
卢笑
杨宇祥
李仲阳
汪鲁才
张甫
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Hunan Normal University
Original Assignee
Hunan Normal University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Hunan Normal University filed Critical Hunan Normal University
Priority to CN202110408929.8A priority Critical patent/CN113092850B/en
Publication of CN113092850A publication Critical patent/CN113092850A/en
Application granted granted Critical
Publication of CN113092850B publication Critical patent/CN113092850B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
    • G01R19/25—Arrangements for measuring currents or voltages or for indicating presence or sign thereof using digital measurement techniques
    • G01R19/2506—Arrangements for conditioning or analysing measured signals, e.g. for indicating peak values ; Details concerning sampling, digitizing or waveform capturing
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/16—Spectrum analysis; Fourier analysis
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/16—Spectrum analysis; Fourier analysis
    • G01R23/165—Spectrum analysis; Fourier analysis using filters
    • G01R23/167—Spectrum analysis; Fourier analysis using filters with digital filters

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Measuring Frequencies, Analyzing Spectra (AREA)

Abstract

The invention discloses a time-frequency spectrum analysis method and a system for simplifying S transformation, wherein the implementation steps of the time-frequency spectrum analysis method for simplifying S transformation comprise: filtering and analog-to-digital converting the original signal to obtain a digital sampling sequence; obtaining a time-frequency spectrum of the signal by simplifying S transformation; selecting sampling points to be calculated according to the distribution of the signal spectrum and a 3 sigma criterion; the parameter information of the original signal is calculated according to the key frequency points and the interpolation method. The method based on simplified S transformation can effectively simplify the calculated amount and reduce the storage requirement of the signal processor while realizing the time-frequency analysis of the signal. Compared with ST, the calculation efficiency of simplifying ST is greatly improved, but the effect of spectrum analysis is nearly consistent when signals are received.

