CN109460614B - Signal time-frequency decomposition method based on instantaneous bandwidth - Google Patents

Signal time-frequency decomposition method based on instantaneous bandwidth Download PDF

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CN109460614B
CN109460614B CN201811342173.6A CN201811342173A CN109460614B CN 109460614 B CN109460614 B CN 109460614B CN 201811342173 A CN201811342173 A CN 201811342173A CN 109460614 B CN109460614 B CN 109460614B
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frequency
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decomposition
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CN109460614A (en
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黎恒
韦泽贤
徐韶华
杨玉琳
王玲容
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Guangxi Jiaoke Group Co Ltd
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Guangxi Transportation Research and Consulting Co Ltd
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Abstract

The invention provides a signal time-frequency decomposition method based on instantaneous bandwidth, which is characterized in that local cut-off frequency is obtained by optimizing an extraction algorithm of an Intrinsic Mode Function (IMF) in Empirical Mode Decomposition (EMD), a time-varying filter is constructed by utilizing the local cut-off frequency, filtering is carried out by utilizing the time-varying filter, and the solving and filtering processes of the local cut-off frequency are repeated until the filtering obtains the local bandwidth of a signal meeting a termination condition, and then the intrinsic mode function of the local bandwidth is obtained. In the invention, local cut-off frequency estimation and filtering are adopted to separate the signal components which are relatively close to each other in the frequency domain, and a modal aliasing suppression module is adopted simultaneously, so that the time-frequency domain break point generated by noise interference can be suppressed, and the problems of frequency resolution and modal aliasing are solved simultaneously.

Description

Signal time-frequency decomposition method based on instantaneous bandwidth
Technical Field
The invention relates to the field of signal processing, in particular to a signal time-frequency decomposition method based on instantaneous bandwidth.
Background
Time-frequency domain (time-frequency) analysis describes the time-dependent relationship of signal frequency, an important method of nonlinear, non-stationary signal processing. Typical time-frequency analysis methods are linear methods, with short-time fourier transforms, wavelet analysis, wigner-Ville distribution, etc. The time-frequency resolution of these methods is limited to a large extent by the type and width of the basis functions, which often cannot be easily selected, resulting in poor adaptability of these methods. In addition, the time-frequency resolution of these methods is limited by the Heisenberg uncertainty principle, and is constrained in measurement of both physical quantities, time and frequency, so that it is impossible to obtain high resolution at the same time.
The Hilbert-yellow transform (HHT) is a nonlinear adaptive time-frequency analysis method, and includes two steps: first, the signal is decomposed into a combination of a series of eigenmode functions (intrinsic mode function, IMF) using empirical mode decomposition (empirical mode decomposition, EMD) that satisfy the requirements of the hilbert transform (Hilbert transform) for single-component characteristics of the signal. Then, performing time-frequency feature extraction on the IMF by using Hilbert transform; finally, a three-dimensional distribution with respect to time-frequency-amplitude, called HHT spectrum, is obtained. HHT is not limited by the basic function and Heisenberg uncertainty principle any more, is an adaptive time-frequency analysis method, is widely applied to the fields of biomedicine, fault diagnosis, finance and the like, and has some limitations (EMD limitations): firstly, the problem of frequency resolution is that EMD can not decompose signals with the frequency ratio smaller than 0.65; secondly, the problem of modal aliasing is that IMF splitting phenomenon can occur when EMD decomposes noise-containing signals.
At present, aiming at the EMD limitation, some researches at home and abroad improve by changing signal interpolation points, using methods such as signal masking and noise assistance, but only aiming at one problem, namely the problem of frequency resolution or the problem of modal aliasing, the decomposition performance is improved. There is no effective solution to the problem of frequency resolution and modal aliasing at the same time.
Therefore, a signal time-frequency decomposition method based on instantaneous bandwidth is needed, which can improve the frequency resolution of signal decomposition and extract the time-frequency domain characteristics of the signal.
Disclosure of Invention
The invention aims to provide a technical scheme which can simultaneously improve the frequency resolution of signal decomposition and the robustness of noise-containing signal decomposition, thereby being beneficial to better extracting the time-frequency characteristics of signals.
