CN113742645B - Time-frequency analysis method for linear group delay frequency-variable signal - Google Patents
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Abstract
The invention discloses a time-frequency analysis method of a linear group delay frequency-variable signal, which comprises the following steps: determining the inclination angle of the linear group delay frequency-varying signal according to a time rearrangement operator and a frequency rearrangement operator of a time-frequency rearrangement algorithm; constructing a novel time rearrangement operator by utilizing a time rearrangement operator in the time-frequency rearrangement algorithm of the transformation of the inclination angle; and rearranging the time-frequency energy of the linear group delay frequency-varying signal subjected to the short-time Fourier transform along the time direction by using a novel time rearrangement operator. The invention constructs a novel time rearrangement operator by using the frequency rearrangement operator and the time rearrangement operator in the time-frequency rearrangement algorithm, only three times of short-time Fourier transform are needed, and the calculation burden is obviously reduced. In addition, the invention compresses the time-frequency energy along the time direction in the time direction synchronous compression transformation frame, so that the processed time-frequency distribution result supports signal reconstruction.
Description
Technical Field
The invention relates to the field of non-stationary signal time-frequency analysis, in particular to a time-frequency analysis method for a linear group delay frequency-variable signal.
Background
The energy aggregation and the reconfigurability of time-frequency distribution are key indexes for measuring the quality of the time-frequency distribution method. At present, researchers have proposed various time-frequency analysis methods for frequency-varying signals with linearly varying group delay. Such as: time frequency rearrangement, second-order time rearrangement synchronous compression transformation and second-order transient extraction transformation. However, these methods have some disadvantages in practical application: the time rearrangement processing of the linear group delay frequency change signal can obtain an ideal time frequency distribution result, but the time frequency distribution processed by the method cannot be utilized for signal reconstruction. The linear group delay frequency-variable signals are processed by utilizing second-order time rearrangement synchronous compression transformation and second-order transient extraction transformation, an ideal time-frequency distribution result can be obtained, and reconstruction can be carried out according to the time-frequency distribution result.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a time-frequency analysis method for linear group delay frequency-variable signals.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a time-frequency analysis method of a linear group delay frequency-variable signal comprises the following steps:
s1: determining the inclination angle of the linear group delay frequency-varying signal according to a time rearrangement operator and a frequency rearrangement operator of a time-frequency rearrangement algorithm;
s2: constructing a novel time rearrangement operator by utilizing a time rearrangement operator in the time-frequency rearrangement algorithm of the transformation of the inclination angle;
s3: and rearranging the time-frequency energy of the linear group delay frequency-change signal subjected to the short-time Fourier transform along the time direction by using a novel time rearrangement operator.
Preferably, step S1 comprises:
the frequency-varying signal is processed by using a time-frequency rearrangement algorithm, and the obtained time-frequency distribution result is as follows:
wherein RM (u, eta) represents the time-frequency energy distribution result when the time is u and the frequency is eta; t represents time, ω represents frequency; δ represents a delta function;
representing a temporal rearrangement operator;
representing a frequency rearrangement operator; ge (t, omega) represents the time-frequency distribution after the short-time Fourier transform processing the linear group delay frequency-variable signal;
wherein the content of the first and second substances,
representing partial derivative of ω; arg represents the real part of the retained complex operation result; i represents an imaginary unit; ge (germanium) oxide tg (t, ω) represents performing short-time fourier transform on the linear group delay frequency-variant signal using a window function tg; tg denotes the multiplication of the gaussian window function g with time t;
wherein the content of the first and second substances,
representing partial derivative of t; ge (germanium) oxide g′ (t, ω) represents the short-time fourier transform of the linear group delay frequency-variant signal using a window function g'; g' represents the derivation of the gaussian window function g along the time t direction;
wherein the content of the first and second substances,
in order to be a linear group delay frequency-dependent signal,
is a frequency domain gaussian window function; ξ represents the frequency range;
aiming at the linear group delay frequency-variable signal, determining the inclination angle of the linear group delay frequency-variable signal by utilizing the rearrangement time-frequency position of the time-frequency point (t, omega) and the (t + delta t, omega) after being mapped by the time rearrangement operator and the frequency rearrangement operator as follows:
where α is the tilt angle of the linear group delay frequency-varying signal, and Δ t represents the time variation.