Description

Time-frequency spectrum analysis method and system for simplifying S transformation
Technical Field
The invention relates to a signal time-frequency spectrum analysis and local spectrum detection technology. The time frequency spectrum analysis method and system based on simplified S transformation are specifically designed and used for signal detection and time frequency spectrum analysis.
Background
As a classical signal analysis method, Fast Fourier Transform (FFT) has many advantages such as orthogonality and completeness, and thus is widely used in the field of signal processing. However, FFT faces the local contradiction between time domain and frequency domain in signal analysis, and is only suitable for analyzing stationary signals, and cannot meet the analysis requirements for non-stationary signals with characteristics such as transient state and abrupt change. In order to solve the localized contradiction between the FFT time domain and the frequency domain, scholars at home and abroad propose a plurality of time-frequency spectrum analysis methods, which mainly comprise a wavelet transform method, a Hilbert-Huang transform method, an S transform method and the like.
Wavelet Transform (WT) is a time-frequency localization analysis method with multi-resolution characteristics, which overcomes some disadvantages of FFT and its improved algorithm, and is especially suitable for analysis of abrupt non-stationary signals. Its limitations, however, preclude its use: 1) the frequency domain resolution in WT is coarse and there may be severe frequency aliasing between bands, far from the level of FFT and its improved algorithms. 2) Wavelet functions of different scales interfere with each other in a frequency domain, are easily influenced by noise, and cannot well separate harmonics and inter-harmonics with relatively close frequencies. 3) The signal can be qualitatively analyzed by using the characteristics of the WT at the mutation point, and the WT has certain difficulty in directly detecting the amplitude of the signal. 4) WT has the disadvantages of large calculation amount, difficulty in real-time calculation, difficulty in realization by an embedded system and the like to different degrees.
Hilbert-Huang Transform (HHT) is a new method applied to non-stationary signal analysis in recent years, and relies on Empirical Mode Decomposition (EMD) to decompose a disturbance signal into Intrinsic Mode components (IMF) on different frequency bands. The HHT method has the disadvantages that: 1) in the voltage dip problem, the HHT method cannot be accurately analyzed on-line, and the noise immunity is poor. 2) The EMD algorithm using high-order spline interpolation can remarkably improve the accuracy of the EMD algorithm, but the consumed computing time is increased. 3) EMD is not complete, it easily causes band aliasing, and the physical meaning of IMF is not clear, so the practical application still lacks reliability.
The S transformation is a novel time-frequency analysis method combining continuous WT and STFT, inherits and develops the localization ideas of STFT and WT, and can be derived by the two transformations, thereby overcoming the defect of fixed height and width of an STFT window. Therefore, not only frequency information at a certain time but also signal amplitude information at a certain frequency can be obtained by S-conversion. Compared with time-frequency domain analysis methods such as continuous WT and STFT, S transformation has the unique advantages that: 1) the resolution of the signal S transform is frequency (i.e., scale) dependent; 2) the S transformation result of the signal is directly connected with the Fourier transformation of the signal; 3) the basic wavelet does not have to satisfy the tolerance condition. However, the ST is used to calculate signals with high computational complexity, which makes high demands on the memory storage of the computer.
Disclosure of Invention
In order to solve the technical problems, the invention adopts the technical scheme that: the invention provides a time-frequency spectrum analysis method and a time-frequency spectrum analysis system based on simplified S transformation, which can effectively simplify the calculation amount and reduce the storage requirement of a signal processor while realizing the time-frequency analysis of signals, greatly improve the calculation efficiency of simplified ST compared with ST, and have nearly consistent effect of the spectrum analysis of the signals.
In order to solve the technical problems, the invention adopts the technical scheme that:
a time frequency spectrum analysis method and system based on simplified S transformation is characterized in that the implementation steps comprise:
1) filtering and analog-to-digital converting the original signal to obtain a digital sampling sequence;
2) obtaining a time-frequency spectrum of the signal by simplifying S transformation;
3) selecting sampling points to be calculated according to the distribution of the signal spectrum and a 3 sigma criterion;
4) calculating parameter information of the original signal according to the key frequency points and an interpolation method;
optionally, the detailed steps of step 1) include:
1.1) to prevent the spectrum aliasing and power frequency interference of the original signal, the analog signal needs to be pre-filtered and then sent to an ADC;
1.2) ADC with a fixed sampling rate fsAnd sampling the analog voice signal and sending the converted digital sampling sequence to the DSP.
Optionally, the detailed steps of step 2) include:
2.1) constructing a Gaussian window with adjustable width as shown in the following formula:
Figure BDA0003023374940000021