The method has the following overall thought: and solving in the Hilbert transform domain to obtain local cut-off frequency by optimizing an extraction algorithm of an Intrinsic Mode Function (IMF) in Empirical Mode Decomposition (EMD), constructing a time-varying filter by using the local cut-off frequency, filtering by using the time-varying filter, and repeating the solving and filtering processes of the local cut-off frequency until the filtering obtains a signal local bandwidth meeting a termination condition, thereby obtaining an intrinsic mode function of the local bandwidth.
The invention provides a signal time-frequency decomposition method based on instantaneous bandwidth, which comprises the following steps:
step one: performing Empirical Mode Decomposition (EMD) on the signal by adopting a signal decomposition method, and decomposing the signal into a series of combinations of Intrinsic Mode Functions (IMFs);
step two: performing time-frequency characteristic extraction on an Intrinsic Mode Function (IMF) by using Hilbert transformation, and solving in a Hilbert transformation domain to obtain local cut-off frequency;
step three: constructing a time-varying filter by using the local cut-off frequency, and filtering by using the time-varying filter;
step four: repeating the second step and the third step until the local bandwidth of the signal meeting the termination condition is obtained through filtering, so that the eigen mode function of the local bandwidth is obtained;
the local cut-off frequency estimation module is used for estimating the local cut-off frequency
Figure GDA0004199693700000021
The method comprises the following steps:
1) The time of occurrence of all maximum value points and minimum value points of the instantaneous bandwidth A (t) is calculated as { t }, respectively max Sum { t } min }；
2) For series point A ({ t) min -cubic spline interpolation) and the curve obtained is marked as beta 1 (t); for series point A ({ t) max -cubic spline interpolation) and the curve obtained is marked as beta 2 (t)；
3) Calculating a according to the following 1 (t) and a 2 (t)：
a 1 (t)＝[β 1 (t)+β 2 (t)]/2
a 2 (t)＝[β 2 (t)-β 1 (t)]/2
Wherein a is 1 (t)、a 2 (t) obtaining predicted curves of instantaneous envelopes of the two signals after decomposition;
4) For series of points
Figure GDA0004199693700000031
Performing cubic spline interpolation to obtain curve eta 1 (t) for series points
Figure GDA0004199693700000032
Performing cubic spline interpolation to obtain curve eta 2 (t) wherein, the%>
Figure GDA0004199693700000033
Is the instantaneous bandwidth
Figure GDA0004199693700000034
Is the reciprocal of (2);
5) According to the following calculation
Figure GDA0004199693700000035
And->
Figure GDA0004199693700000036
Figure GDA0004199693700000037
Figure GDA0004199693700000038
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure GDA0004199693700000039
and->
Figure GDA00041996937000000310
Respectively obtaining the predicted curves of the instantaneous frequencies of the two signals after decomposition;
6) Calculating local cut-off frequency
Figure GDA00041996937000000311
Figure GDA00041996937000000312
The modal aliasing suppression module is used for calculating to obtain a new local cut-off frequency
Figure GDA00041996937000000313
The method comprises the following steps:
1) The appearance time of the maximum value of the input signal x (t) is calculated and recorded as u i ,i＝1,2,3...；
2) Finding a break point according to the following formula, denoted as e j : satisfy the following requirements
Figure GDA00041996937000000314
Wherein ρ is a preset constant;
Figure GDA00041996937000000315
equivalent to->
Figure GDA00041996937000000316
u i Time instant of break point, i.e. e j ＝u i 。
3) For each break point e j Judging the category if there is
Figure GDA0004199693700000041
e j At the position of
Figure GDA0004199693700000042
Rising edge of (2); if there is->
Figure GDA0004199693700000043
e j At->
Figure GDA0004199693700000044
Is arranged on the falling edge of the first part;
4) For each break point e j If in a position of
Figure GDA0004199693700000045
Rising edge of>
Figure GDA0004199693700000046
Marked as non-interpolation points; if at->
Figure GDA0004199693700000047
Falling edge of>
Figure GDA0004199693700000048
Marked as non-interpolation points;
5) For a pair of
Figure GDA0004199693700000049
Interpolation is performed on all interpolation points (points not obtained in step 4) to obtain a new +.>
Figure GDA00041996937000000410
Preferably, in the first step, the specific process of the signal decomposition method is as follows: and extracting an intrinsic mode function imf (t) from the input signal x (t) by a screening method, calculating a residual signal r (t), stopping decomposing if the number of extreme points of r (t) is less than 3, otherwise, taking r (t) as a new x (t), and performing a new round of decomposition process. After the algorithm is finished, the output result is a set of a series of imfs (t).