Preferably, step S2 comprises:
and (2) reconstructing a time rearrangement operator in the time-frequency rearrangement algorithm by using the inclination angle determined in the step (S1), and constructing a novel time rearrangement operator as follows:
wherein the content of the first and second substances,
a novel time rearrangement operator;
a time rearrangement operator;
a frequency rearrangement operator; t represents time, ω represents frequency; alpha is the inclination angle of the linear group delay frequency-variable signal;
preferably, step S3 comprises: using a novel temporal rearrangement operator
Rearranging the time-frequency energy of the linear group delay frequency-change signal after the short-time Fourier transform processing along the time direction to obtain the final time-frequency distribution result as follows:
wherein RTs (u, omega) represents a final time-frequency energy distribution result when the time is u and the frequency is omega; t represents time; δ represents a delta function;
representing a new temporal rearrangement operator; g (t, omega) represents the time-frequency distribution after the linear group delay frequency-change signal is processed by short-time Fourier transform after the frequency shift term is added;
wherein the content of the first and second substances,
in order to be a linear group delay frequency-varying signal,
is a frequency domain gaussian window function; ξ represents the frequency range; and G (t, ω) · e iωt = Ge (t, ω); ge (t, omega) is the time frequency distribution after the short-time Fourier transform processing linear group delay frequency conversion signal.
Preferably, the method further comprises the step S4: and restoring the final time-frequency energy distribution result to the one-dimensional linear group delay frequency-variable signal again as follows:
wherein s (t) is a one-dimensional linear group delay frequency-varying signal, RTs (u, omega) is a final time-frequency energy distribution result when time is u and frequency is omega;
frequency domain gaussian window function
Value at frequency ω =0 Hz.
Compared with the prior art, the invention has the beneficial effects that:
estimating a group delay inclination angle of a linear group delay frequency-variable signal according to a relation between a rearrangement time-frequency position estimated by a frequency rearrangement operator and a time rearrangement operator and an original time-frequency position in a time-frequency rearrangement algorithm; improving a time rearrangement operator in the original time frequency rearrangement algorithm by using the estimated group delay inclination angle, constructing a novel time rearrangement operator, and accurately estimating the time frequency position of the linear group delay signal; and rearranging the time-frequency energy along the time direction by using the constructed novel time rearrangement operator, and compressing the time-frequency energy of the linear group delay frequency-variable signal to a real group delay position. Because the invention utilizes the frequency rearrangement operator and the time rearrangement operator in the time-frequency rearrangement algorithm to construct the novel time rearrangement operator, only three times of short-time Fourier transform is needed, and the calculation burden is obviously reduced. In addition, the time-frequency energy is compressed along the time direction in the time direction synchronous compression transformation frame, so that the processed time-frequency distribution result supports signal reconstruction.
Drawings
In order to more clearly illustrate the embodiments or technical solutions of the present invention, the drawings used in the embodiments or technical solutions of the present invention will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained based on these drawings without creative efforts.
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a time-frequency diagram of the method of the present invention for processing single-component linear group delay-variable signals;
FIG. 3 is a time-frequency slice diagram of the method of the present invention for processing a single-component linear group delay-variable signal;
fig. 4 is a comparison graph of the reconstructed signal and the original signal according to the method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
A time-frequency analysis method of a linear group delay frequency-variable signal comprises the following steps:
s1: determining the tilt angle of the linear group delay frequency-varying signal according to a time rearrangement operator and a frequency rearrangement operator of a time-frequency rearrangement algorithm, which specifically comprises the following steps:
the frequency-varying signal is processed by using a time-frequency rearrangement algorithm, and the obtained time-frequency distribution result is as follows:
wherein RM (u, eta) represents the time-frequency energy distribution result when the time is u and the frequency is eta; t represents time, ω represents frequency; δ represents a delta function;
representing a temporal rearrangement operator;
representing a frequency rearrangement operator; ge (t, omega) represents the time-frequency distribution after the short-time Fourier transform processing the linear group delay frequency-variable signal;
wherein the content of the first and second substances,
representing partial derivative of ω; arg represents the real part of the reserved complex operation result; i represents an imaginary unit; ge (germanium) oxide tg (t, ω) represents performing short-time fourier transform on the linear group delay frequency-varying signal by using the window function tg; tg denotes the multiplication of the gaussian window function g with time t;
wherein the content of the first and second substances,
representing partial derivative of t; ge (germanium) oxide g′ (t, ω) represents the short-time fourier transform of the linear group delay frequency-variant signal using a window function g'; g' meterShowing the derivation of the Gaussian window function g along the time t direction;
wherein the content of the first and second substances,
in order to be a linear group delay frequency-dependent signal,
is a frequency domain gaussian window function; ξ represents the frequency range;
aiming at the linear group delay frequency-variable signal, determining the inclination angle of the linear group delay frequency-variable signal by utilizing the rearrangement time-frequency position of the time-frequency point (t, omega) and the (t + delta t, omega) after being mapped by the time rearrangement operator and the frequency rearrangement operator as follows:
wherein, α is the tilt angle of the linear group delay frequency-varying signal, and Δ t represents the time variation.