in the above formula, t is time; f is the frequency; σ is the standard deviation.
2.2) the expression of S Transform (ST) is shown as follows:
Figure BDA0003023374940000022
in the above formula, τ is a position parameter; h (t) is a speech signal.
Substituting the width-adjustable Gaussian window number into the above formula to obtain the time-frequency domain expression of ST, which is shown as the following formula:
Figure BDA0003023374940000023
with S (tau)KAnd f) represents the time τKLocal spectral lines of (c).
2.3) the discrete expression of ST is shown as follows:
Figure BDA0003023374940000024
in the above formula, N is the number of sampling points; t is a sampling period;
Figure BDA0003023374940000025
h (KT) is a discrete time sampling sequence, which can be obtained by sampling h (T) at a time interval T.
In the above formula, N is the number of sampling points, T is the optional sampling period, and the detailed step of step 3) includes:
3.1) each vnRepresents discrete positive and negative frequency components of h (kt) over time, where N is 0,1,2, N-1, s [ N, j ]]And vnAre used interchangeably and each vnAll go through gnPerforming a calculation from v at zero frequency0The calculation is started.
3.2) through detecting the sampling data of the signal spectrum distribution in the middle-3 sigma to +3 sigma area, wherein, each section of spectrum interval is 6 sigma/fnEach frequency vnThrough its corresponding gaussian window gnAnd (4) calculating. If the Gaussian window gnSpanning sample and gaussian window gn-1If the number of samples crossed is different, the voice v is calculatednOtherwise v will be skippedn. Repeating the whole calculation process until the sampling sequence is finished;
3.3) the simplified S-transformed time-frequency spectrum has an un-calculated signal gap compared to the original ST time-frequency spectrum. The portion of the data is fitted by least squares to obtain the desired calculated signal time spectrum.
Optionally, the detailed steps of step 4) include:
4.1) calculation of key frequency points:
for an N-point sampling sequence of a fixed sampling time T, there is a key frequency point fc. When the signal frequency is higher than the critical frequency point fcWhen Δ s is less than T; when the signal frequency is lower than the critical frequency point, Δ s>T。
Due to signal frequency fkIs spanned by
Figure BDA0003023374940000031
Therefore continuous frequency fkAnd fk+1The difference in the upper span is shown by the following equation:
Figure BDA0003023374940000032
when the signal frequency is lower than the critical frequency point, the relationship can be established as follows:
k2+k-6N＝0
the solution of the above equation can be obtained,
Figure BDA0003023374940000033
finally, the key frequency points can be represented by the following formula:
Figure BDA0003023374940000034
4.2) calculating the parameter information of the signal by interpolation.
The phase of the ST signal consists of a base portion and a data portion. The time difference between successive frequencies is called the fundamental phase, and the sum of the local phase and the fundamental phase of a given time series h (t) becomes the data phase. The fundamental phase is calculated from each frequency point where the frequency n and the time j are ST [ n, j ]. The data phase at any frequency point can be obtained by subtracting the base phase from the total ST phase. When the time-frequency spectrum gap is reconstructed, firstly, calculating an S transformation phase matrix of the time-frequency spectrum gap by using key frequency points, and then, subtracting a basic phase of a local spectrum to obtain a corresponding data phase; the data phase in the frequency gap can be determined by interpolation through the frequency spectrum line of the key frequency point, and then the phase information of the data phase is calculated, so that the parameter information of the frequency point in the frequency gap is obtained.
In addition, the invention also provides a time-frequency spectrum analysis method system based on simplified S transformation, which comprises the following steps:
a time frequency spectrum analysis method system based on simplified S transformation is characterized by comprising the following steps:
a signal input unit for acquiring an analog signal;
and the signal conditioning unit is used for pre-filtering the analog signal and sending the filtered analog signal to the ADC to output a digital sampling sequence.
Furthermore, a simplified S transform based time-frequency spectrum analysis method system comprising a digital signal processing device, characterized in that the digital signal processing device is programmed or configured to perform the steps of the simplified S transform based time-frequency spectrum analysis method according to any of claims 1 to 5.
Furthermore, a simplified S-transform based time-frequency spectrum analysis method system comprises a digital signal processing device, wherein the digital signal processing device has stored on its memory an embedded program programmed or configured to perform the simplified S-transform based time-frequency spectrum analysis method according to any of claims 1 to 5.
In addition, a time-frequency spectrum analysis method system based on simplified S transformation is characterized by comprising a power module (1), a signal conditioning circuit (2), an analog-to-digital converter (3) and a digital signal processor (4), wherein the output end of the power module (1) is respectively and electrically connected with the signal conditioning circuit (2), the analog-to-digital converter (3) and the digital signal processor (4), the output end of the signal conditioning circuit (2) is connected with the digital signal processor (4) through a low-pass filter (3), the analog-to-digital converter (3), and the digital signal processor (4) is programmed or configured to execute the steps of the time-frequency spectrum analysis method based on simplified S transformation according to any one of claims 1 to 5.