Preferably, the screening method in the second step includes: the device comprises an instantaneous amplitude and instantaneous bandwidth module, a local cut-off frequency estimation module, a modal aliasing suppression module, a time-varying filtering module and a local bandwidth judgment module; the local cut-off frequency estimation module and the time-varying filtering module are used for separating signal components which are relatively close to each other in a frequency domain; the modal aliasing suppression module is used for suppressing a time-frequency domain break point generated by noise interference, so that the robustness of signal decomposition under noise is improved.
More preferably, the instantaneous amplitude and instantaneous bandwidth module is used for calculating instantaneous amplitude A (t) and instantaneous bandwidth
Figure GDA00041996937000000411
The method comprises the following steps:
1) Hilbert transform for determining an input signal x (t)
Figure GDA00041996937000000412
2) Obtaining an analysis signal z (t) of the input signal x (t) to obtain A (t) and A (t)
Figure GDA00041996937000000413
Figure GDA00041996937000000414
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure GDA00041996937000000415
more preferably, the mode aliasing suppression module is used for obtaining
Figure GDA00041996937000000416
Then, the time-varying filtering module inputs a signal x (t) for fitting, and a fitting result is obtained and used as the output of the time-varying filter, and the method specifically comprises the following steps:
1) Calculate h (t) according to the following
Figure GDA0004199693700000051
h (t) is a filter cut-off frequency reference signal;
2) Calculating all extreme point moments of h (t), and recording as k i ，i＝1,2,3...；
3) At k i B spline fitting is carried out on the input signal x (t) as a node, and a fitting result is recorded as a mean signalm (t) as the output of the time-varying filter.
More preferably, m (t), a are calculated according to the above modules 1 (t) and a 2 (t)、
Figure GDA0004199693700000052
And->
Figure GDA0004199693700000053
The local bandwidth judging module comprises the following steps:
1) Calculating instantaneous average frequency of input signal
Figure GDA0004199693700000054
Figure GDA0004199693700000055
2) Calculating the instantaneous bandwidth of Loughlin of an input signal:
Figure GDA0004199693700000056
wherein a is 1 ′(t)、a 2 ' (t) is a respectively 1 (t)、a 2 Inverse of (t);
3) Calculating an instantaneous bandwidth shift factor θ (t):
Figure GDA0004199693700000057
in the invention, local cut-off frequency estimation and filtering are adopted to separate the signal components which are relatively close to each other in the frequency domain, and a modal aliasing suppression module is adopted simultaneously, so that the time-frequency domain break point generated by noise interference can be suppressed, and the problems of frequency resolution and modal aliasing are solved simultaneously. The amplitude and frequency of the time-varying filter of the signal time-frequency decomposition method can change along with the time, and the amplitude and frequency of the obtained signal can also change along with the time. Therefore, the invention has good decomposition effect on stationary signals (such as sine wave signals) and non-stationary signals (such as frequency modulation signals).
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention as claimed.
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Further objects, functions and advantages of the present invention will be clarified by the following description of embodiments of the present invention with reference to the accompanying drawings, in which:
fig. 1 shows a flow chart of a signal decomposition method of the present invention.
Figure 2 shows a flow chart of the screening method of the present invention.
FIG. 3 shows a spectrum obtained by decomposing x (t) by the method of the present invention.
Fig. 4 shows a spectrum obtained by decomposing x (t) by the conventional EMD method.