S2: the method for constructing the novel time rearrangement operator by utilizing the time rearrangement operator in the time-frequency rearrangement algorithm for the transformation of the inclination angle specifically comprises the following steps:
and (2) reconstructing a time rearrangement operator in the time-frequency rearrangement algorithm by using the inclination angle determined in the step (S1), and constructing a novel time rearrangement operator as follows:
wherein the content of the first and second substances,
a novel time rearrangement operator;
rearranging operators for time;
rearranging operators for frequencies; t represents time, ω represents frequency; alpha is the tilt angle of the linear group delay frequency-varying signal.
S3: the time-frequency energy of the linear group delay frequency-variable signal after the short-time fourier transform processing is rearranged along the time direction by using a novel time rearrangement operator, and the method specifically comprises the following steps:
using novel time rearrangement operators
Rearranging the time-frequency energy of the linear group delay frequency-change signal after the short-time Fourier transform processing along the time direction to obtain the final time-frequency distribution result as follows:
wherein RTs (u, omega) represents a final time-frequency energy distribution result when time is u and frequency is omega; t represents time; δ represents a delta function;
representing a novel temporal rearrangement operator; g (t, omega) represents the time-frequency distribution after the linear group delay frequency-change signal is processed by short-time Fourier transform after the frequency shift term is added;
wherein the content of the first and second substances,
in order to be a linear group delay frequency-varying signal,
is a frequency domain gaussian window function; ξ represents the frequency range; and G (t, ω) · e iωt = Ge (t, ω); ge (t, ω) is short-time FourierAnd transforming the time-frequency distribution after the linear group delay frequency-changing signal is processed.
And step S4: and restoring the final time-frequency energy distribution result to the one-dimensional linear group delay frequency-variable signal again as follows:
wherein s (t) is a one-dimensional linear group delay frequency-variable signal, RTs (u, omega) is a final time-frequency energy distribution result when time is u and frequency is omega;
frequency domain gaussian window function
Value at frequency ω =0 Hz.
Example 2
In order to verify the effectiveness of the method, a single-component linear group delay frequency-variable signal is constructed, and the expression is as follows:
s 1 (ω)＝20·exp(-i(0.01·ω 2 +4·ω))
the sampling frequency of the single-component linear group delay frequency-variable signal is 200Hz, and the sampling time is 10s. The signal amplitude modulation function is 20 in the whole frequency range [0Hz,100Hz ], and the group delay function can be expressed as:
GD 1 (ω)＝4+0.02·ω
from the group delay function, GD is known when ω =0Hz 1 (0) =4, GD when ω =100Hz 1 (100) And (6). The group delay function of the linear group delay frequency dependent signal increases monotonically with increasing frequency. The time-frequency result obtained by processing the signal by the method of the invention is shown in figure 2. Fig. 3 shows time-frequency slices at frequencies f =30Hz and f =60Hz of the time-frequency results processed by the method of the invention. As can be seen from fig. 3, the maximum value of the amplitude of the time-frequency slice with the frequency f =30Hz is 20, which is equal to the value of the amplitude modulation function, and the corresponding time position is 4.6s; time-frequency slice with frequency f =60Hz, with maximum amplitude20, equal to the value of the amplitude modulation function, corresponding to a time position of 5.2s. The phenomenon is consistent with the time-frequency distribution result of the frequency-varying signals in an ideal state, and therefore the effectiveness of the method is proved.
To further illustrate the signal reconstruction capability of the method of the present invention, fig. 4 shows a comparison graph of the time domain signal reconstructed and recovered according to the time-frequency distribution result of the method of the present invention and the original signal. As can be seen from fig. 4, the reconstruction error between the reconstructed signal and the original signal is very small, and the method of the present invention can effectively reconstruct the signal.
Claims (4)
1. A time-frequency analysis method of a linear group delay frequency-variable signal is characterized by comprising the following steps:
s1: determining the inclination angle of the linear group delay frequency-varying signal according to a time rearrangement operator and a frequency rearrangement operator of a time-frequency rearrangement algorithm; the method comprises the following steps:
the frequency-varying signal is processed by using a time-frequency rearrangement algorithm, and the obtained time-frequency distribution result is as follows:
wherein RM (u, eta) represents the time-frequency energy distribution result when the time is u and the frequency is eta; t represents time, ω represents frequency; δ represents a delta function;
representing a temporal rearrangement operator;
representing a frequency rearrangement operator; ge (t, omega) represents time-frequency distribution after short-time Fourier transform processing of the linear group delay frequency-variable signal;
wherein the content of the first and second substances,
representing partial derivative of ω; arg represents the real part of the retained complex operation result; i represents an imaginary unit; ge (germanium) oxide tg (t, ω) represents performing short-time fourier transform on the linear group delay frequency-varying signal by using the window function tg; tg denotes the multiplication of the gaussian window function g with time t;
wherein the content of the first and second substances,
representing partial derivative of t; ge (germanium) oxide g′ (t, ω) represents performing short-time fourier transform on the linear group delay frequency-varying signal by using a window function g'; g' represents the derivation of the gaussian window function g along the time t direction;
wherein the content of the first and second substances,
in order to be a linear group delay frequency-dependent signal,
is a frequency domain gaussian window function; ξ represents the frequency range;
aiming at the linear group delay frequency-variable signal, determining the inclination angle of the linear group delay frequency-variable signal by utilizing the rearrangement time-frequency positions of time-frequency points (t, omega), (t + delta t, omega) after being mapped by a time rearrangement operator and a frequency rearrangement operator as follows:
wherein, alpha is the inclination angle of the linear group delay frequency-variable signal, and delta t represents the time variation;
s2: constructing a novel time rearrangement operator by utilizing a time rearrangement operator in the time-frequency rearrangement algorithm of the transformation of the inclination angle;
s3: and rearranging the time-frequency energy of the linear group delay frequency-change signal subjected to the short-time Fourier transform along the time direction by using a novel time rearrangement operator.