Optionally, the digital signal processor (4) is further connected with a synchronous dynamic random access memory (5), a flash memory (6), an active crystal oscillator (7), a reset module (8) and an emulation debugging interface (9), respectively.
Compared with the prior art, the invention has the following advantages: after the digital signal after pre-filtering and A/D conversion is obtained, the digital signal is sent to a Digital Signal Processor (DSP) to complete text algorithm processing, and parameter information of an original signal is obtained. The invention can effectively simplify the calculation amount and reduce the storage requirement of the signal processor while realizing the time-frequency analysis of the signal, and compared with the ST, the calculation efficiency of simplifying the ST is greatly improved, and the frequency spectrum analysis effect of the signal is nearly consistent.
Drawings
FIG. 1 is a schematic diagram of a basic flow of a method according to an embodiment of the present invention.
FIG. 2 shows a sequence of sampled signals and Gaussian window functions with different widths according to an embodiment of the present invention.
FIG. 3 is a simplified S-transform time-frequency spectrum according to an embodiment of the present invention.
FIG. 4 is a simplified S-transform magnitude and phase spectra in accordance with an embodiment of the present invention.
Fig. 5 is a schematic diagram of a basic structure of a system according to an embodiment of the present invention.
FIG. 6 is a schematic diagram of a frame structure of a system according to an embodiment of the present invention.
Detailed Description
As shown in fig. 1, the implementation steps of the simplified S-transform-based time-frequency spectrum analysis method include:
optionally, the detailed steps of step 1) include:
a time-frequency spectrum analysis method based on simplified S transformation is characterized by comprising the following implementation steps:
1) filtering and analog-to-digital converting the original signal to obtain a digital sampling sequence;
2) obtaining a time-frequency spectrum of the signal by simplifying S transformation;
3) selecting sampling points to be calculated according to the distribution of the signal spectrum and a 3 sigma criterion;
4) calculating parameter information of the original signal according to the key frequency points and an interpolation method;
optionally, the detailed steps of step 1) include:
1.1) to prevent the spectrum aliasing and power frequency interference of the original signal, the analog signal needs to be pre-filtered and then sent to an ADC; (ii) a
1.2) ADC with a fixed sampling rate fsAnd sampling the analog voice signal and sending the converted digital sampling sequence to the DSP.
Optionally, the detailed steps of step 2) include:
2.1) constructing a Gaussian window with adjustable width as shown in the following formula:
Figure BDA0003023374940000051
in the above formula, t is time; f is the frequency; σ is the standard deviation.
2.2) the expression of S Transform (ST) is shown as follows:
Figure BDA0003023374940000052
in the above formula, τ is a position parameter; h (t) is a speech signal.
Substituting the width-adjustable Gaussian window number into the above formula to obtain the time-frequency domain expression of ST, which is shown as the following formula:
Figure BDA0003023374940000053
with S (tau)KAnd f) represents the time τKLocal spectral lines of (c).
2.3) the discrete expression of ST is shown as follows:
Figure BDA0003023374940000054
in the above formula, N is the number of sampling points; t is a sampling period;
Figure BDA0003023374940000055
h (KT) is a discrete time sampling sequence, which can be obtained by sampling h (T) at a time interval T.
In the above formula, N is the number of sampling points, T is the optional sampling period, and the detailed step of step 3) includes:
3.1) each vnRepresents discrete positive and negative frequency components of h (kt) over time, where N is 0,1,2, N-1, s [ N, j ]]And vnAre used interchangeably and each vnAll go through gnPerforming a calculation from v at zero frequency0The calculation is started.
3.2) through detecting the sampling data of the signal spectrum distribution in the middle-3 sigma to +3 sigma area, wherein, each section of spectrum interval is 6 sigma/fnEach frequency vnThrough its corresponding gaussian window gnAnd (4) calculating. If the Gaussian window gnSpanning sample and gaussian window gn-1If the number of samples crossed is different, the voice v is calculatednOtherwise v will be skippedn. Repeating the whole calculation process until the sampling sequence is finished;
3.3) the simplified S-transformed time-frequency spectrum has an un-calculated signal gap compared to the original ST time-frequency spectrum. The portion of the data is fitted by least squares to obtain the desired calculated signal time spectrum.
Optionally, the detailed steps of step 4) include:
4.1) calculation of key frequency points:
for an N-point sampling sequence of a fixed sampling time T, there is a key frequency point fc. When the signal frequency is higher than the critical frequency point fcWhen Δ s is less than T; when the signal frequency is lower than the critical frequency point, Δ s>T。
Due to signal frequency fkIs spanned by
Figure BDA0003023374940000061
Therefore continuous frequency fkAnd fk+1The difference in the upper span is shown by the following equation:
Figure BDA0003023374940000062
when the signal frequency is lower than the critical frequency point, the relationship can be established as follows:
k2+k-6N＝0
the solution of the above equation can be obtained,
Figure BDA0003023374940000063
finally, the key frequency points can be represented by the following formula:
Figure BDA0003023374940000064
4.2) calculating the parameter information of the signal by interpolation.
The phase of the ST signal consists of a base portion and a data portion. The time difference between successive frequencies is called the fundamental phase, and the sum of the local phase and the fundamental phase of a given time series h (t) becomes the data phase. The fundamental phase is calculated from each frequency point where the frequency n and the time j are ST [ n, j ]. The data phase at any frequency point can be obtained by subtracting the base phase from the total ST phase. When the time-frequency spectrum gap is reconstructed, firstly, calculating an S transformation phase matrix of the time-frequency spectrum gap by using key frequency points, and then, subtracting a basic phase of a local spectrum to obtain a corresponding data phase; the data phase in the frequency gap can be determined by interpolation through the frequency spectrum line of the key frequency point, and then the phase information of the data phase is calculated, so that the parameter information of the frequency point in the frequency gap is obtained.
In addition, this embodiment further provides a time-frequency spectrum analysis system based on simplified S transform, including:
a signal input unit for acquiring an analog signal;
and the signal conditioning unit is used for pre-filtering the analog signal and sending the filtered analog signal to the ADC to output a digital sampling sequence.
Furthermore, a simplified S transform based time-frequency spectrum analysis system comprising a digital signal processing device, characterized in that the digital signal processing device is programmed or configured to perform the steps of the simplified S transform based time-frequency spectrum analysis method according to any of claims 1-5.
Furthermore, a simplified S-transform based time-frequency spectrum analysis system comprising a digital signal processing device, characterized in that the memory of the digital signal processing device has stored thereon an embedded program programmed or configured to perform the simplified S-transform based time-frequency spectrum analysis method according to any of claims 1 to 5.
As shown in fig. 5 and fig. 6, the time-frequency spectrum analysis system based on the simplified S-transform in this embodiment includes a power module 1, a signal conditioning circuit 2, an analog-to-digital converter 3, and a digital signal processor 4, where an output end of the power module 1 is electrically connected to the signal conditioning circuit 2, the analog-to-digital converter 3, and the digital signal processor 4 is connected to the signal conditioning circuit 2 through the analog-to-digital converter 3, and the digital signal processor 4 is programmed or configured to execute the steps of the method for performing spectral line analysis and phase recovery based on the simplified S-transform in this embodiment. The time-frequency spectrum analysis method system based on simplified S transformation has the advantages of simple structure and reasonable layout.
In this embodiment, the signal conditioning circuit 2 pre-filters the analog voice signal, and determines the resistance-capacitance value of the analog filter and the sampling rate and the number of bits of the analog-to-digital converter according to the time-frequency resolution requirement of the signal to be measured.
The analog-to-digital converter 3 is used for performing high-speed analog-to-digital conversion on the measured voltage signal and the measured current signal and converting the measured signal into a digital signal. In this embodiment, ADS8556 manufactured by TI corporation is used as the analog-to-digital converter 3.
The digital signal processor 4 is programmed or configured to perform the steps of the method for spectral line analysis and phase recovery based on the simplified S-transform described above in this embodiment. In this embodiment, the CPU of the digital signal processor 4 adopts TMS320C6745 manufactured by TI corporation, and the main parameters are selected as follows: (1) sampling rate: 10 kHz; (2) the sampling length N of the fourier transform data is 1024. The sampling length N can be determined by comprehensively considering the signal detection precision and the running speed of the computer or the embedded system equipment.
As shown in fig. 6, the digital signal processor 4 is further connected with a Synchronous Dynamic Random Access Memory (SDRAM)5, a flash memory 6, an active crystal oscillator 7, a reset module 8, and an emulation debugging interface 9, respectively. In this embodiment, the emulation debugging interface 9 specifically adopts a JTAG emulation debugging interface, and in addition, other types of emulation debugging interfaces may also be adopted as needed.
In this embodiment, the simplified S-transform-based time-frequency spectrum analysis method and other time-frequency domain analysis methods of this embodiment are respectively used for comparative analysis on N-point sample data, and specific results are shown in table 1.
TABLE 1 comparison of different time-frequency analysis methods
Figure BDA0003023374940000071
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may occur to those skilled in the art without departing from the principle of the invention, and are considered to be within the scope of the invention.