Fig. 5 (a) shows a time-frequency spectrum obtained by the method of the present invention.
Fig. 5 (b) shows a time-frequency spectrum obtained by the conventional EMD method.
Detailed Description
The objects and functions of the present invention and methods for achieving these objects and functions will be elucidated by referring to exemplary embodiments. However, the present invention is not limited to the exemplary embodiments disclosed below; this may be implemented in different forms. The essence of the description is merely to aid one skilled in the relevant art in comprehensively understanding the specific details of the invention.
Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the drawings, the same reference numerals represent the same or similar components, or the same or similar steps.
The invention provides a signal time-frequency decomposition method based on instantaneous bandwidth, which comprises the following steps: performing Empirical Mode Decomposition (EMD) on the signal by adopting a signal decomposition method, and decomposing the signal into a series of combinations of Intrinsic Mode Functions (IMFs); performing time-frequency characteristic extraction on an Intrinsic Mode Function (IMF) by using Hilbert transformation, and solving in a Hilbert transformation domain to obtain local cut-off frequency; constructing a time-varying filter by using the local cut-off frequency, and filtering by using the time-varying filter; and repeating the Hilbert transform domain solving and filtering until the filtering obtains the local bandwidth of the signal meeting the termination condition, thereby obtaining the eigenmode function of the local bandwidth.
Referring to fig. 1 and 2, the specific process of the signal decomposition method is as follows: and extracting an intrinsic mode function imf (t) from the input signal x (t) by a screening method, calculating a residual signal r (t), stopping decomposing when the number of extreme points of r (t) is less than 3, and otherwise, taking r (t) as a new x (t) to perform a new round of decomposition process. After the algorithm is finished, the output result is a set of a series of imfs (t), as shown in fig. 1.
Specifically, the screening method in the second step includes: the device comprises an instantaneous amplitude and instantaneous bandwidth module, a local cut-off frequency estimation module, a modal aliasing suppression module, a time-varying filtering module and a local bandwidth judgment module; the local cut-off frequency estimation module and the time-varying filtering module are used for separating signal components which are relatively close to each other in a frequency domain; the modal aliasing suppression module is configured to suppress a time-frequency domain break point generated by noise interference, so as to improve robustness of signal decomposition under noise, as shown in fig. 2.
Further, the instantaneous amplitude and instantaneous bandwidth module is used for calculating the instantaneous amplitude A (t) and the instantaneous bandwidth
Figure GDA0004199693700000071
The method comprises the following steps:
1) Hilbert transform for determining an input signal x (t)
Figure GDA0004199693700000072
2) Obtaining an analysis signal z (t) of the input signal x (t) to obtain A (t) and A (t)
Figure GDA0004199693700000073
Figure GDA0004199693700000074
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure GDA0004199693700000075
further, the local cut-off frequency estimation module is used for estimating the local cut-off frequency
Figure GDA0004199693700000076
The method comprises the following steps:
1) The time of occurrence of all maximum value points and minimum value points of the instantaneous bandwidth A (t) is calculated as { t }, respectively max Sum { t } min }；
2) For series point A ({ t) min -cubic spline interpolation) and the curve obtained is marked as beta 1 (t); for series point A ({ t) max -cubic spline interpolation) and the curve obtained is marked as beta 2 (t)；
3) Calculating a according to the following 1 (t) and a 2 (t)：
a 1 (t)＝[β 1 (t)+β 2 (t)]/2
a 2 (t)＝[β 2 (t)-β 1 (t)]/2
Wherein a is 1 (t)、a 2 (t) obtaining predicted curves of instantaneous envelopes of the two signals after decomposition;
4) For series of points
Figure GDA0004199693700000077
Performing cubic spline interpolation to obtain curve eta 1 (t) for series points
Figure GDA0004199693700000078
Performing cubic spline interpolation to obtain curve eta 2 (t) wherein, the%>
Figure GDA0004199693700000079
Is the instantaneous bandwidth