2. The time-frequency analysis method of linear group delay-variable signals according to claim 1, wherein step S2 comprises:
and (2) reconstructing a time rearrangement operator in the time-frequency rearrangement algorithm by using the inclination angle determined in the step (S1), and constructing a novel time rearrangement operator as follows:
wherein the content of the first and second substances,
rearranging operators for the novel time;
a time rearrangement operator;
a frequency rearrangement operator; t represents time, ω represents frequency; alpha is the tilt angle of the linear group delay frequency-varying signal.
3. The time-frequency analysis method for linear group delay variation signals according to claim 1, wherein step S3 comprises:
using novel time rearrangement operators
For short-time Fourier transformRearranging the time-frequency energy of the processed linear group delay frequency-varying signals along the time direction to obtain the final time-frequency distribution result as follows:
wherein RTs (u, omega) represents a final time-frequency energy distribution result when time is u and frequency is omega; t represents time; δ represents a delta function;
representing a novel temporal rearrangement operator; g (t, omega) represents the time-frequency distribution after the linear group delay frequency-change signal is processed by short-time Fourier transform after the frequency shift term is added;
wherein the content of the first and second substances,
in order to be a linear group delay frequency-dependent signal,
is a frequency domain gaussian window function; ξ represents the frequency range; and G (t, ω) · e iωt = Ge (t, ω); ge (t, omega) is the time frequency distribution after the short-time Fourier transform processing of the linear group delay frequency-variable signal.
4. The time-frequency analysis method of linear group delay-variable signals according to claim 1, further comprising step S4: and restoring the final time-frequency energy distribution result to the one-dimensional linear group delay frequency-variable signal again as follows:
wherein s (t) is a one-dimensional linear group delay frequency-varying signal, RTs (u, omega) is a final time-frequency energy distribution result when time is u and frequency is omega;
frequency domain gaussian window function
Value at frequency ω =0 Hz.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107608935A (en) * | 2017-08-30 | 2018-01-19 | 西安交通大学 | Impact class signal time frequency analysis and reconstructing method based on time rearrangement compressed transform |
| JP2018097430A (en) * | 2016-12-08 | 2018-06-21 | 日本電信電話株式会社 | Time series signal feature estimating apparatus and program |
| CN109034043A (en) * | 2018-07-20 | 2018-12-18 | 东北大学 | Based on the synchronous nonstationary random response method for extracting transformation of high-order |
| CN109063613A (en) * | 2018-07-20 | 2018-12-21 | 东北大学 | Based on the synchronous nonstationary random response method for extracting transformation of Generalized parametering |
| CN112328956A (en) * | 2020-09-22 | 2021-02-05 | 东北大学 | Strong frequency variable signal time-frequency analysis method |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2018097430A (en) * | 2016-12-08 | 2018-06-21 | 日本電信電話株式会社 | Time series signal feature estimating apparatus and program |
| CN107608935A (en) * | 2017-08-30 | 2018-01-19 | 西安交通大学 | Impact class signal time frequency analysis and reconstructing method based on time rearrangement compressed transform |
| CN109034043A (en) * | 2018-07-20 | 2018-12-18 | 东北大学 | Based on the synchronous nonstationary random response method for extracting transformation of high-order |
| CN109063613A (en) * | 2018-07-20 | 2018-12-21 | 东北大学 | Based on the synchronous nonstationary random response method for extracting transformation of Generalized parametering |
| CN112328956A (en) * | 2020-09-22 | 2021-02-05 | 东北大学 | Strong frequency variable signal time-frequency analysis method |
Non-Patent Citations (2)
| Title |
|---|
| 《机械工程学报》2019年度1～24期总目次;俞昆 等;《机械工程学报》(第24期);全文 * |
| 一种快速线性时频变换方法;边静;《计算机光盘软件与应用》(第01期);全文 * |
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