Claims (10)

1. A time frequency spectrum analysis method and system based on simplified S transformation is characterized in that the implementation steps comprise:
1) filtering and A/D converting the original signal to obtain a digital sampling sequence;
2) obtaining a time-frequency spectrum of the signal by simplifying S transformation;
3) selecting sampling data to be calculated according to data of signal spectrum distribution in a region from-3 sigma to +3 sigma;
4) and calculating the parameter information of the original signal according to the key frequency points and an interpolation method.
2. The simplified S-transform-based time-frequency spectrum analysis method and system according to claim 1, wherein the detailed steps of step 1) comprise:
1.1) to prevent the spectrum aliasing and power frequency interference of the original signal, the analog signal needs to be pre-filtered and then sent to an ADC;
1.2) ADC with a fixed sampling rate fsThe analog signal is sampled and the converted digital sample sequence is sent to the DSP.
3. The method and system for line analysis by simplified S-transform as claimed in claim 1, wherein the detailed steps of step 2) include:
2.1) constructing a Gaussian window with adjustable width as shown in the following formula:
Figure FDA0003023374930000011
in the above formula, t is time; f is the frequency; σ is the standard deviation.
2.2) the expression of S Transform (ST) is shown as follows:
Figure FDA0003023374930000012
in the above formula, τ is a position parameter; h (t) is a signal.
Substituting the width-adjustable Gaussian window number into the above formula to obtain the time-frequency domain expression of ST, which is shown as the following formula:
Figure FDA0003023374930000013
with S (tau)KAnd f) represents the time τKLocal spectral lines of (c).
2.3) the discrete expression of ST is shown as follows:
Figure FDA0003023374930000014
in the above formula, N is the number of sampling points; t is a sampling period;
Figure FDA0003023374930000015
h (KT) is a discrete time sampling sequence, which can be obtained by sampling h (T) at a time interval T.
4. The simplified S-transform-based time-frequency spectrum analysis method and system according to claim 1, wherein the detailed step of step 3) comprises:
3.1) each vnRepresents discrete positive and negative frequency components of h (kt) over time, where N is 0,1,2, N-1, s [ N, j ]]And vnAre used interchangeably and each vnAll go through gnPerforming a calculation from v at zero frequency0The calculation is started.
3.2) through detecting the sampling data of the signal spectrum distribution in the middle-3 sigma to +3 sigma area, wherein, each section of spectrum interval is 6 sigma/fnEach frequency vnThrough its corresponding gaussian window gnAnd (4) calculating. If the Gaussian window gnSpanning sample and gaussian window gn-1If the number of samples spanned is different, the frequency v is calculatednOtherwise v will be skippedn. Repeating the whole calculation process until the sampling sequence is finished;
3.3) the simplified S-transformed time-frequency spectrum has an un-calculated signal gap compared to the original ST time-frequency spectrum. The portion of the data is fitted by least squares to obtain the desired calculated signal time spectrum.
5. The simplified S-transform-based time-frequency spectrum analysis method and system according to claim 1, wherein the detailed step of step 4) comprises:
4.1) calculation of key frequency points:
for an N-point sampling sequence of a fixed sampling time T, there is a key frequency point fc. When the signal frequency is higher than the critical frequency point fcWhen Δ s is less than T; when the signal frequency is lower than the key frequency point, deltas > T.
Due to signal frequency fkIs spanned by
Figure FDA0003023374930000021
Therefore continuous frequency fkAnd fkt1The difference in the upper span is shown by the following equation:
Figure FDA0003023374930000022
when the signal frequency is lower than the critical frequency point, the relationship can be established as follows:
k2+k-6N＝0