Figure GDA00041996937000000710
Is the reciprocal of (2);
5) According to the following calculation
Figure GDA00041996937000000711
And->
Figure GDA00041996937000000712
Figure GDA0004199693700000081
Figure GDA0004199693700000082
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure GDA0004199693700000083
and->
Figure GDA0004199693700000084
Respectively obtaining the predicted curves of the instantaneous frequencies of the two signals after decomposition;
6) Calculating local cut-off frequency
Figure GDA0004199693700000085
Figure GDA0004199693700000086
Further, the modal aliasing suppression module is used for calculating a new local cut-off frequency
Figure GDA0004199693700000087
The method comprises the following steps:
1) The appearance time of the maximum value of the input signal x (t) is calculated and recorded as u i ,i＝1,2,3...；
2) Finding a break point according to the following formula, denoted as e j : satisfy the following requirements
Figure GDA0004199693700000088
Wherein ρ is a preset constant;
Figure GDA0004199693700000089
equivalent to->
Figure GDA00041996937000000810
u i Time instant of break point, i.e. e j ＝u i 。
3) For each break point e j Judging the category if there is
Figure GDA00041996937000000811
e j At the position of
Figure GDA00041996937000000812
Rising edge of (2); if there is->
Figure GDA00041996937000000813
e j At->
Figure GDA00041996937000000814
Is arranged on the falling edge of the first part;
4) For each break point e j If in a position of
Figure GDA00041996937000000815
Rising edge of>
Figure GDA00041996937000000816
Marked as non-interpolation points; if at->
Figure GDA00041996937000000817
Falling edge of>
Figure GDA00041996937000000818
Quilt labelMarking as non-interpolation points;
5) For a pair of
Figure GDA00041996937000000819
Interpolation is performed on all interpolation points (points not obtained in step 4) to obtain a new +.>
Figure GDA00041996937000000820
Further, according to the mode aliasing suppression module
Figure GDA00041996937000000821
Then, the time-varying filtering module inputs a signal x (t) for fitting, and a fitting result is obtained and used as the output of the time-varying filter, and the method specifically comprises the following steps:
1) Calculate h (t) according to the following
Figure GDA0004199693700000091
h (t) is the filter cut-off frequency reference signal.
2) Calculating all extreme point moments of h (t), and recording as k i ，i＝1,2,3...；
3) At k i B spline fitting is carried out on the input signal x (t) to obtain a fitting result which is marked as an average signal m (t) and is used as the output of the time-varying filter. The least square of B-spline is an important tool for fitting linear and nonlinear curves, and a series of B-spline basis functions are used for least square fitting of input signals, and the basis functions are spliced at nodes to obtain smooth output functions.
Further, m (t), a are calculated according to the above modules 1 (t) and a 2 (t)、
Figure GDA0004199693700000092
And->
Figure GDA0004199693700000093
The local bandwidth judging module comprises the following steps:
1) Calculating instantaneous average frequency of input signal
Figure GDA0004199693700000094
Figure GDA0004199693700000095
2) Calculating the instantaneous bandwidth of Loughlin of an input signal:
Figure GDA0004199693700000096
wherein a is 1 ′(t)、a 2 ' (t) is a respectively 1 (t)、a 2 Inverse of (t);
3) Calculating an instantaneous bandwidth shift factor θ (t):
Figure GDA0004199693700000097
the non-stationary signal is tested and validated by the signal time-frequency decomposition method of the invention.
Let the input signal x (t) be a combined signal of three FM signals
x(t)＝cos(40πt+10πt 2 )+cos(20πt+5πt 2 )+cos(10πt+5πt 2 )
X (t) is decomposed by the method of the invention and the traditional EMD method to obtain the spectrograms shown in fig. 3 and 4. As can be seen from fig. 3: the invention can completely obtain the three component signals by using the time-varying filter. As can be seen from fig. 4: the signal component obtained by the EMD method is split, and the signal component is expressed as a complete signal decomposed into a plurality of spurious signals. This is because the conventional EMD method (including the current modification of EMD) is based on a fixed-cut-frequency filter, and thus frequency-modulated signal components having frequencies higher (lower) than the cut-off frequency of the filter are split when frequency-modulated signals having significant time-dependent changes are decomposed.
Referring to fig. 5, fig. 5 (a) is a time-frequency spectrum obtained after decomposition by the method of the present invention, and fig. 5 (b) is a time-frequency spectrum obtained after decomposition by the conventional EMD method. As can be seen from the figure: the method obtains complete and correct time-frequency distribution of the three frequency modulation signals, and the traditional EMD method has obvious distortion, which is shown as false and oscillating frequency components.
In summary, the method of the present invention has a stronger decomposition capability for non-stationary signals than conventional EMD and improved methods (e.g., fixed-mask signal based on cut-off frequency).
The invention provides a signal time-frequency decomposition method based on instantaneous bandwidth, which adopts local cut-off frequency estimation and filtering to separate signal components which are relatively close to each other in a frequency domain, and simultaneously adopts a mode aliasing suppression module in a combined mode, so that a time-frequency domain break point generated by noise interference can be suppressed, and the problems of frequency resolution and mode aliasing are solved. According to the invention, a time-varying filter is further constructed through instantaneous bandwidth analysis, and IMF is obtained through iterative filtering, the amplitude and the frequency of the time-varying filter can be changed along with time, and the amplitude and the frequency of the obtained signal can be changed along with time. Therefore, the invention has good decomposition effect on stationary signals (such as sine wave signals) and non-stationary signals (such as frequency modulation signals).
Other embodiments of the invention will be apparent to and understood by those skilled in the art from consideration of the specification and practice of the invention disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.

Claims (6)

1. A method of time-frequency decomposition of a signal based on instantaneous bandwidth, comprising the steps of:
step one: adopting a signal decomposition method to perform empirical mode decomposition on the signal, and decomposing the signal into a series of combinations of eigenmode functions;
step two: extracting time-frequency characteristics of the eigenmode function by using Hilbert transformation, and solving in a Hilbert transformation domain to obtain local cut-off frequency;
step three: constructing a time-varying filter by using the local cut-off frequency, and filtering by using the time-varying filter;
step four: repeating the second step and the third step until the local bandwidth of the signal meeting the termination condition is obtained through filtering, and obtaining an eigenmode function of the local bandwidth;
the local cut-off frequency estimation module is used for estimating the local cut-off frequency
Figure FDA0004199693690000011
The method comprises the following steps:
1) The time of occurrence of all maximum value points and minimum value points of the instantaneous bandwidth A (t) is calculated as { t }, respectively max Sum { t } min }；
2) For series point A ({ t) min -cubic spline interpolation) and the curve obtained is marked as beta 1 (t); for series point A ({ t) max -cubic spline interpolation) and the curve obtained is marked as beta 2 (t)；
3) Calculating a according to the following 1 (t) and a 2 (t)：
a 1 (t)＝[β 1 (t)+β 2 (t)]/2
a 2 (t)＝[β 2 (t)-β 1 (t)]/2
Wherein a is 1 (t)、a 2 (t) obtaining predicted curves of instantaneous envelopes of the two signals after decomposition;
4) For series of points
Figure FDA0004199693690000012
Performing cubic spline interpolation to obtain curve eta 1 (t) for series points
Figure FDA0004199693690000013
Performing cubic spline interpolation to obtain curve eta 2 (t) wherein, the%>
Figure FDA0004199693690000014
Is the instantaneous bandwidth
Figure FDA0004199693690000015
Is the reciprocal of (2);
5) According to the following calculation
Figure FDA0004199693690000016
And->
Figure FDA0004199693690000017
Figure FDA0004199693690000021
Figure FDA0004199693690000022
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA0004199693690000023
and->
Figure FDA0004199693690000024
Respectively obtaining the predicted curves of the instantaneous frequencies of the two signals after decomposition;
6) Calculating local cut-off frequency
Figure FDA0004199693690000025
Figure FDA0004199693690000026
The modal aliasing suppression module is used for calculating to obtain a new local cut-off frequency
Figure FDA0004199693690000027
The method comprises the following steps:
1) Finding the occurrence of the maximum value of the input signal x (t)The interval is denoted as u i ,i＝1,2,3...；
2) Finding a break point according to the following formula, denoted as e j : satisfy the following requirements
Figure FDA0004199693690000028
Wherein ρ is a preset constant;
Figure FDA0004199693690000029
equivalent to->
Figure FDA00041996936900000210
u i Time instant of break point, i.e. e j ＝u i ；
3) For each break point e j Judging the category if there is
Figure FDA00041996936900000211
e j At->
Figure FDA00041996936900000212
Rising edge of (2); if there is->
Figure FDA00041996936900000213
e j At->
Figure FDA00041996936900000214
Is arranged on the falling edge of the first part;
4) For each break point e j If in a position of
Figure FDA00041996936900000215
Rising edge of>
Figure FDA00041996936900000216
Marked as non-interpolation points; if at->
Figure FDA00041996936900000217
Falling edge of>
Figure FDA00041996936900000218
Marked as non-interpolation points;
5) For a pair of
Figure FDA00041996936900000219
Interpolation is carried out on all interpolation points in the formula (I) to obtain new +.>
Figure FDA00041996936900000220
2. The method of time-frequency signal decomposition according to claim 1, wherein in step one, the specific process of the method of time-frequency signal decomposition is: extracting an intrinsic mode function imf (t) of an input signal x (t) through a screening method, calculating a residual signal r (t), stopping decomposing when the number of extreme points of r (t) is less than 3, otherwise, taking r (t) as a new x (t) and performing a new round of decomposition process; after the algorithm is finished, the output result is a set of a series of imfs (t).
3. The signal time-frequency decomposition method according to claim 2, wherein said screening method comprises: the device comprises an instantaneous amplitude and instantaneous bandwidth module, a local cut-off frequency estimation module, a modal aliasing suppression module, a time-varying filtering module and a local bandwidth judgment module; the local cut-off frequency estimation module and the time-varying filtering module are used for separating signal components which are relatively close to each other in a frequency domain; the modal aliasing suppression module is used for suppressing a time-frequency domain break point generated by noise interference.
4. A signal time-frequency decomposition method according to claim 3, wherein said instantaneous amplitude and instantaneous bandwidth module is adapted to calculate instantaneous amplitude a (t) and instantaneous bandwidth
Figure FDA0004199693690000031
The method comprises the following steps:
1) Hilbert transform for determining an input signal x (t)
Figure FDA0004199693690000032
2) Obtaining an analysis signal z (t) of the input signal x (t) to obtain A (t) and A (t)
Figure FDA0004199693690000033
Figure FDA0004199693690000034
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA0004199693690000035
5. the method of time-frequency decomposition of signals according to claim 4, wherein said mode aliasing suppression module is configured to obtain
Figure FDA0004199693690000036
Then, the time-varying filtering module inputs a signal x (t) for fitting, and a fitting result is obtained and used as the output of the time-varying filter, and the method specifically comprises the following steps:
1) H (t) is calculated according to the following formula:
Figure FDA0004199693690000037
h (t) is a filter cut-off frequency reference signal;
2) Calculating all extreme point moments of h (t), and recording as k i ，i＝1,2,3...；
3) At k i B spline fitting is carried out on the input signal x (t) to obtain a fitting result which is marked as an average signal m (t) and is used as the output of the time-varying filter.
6. The method of time-frequency decomposition of signals according to claim 5, wherein m (t), a are calculated from said modules 1 (t) and a 2 (t)、
Figure FDA0004199693690000038
And->
Figure FDA0004199693690000039
The local bandwidth judging module comprises the following steps:
1) Calculating instantaneous average frequency of input signal
Figure FDA00041996936900000310
Figure FDA0004199693690000041
2) Calculating the instantaneous bandwidth of Loughlin of an input signal:
Figure FDA0004199693690000042
wherein a' 1 (t)、a′ 2 (t) is a respectively 1 (t)、a 2 Inverse of (t);
3) Calculating an instantaneous bandwidth shift factor θ (t):
Figure FDA0004199693690000043
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