the solution of the above equation can be obtained,
Figure FDA0003023374930000023
finally, the key frequency points can be represented by the following formula:
Figure FDA0003023374930000024
4.2) calculating the parameter information of the signal by interpolation.
The phase of the ST signal consists of a base portion and a data portion. The time difference between successive frequencies is called the fundamental phase, and the sum of the local phase and the fundamental phase of a given time series h (t) becomes the data phase. The fundamental phase is calculated from each frequency point where the frequency n and the time j are ST [ n, j ]. The data phase at any frequency point can be obtained by subtracting the base phase from the total ST phase. When the time-frequency spectrum gap is reconstructed, firstly, calculating an S transformation phase matrix of the time-frequency spectrum gap by using key frequency points, and then, subtracting a basic phase of a local spectrum to obtain a corresponding data phase; the data phase in the frequency gap can be determined by interpolation through the frequency spectrum line of the key frequency point, and then the phase information of the data phase is calculated, so that the parameter information of the frequency point in the frequency gap is obtained.
6. A time frequency spectrum analysis method and system based on simplified S transformation are characterized by comprising the following steps:
a signal input unit for acquiring an analog signal;
and the signal conditioning unit is used for pre-filtering the analog signal and sending the filtered analog signal to the ADC to output a digital sampling sequence.
7. A simplified S transform based time-frequency spectrum analysis method and system comprising a digital signal processing device, characterized in that the digital signal processing device is programmed or configured to perform the steps of the simplified S transform based time-frequency spectrum analysis method according to any of claims 1 to 5.
8. A simplified S-transform-based time-frequency spectrum analysis method and system, comprising a digital signal processing device, characterized in that the memory of the digital signal processing device has stored thereon an embedded program programmed or configured to execute the simplified S-transform-based time-frequency spectrum analysis method according to any one of claims 1 to 5.
9. A time-frequency spectrum analysis method and system based on simplified S transformation are characterized by comprising a power module (1), a signal conditioning circuit (2), an analog-to-digital converter (3) and a digital signal processor (4), wherein the output end of the power module (1) is respectively and electrically connected with the signal conditioning circuit (2), the analog-to-digital converter (3) and the digital signal processor (4), the output end of the signal conditioning circuit (2) is connected with the digital signal processor (4) through a low-pass filter (3), the analog-to-digital converter (3), and the digital signal processor (4) is programmed or configured to execute the steps of the time-frequency spectrum analysis method based on the simplified S transformation according to any one of claims 1-5.
10. The simplified S-transform-based time-frequency spectrum analysis method and system according to claim 9, wherein the digital signal processor (4) is further connected with a synchronous dynamic random access memory (5), a flash memory (6), an active crystal oscillator (7), a reset module (8) and an emulation debugging interface (9), respectively.
CN202110408929.8A 2021-04-16 2021-04-16 Time-frequency spectrum analysis method and system for simplifying S transformation Active CN113092850B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110408929.8A CN113092850B (en) 2021-04-16 2021-04-16 Time-frequency spectrum analysis method and system for simplifying S transformation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110408929.8A CN113092850B (en) 2021-04-16 2021-04-16 Time-frequency spectrum analysis method and system for simplifying S transformation

Publications (2)

Publication Number Publication Date
CN113092850A true CN113092850A (en) 2021-07-09
CN113092850B CN113092850B (en) 2022-03-15

Family

ID=76677948

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110408929.8A Active CN113092850B (en) 2021-04-16 2021-04-16 Time-frequency spectrum analysis method and system for simplifying S transformation

Country Status (1)

Country Link
CN (1) CN113092850B (en)

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH01296169A (en) * 1988-05-24 1989-11-29 Sony Corp Spectrum analyzer
US5068597A (en) * 1989-10-30 1991-11-26 General Electric Company Spectral estimation utilizing a minimum free energy method with recursive reflection coefficients
CN103245832A (en) * 2013-05-16 2013-08-14 湖南大学 Harmonic time frequency characteristic parameter estimating method based on fast S conversion and analysis meter
CN203376400U (en) * 2013-05-16 2014-01-01 湖南大学 Harmonic wave time-frequency characteristic parameter analyzer
CN106250904A (en) * 2016-05-18 2016-12-21 国网新疆电力公司电力科学研究院 Based on Power Disturbance analyser and the sorting technique of improving S-transformation
CN107402326A (en) * 2017-07-20 2017-11-28 南京理工大学 A kind of long Time-Frequency Analysis Method of limited window for improving S-transformation

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH01296169A (en) * 1988-05-24 1989-11-29 Sony Corp Spectrum analyzer
US5068597A (en) * 1989-10-30 1991-11-26 General Electric Company Spectral estimation utilizing a minimum free energy method with recursive reflection coefficients
CN103245832A (en) * 2013-05-16 2013-08-14 湖南大学 Harmonic time frequency characteristic parameter estimating method based on fast S conversion and analysis meter
CN203376400U (en) * 2013-05-16 2014-01-01 湖南大学 Harmonic wave time-frequency characteristic parameter analyzer
CN106250904A (en) * 2016-05-18 2016-12-21 国网新疆电力公司电力科学研究院 Based on Power Disturbance analyser and the sorting technique of improving S-transformation
CN107402326A (en) * 2017-07-20 2017-11-28 南京理工大学 A kind of long Time-Frequency Analysis Method of limited window for improving S-transformation

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
徐方维等: ""基于改进S变换的电能质量扰动分类"", 《中国电机工程学报》 *

Also Published As

Publication number Publication date
CN113092850B (en) 2022-03-15

Similar Documents

Publication Publication Date Title
CN107102255B (en) Single ADC acquisition channel dynamic characteristic test method
CN107543962B (en) Calculation method of dominant inter-harmonic frequency spectrum distribution
CN106841915B (en) Power transmission line fault positioning method based on compressed sensing
CN115575707A (en) Harmonic detection device and method based on combination of improved FFT algorithm and wavelet transform
CN108197073B (en) Improved electric vehicle charging electric energy signal characteristic analysis method
CN110687595B (en) Seismic data processing method based on time resampling and synchronous extrusion transformation
CN115618213A (en) Charger voltage disturbance analysis method, system, equipment and storage medium
CN103543331B (en) A kind of method calculating electric signal harmonic wave and m-Acetyl chlorophosphonazo
CN110068729B (en) Signal phasor calculation method
Lv et al. Longitudinal synchroextracting transform: A useful tool for characterizing signals with strong frequency modulation and application to machine fault diagnosis
CN108090270B (en) Transient oscillation parameter identification method based on morphological filtering and blind source separation
CN113092850B (en) Time-frequency spectrum analysis method and system for simplifying S transformation
CN112730982A (en) Harmonic detection method of hybrid direct-current power transmission system
CN109254202B (en) Synchronous phasor measurement device applied to power distribution network
CN116046968A (en) Liquid chromatography workstation data processing method, system and storable medium
Yi et al. Instantaneous harmonic decomposition technique for three‐phase current based on multiple reference coordinates
CN114184838A (en) Power system harmonic detection method, system and medium based on SN mutual convolution window
CN115932389A (en) HHT (Hilbert-Huang transform) -based voltage quality disturbance detection method
CN112505413B (en) Time-frequency analysis method and system
CN111551785B (en) Frequency and harmonic detection method based on unscented Kalman filter
CN114689991A (en) Method and system for determining fault time of high-voltage cable and related components
CN114487589A (en) Power grid broadband signal self-adaptive measurement method, device and system
Zhang et al. Determining the length of sliding window by using frequency decomposition
CN114705913B (en) Harmonic analysis method of rotary transformer
CN113917226A (en) Voltage sag detection method and system based on threshold detection and windowed interpolation FFT

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant