CN109460614A - Signal time based on instant bandwidth-frequency decomposition method - Google Patents
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Abstract
The signal time based on instant bandwidth-frequency decomposition method that the present invention provides a kind of, pass through the extraction algorithm of intrinsic mode function (IMF) in Optimization Experience mode decomposition (EMD), it solves to obtain local cutoff frequency in Hilbert transform domain, time varing filter is constructed using the local cutoff frequency, it is filtered using the time varing filter, repeat solution and the filtering of the local cutoff frequency, it obtains meeting the signal part bandwidth of termination condition until filtering, and then obtains the intrinsic mode function of local bandwidth.In the present invention, it is estimated and is filtered using local cutoff frequency, the signal component being closer on separation frequency domain, in combination with using modal overlap suppression module, it is able to suppress the time-frequency domain discontinuous point of noise jamming generation, and then solves the problems, such as frequency resolution and modal overlap simultaneously.
Description
Technical field
The present invention relates to field of signal processing, and in particular to a kind of signal time-frequency decomposition side based on instant bandwidth
Method.
Background technique
Time-frequency domain (time-frequency) analysis describes signal frequency and changes with time relationship, is non-linear, non-stationary letter
Number processing important method.Typical Time-Frequency Analysis Method is linear method, have Short Time Fourier Transform, wavelet analysis,
Wigner-Ville distribution etc..The time frequency resolution of these methods is largely limited to the type and width of basic function,
And the parameters such as the type of basic function and width are often not easy to select, and cause these adaptations of methods poor.In addition, these sides
The time frequency resolution of method is limited to Heisenberg uncertainty principle, in the measurement of the two physical quantitys of time and frequency by
To constraint, it is impossible to while obtaining high-resolution.
Hilbert-Huang transform (Hilbert-Huang transform, abbreviation HHT) is a kind of nonlinear with certainly
The Time-Frequency Analysis Method of adaptability, Hilbert-Huang transform (HHT) include two steps: firstly, utilizing empirical mode decomposition
(empirical mode decomposition, abbreviation EMD) is by signal decomposition at a series of intrinsic mode functions
The combination of (intrinsic mode function, abbreviation IMF), these intrinsic mode functions meet Hilbert transform
The requirement of (Hilbert transform) to signal simple component characteristic.Then, time-frequency is carried out using Hilbert transform pairs IMF
Feature extraction；It finally obtains about T/F-amplitude distributed in three dimensions, referred to as HHT spectrum.The no longer limited basic function of HHT,
The limitation of Heisenberg uncertainty principle is a kind of adaptive Time-Frequency Analysis Method, biomedicine, fault diagnosis,
The fields such as finance are widely applied, but itself have some limitations (EMD limitation): first is that frequency resolution problem, EMD
Frequency can not be decomposed than the signal less than 0.65；Second is that modal overlap problem, EMD, which decompose to noisy acoustical signal, will appear
The phenomenon that IMF is divided.
Currently, limit to for above-mentioned EMD, some researchs both at home and abroad by changing signal interpolation point, using covering signal, noise
The methods of auxiliary improves, but can only improve decomposability, i.e. frequency resolution problem or modal overlap for a problem
Problem.It solves the problems, such as on frequency resolution problem and modal overlap at the same time, there is no effective solution scheme.
The frequency resolution decomposed of promotion signal and the bases of signal time and frequency domain characteristics can be extracted therefore, it is necessary to a kind of
In the signal time-frequency Decomposition of instant bandwidth.
Summary of the invention
The purpose of the present invention is to provide a kind of technical solutions, are capable of the frequency resolution of promotion signal decomposition simultaneously and mention
The robustness to Noise signal decomposition is risen, to be conducive to preferably extract signal time-frequency characteristics.
The Integral Thought of this method is: passing through the extraction of intrinsic mode function (IMF) in Optimization Experience mode decomposition (EMD)
Algorithm, it solves to obtain local cutoff frequency in Hilbert transform domain, constructs time-variable filtering using the local cutoff frequency
Device is filtered using the time varing filter, solution and the filtering of the local cutoff frequency is repeated, until filtering
To meeting the signal part bandwidth of termination condition, and then obtain the intrinsic mode function of local bandwidth.
The present invention provides a kind of signal time based on instant bandwidth-frequency decomposition method, comprising the following steps:
Step 1: carrying out empirical mode decomposition (EMD) to signal using signal decomposition method, is a series of by signal decomposition
The combination of intrinsic mode function (IMF)；
Step 2: time-frequency characteristics extraction is carried out using Hilbert transform pairs intrinsic mode function (IMF), in Hilbert
Transform domain solves to obtain local cutoff frequency；
Step 3: time varing filter is constructed using the local cutoff frequency, is filtered using the time varing filter；
Step 4: repeating step 2 and step 3, obtains meeting the signal part bandwidth of termination condition until filtering, thus
Obtain the intrinsic mode function of local bandwidth.
Preferably, in step 1, the detailed process of signal decomposition method are as follows: input signal x (t) is extracted by method for sieving
One intrinsic mode function imf (t), and residual signal r (t) is calculated, stop decomposing if the extreme point number of r (t) is less than 3,
Otherwise r (t) is subjected to a new wheel decomposable process as new x (t).After algorithm, the result of output is a series of imf
(t) set.
Preferably, method for sieving described in step 2 includes: that instantaneous amplitude is estimated with instant bandwidth module, local cutoff frequency
It calculates module, modal overlap suppression module, time-variable filtering module and local bandwidth and judges module；The part cutoff frequency estimation
Module and the time-variable filtering module, the signal component being closer on separation frequency domain；The modal overlap suppression module,
Time-frequency domain discontinuous point for inhibiting noise jamming to generate, to improve the robustness of the signal decomposition under noise.
It is highly preferred that the instantaneous amplitude and instant bandwidth module are for calculating instantaneous amplitude A (t) and instant bandwidthThe following steps are included:
1) Hilbert transform of input signal x (t) is asked
2) the analytic signal z (t) for seeking input signal x (t), obtain A (t) and
Wherein,
It is highly preferred that the part cutoff frequency estimation block is for estimating local cutoff frequencyIncluding following
Step:
1) all maximum points of instant bandwidth A (t) and the time of minimum point appearance are asked, are denoted as { t respectivelymaxAnd
{tmin}；
2) to point A ({ tmin) cubic spline interpolation is done, obtained curve is denoted as β1(t)；To point A ({ tmax})
Cubic spline interpolation is done, obtained curve is denoted as β2(t)；
3) a is calculated according to the following formula1(t) and a2(t):
a1(t)=[β1(t)+β2(t)]/2
a2(t)=[β2(t)-β1(t)]/2
Wherein, a1(t)、a2(t) it is respectively the pre- index contour that the instantaneous envelope of two signals is obtained after decomposing:
4) to pointCubic spline interpolation is done, curve η is obtained1(t), to pointCubic spline interpolation is done, curve η is obtained2(t)；
5) it calculates according to the following formulaWith
Wherein,WithThe pre- index contour of the instantaneous frequency of two signals is obtained after respectively decomposing；
6) local cutoff frequency is calculated
It is highly preferred that the modal overlap suppression module is for being calculated new local cutoff frequencyIncluding
Following steps:
1) time of occurrence for seeking input signal x (t) maximum, is denoted as ui, i=1,2,3...；
2) discontinuous point is found according to the following formula, is denoted as ej: meet
Wherein, ρ is preset constant, such as sets ρ=0.25；It is equal to
uiAt the time of, that is, discontinuous point, i.e. ej=ui。
3) to each discontinuous point ej, judge its classification, if there isejIt is inRising edge；If there isejIt is inFailing edge；
4) to each discontinuous point ejIf be inRising edge, thenIt is marked as non-interpolative
Point；If be inFailing edge, thenIt is marked as non-interpolative point；
5) rightIn all interpolation points (point obtained in non-step 4) carry out interpolation, obtain new
It is highly preferred that being obtained according to modal overlap suppression moduleAfterwards, the time-variable filtering module input signal x
(t) it is fitted, obtains output of the fitting result as time varing filter, specifically includes the following steps:
1) h (t) is calculated according to the following formula
H (t) is filter cutoff frequency reference signal；
2) all extreme value point moments for calculating h (t), are denoted as ki, i=1,2,3...；
3) with kiFor node, B-spline fitting is carried out to input signal x (t), fitting result is obtained and is denoted as mean value signal m
(t), as the output of time varing filter.
It is highly preferred that m (t), a is calculated according to above-mentioned module1(t) and a2(t)、WithThe part
Bandwidth judges module, comprises the following steps that
1) Instantaneous mean frequency of input signal is calculated
2) the Loughlin instant bandwidth of input signal is calculated:
3) instant bandwidth displacement factor θ (t) is calculated:
In the present invention, is estimated and filtered using local cutoff frequency, the signal component being closer on separation frequency domain, simultaneously
In conjunction with modal overlap suppression module is used, it is able to suppress the time-frequency domain discontinuous point of noise jamming generation, and then solves frequency simultaneously
Rate resolution ratio be and modal overlap problem.Amplitude, the frequency of signal time of the invention-frequency decomposition method time varing filter
It can change over time and change, obtain the amplitude of signal, frequency can also change over time and change.Therefore the present invention is for flat
Steady signal (such as sine wave signal) and non-stationary signal (such as FM signal) have good discomposing effect.
It should be appreciated that aforementioned description substantially and subsequent detailed description are exemplary illustration and explanation, it should not
As the limitation to the claimed content of the present invention.
Detailed description of the invention
With reference to the attached drawing of accompanying, the more purposes of the present invention, function and advantage are by the as follows of embodiment through the invention
Description is illustrated, in which:
Fig. 1 shows signal decomposition method flow chart of the invention.
Fig. 2 shows method for sieving flow charts of the invention.
Fig. 3, which is shown, carries out the spectrogram that method of the invention is decomposed to x (t).
Fig. 4, which is shown, carries out the spectrogram that tradition EMD method is decomposed to x (t).
Fig. 5 (a) shows the T/F spectrogram that the method for the present invention obtains.
Fig. 5 (b) shows the T/F spectrogram that traditional EMD method obtains.
Specific embodiment
By reference to exemplary embodiment, the purpose of the present invention and function and the side for realizing these purposes and function
Method will be illustrated.However, the present invention is not limited to exemplary embodiment as disclosed below；Can by different form come
It is realized.The essence of specification is only to aid in those skilled in the relevant arts' Integrated Understanding detail of the invention.
Hereinafter, the embodiment of the present invention will be described with reference to the drawings.In the accompanying drawings, identical appended drawing reference represents identical
Or similar component or same or like step.
The present invention provides a kind of signal time based on instant bandwidth-frequency decomposition method, comprising the following steps: using letter
Number decomposition method carries out empirical mode decomposition (EMD) to signal, is a series of group of intrinsic mode functions (IMF) by signal decomposition
It closes；Time-frequency characteristics extraction is carried out using Hilbert transform pairs intrinsic mode function (IMF), is solved in Hilbert transform domain
To local cutoff frequency；Time varing filter is constructed using the local cutoff frequency, is filtered using the time varing filter；
It repeats Hilbert transform domain to solve and filter, until filtering obtains the signal part bandwidth for meeting termination condition, to obtain
The intrinsic mode function of local bandwidth.
Referring to Fig. 1, Fig. 2, the detailed process of signal decomposition method are as follows: input signal x (t) extracts one by method for sieving
Intrinsic mode function imf (t), and calculate residual signal r (t), when the extreme point number of r (t) stops decomposing less than 3, otherwise
R (t) is subjected to a new wheel decomposable process as new x (t).After algorithm, the result of output is a series of imf (t)
Set, as shown in Figure 1.
Specifically, method for sieving described in step 2 includes: that instantaneous amplitude is estimated with instant bandwidth module, local cutoff frequency
It calculates module, modal overlap suppression module, time-variable filtering module and local bandwidth and judges module；The part cutoff frequency estimation
Module and the time-variable filtering module, the signal component being closer on separation frequency domain；The modal overlap suppression module,
Time-frequency domain discontinuous point for inhibiting noise jamming to generate, so that the robustness of the signal decomposition under noise is improved, such as Fig. 2 institute
Show.
Further, the instantaneous amplitude and instant bandwidth module are for calculating instantaneous amplitude A (t) and instant bandwidthThe following steps are included:
1) Hilbert transform of input signal x (t) is asked
2) the analytic signal z (t) for seeking input signal x (t), obtain A (t) and
Wherein,
Further, the local cutoff frequency estimation block is for estimating local cutoff frequencyIncluding following
Step:
1) all maximum points of instant bandwidth A (t) and the time of minimum point appearance are asked, are denoted as { t respectivelymaxAnd
{tmin}；
2) to point A ({ tmin) cubic spline interpolation is done, obtained curve is denoted as β1(t)；To point A ({ tmax})
Cubic spline interpolation is done, obtained curve is denoted as β2(t)；
3) a is calculated according to the following formula1(t) and a2(t):
a1(t)=[β1(t)+β2(t)]/2
a2(t)=[β2(t)-β1(t)]/2
Wherein, a1(t)、a2(t) it is respectively the pre- index contour that the instantaneous envelope of two signals is obtained after decomposing:
4) to pointCubic spline interpolation is done, curve η is obtained1(t), to pointCubic spline interpolation is done, curve η is obtained2(t)；
5) it calculates according to the following formulaWith
Wherein,WithThe pre- index contour of the instantaneous frequency of two signals is obtained after respectively decomposing；
6) local cutoff frequency is calculated
Further, the modal overlap suppression module is for being calculated new local cutoff frequencyIncluding
Following steps:
1) time of occurrence for seeking input signal x (t) maximum, is denoted as ui, i=1,2,3...；
2) discontinuous point is found according to the following formula, is denoted as ej: meet
Wherein, ρ is preset constant, such as sets ρ=0.25；It is equal to
uiAt the time of, that is, discontinuous point, i.e. ej=ui。
3) to each discontinuous point ej, judge its classification, if there isejIt is inRising edge；If there isejIt is inFailing edge；
4) to each discontinuous point ejIf be inRising edge, thenIt is marked as non-interpolative
Point；If be inFailing edge, thenIt is marked as non-interpolative point；
5) rightIn all interpolation points (point obtained in non-step 4) carry out interpolation, obtain new
Further, it is obtained according to modal overlap suppression moduleAfterwards, the time-variable filtering module input signal x
(t) it is fitted, obtains output of the fitting result as time varing filter, specifically includes the following steps:
1) h (t) is calculated according to the following formula
H (t) is filter cutoff frequency reference signal.
2) all extreme value point moments for calculating h (t), are denoted as ki, i=1,2,3...；
3) with kiFor node, B-spline fitting is carried out to input signal x (t), fitting result is obtained and is denoted as mean value signal m
(t), as the output of time varing filter.Wherein, B-spline least square is the important tool of linear and nonlinear curve,
It carries out least square fitting to input signal using a series of B-spline basic functions, these basic functions are spliced at node,
Obtain smooth output function.
Further, m (t), a are calculated according to above-mentioned module1(t) and a2(t)、WithThe part
Bandwidth judges module, comprises the following steps that
1) Instantaneous mean frequency of input signal is calculated
2) the Loughlin instant bandwidth of input signal is calculated:
3) instant bandwidth displacement factor θ (t) is calculated:
Verification experimental verification discomposing effect is carried out to non-stationary signal in signal time of the invention-frequency decomposition method below.
If input signal x (t) is the combination signal of three FM signals
X (t)=coS (40 π t+10 π t2)+coS(20πt+5πt2)+cos(10πt+5πt2)
The present invention is carried out to x (t) and tradition EMD method is decomposed, obtains spectrogram shown in Fig. 3, Fig. 4.As can be seen from Figure 3: this hair
It is bright to use the time varing filter, it can completely obtain these three component signals.As can be seen from Figure 4: the signal that EMD method obtains
Component occurs isolating phenomenon, shows as the combination that a complete signal decomposition is multiple spurious signals.This is because traditional
EMD method (improved method including current EMD) be based on cutoff frequency fixed filters, therefore decompose frequency at any time
When changing apparent FM signal, frequency is higher than (being lower than) filter and is isolated by the FM signal component of frequency.
Referring to Fig. 5, Fig. 5 (a) is the T/F spectrogram obtained after the method for the present invention is decomposed, and Fig. 5 (b) is traditional side EMD
The T/F spectrogram that method obtains after decomposing.As seen from the figure: it is complete, correct that the method for the present invention has obtained these three FM signals
T/F distribution, and there is apparent distortion in tradition EMD method, shows as false, concussion frequency occur dividing
Amount.
To sum up, the more traditional EMD of the method for the present invention and improved method (as based on the fixed masking signal method of cutoff frequency) are right
The capacity of decomposition of non-stationary signal is stronger.
The present invention provides a kind of signal time based on instant bandwidth-frequency decomposition method, is estimated using local cutoff frequency
It calculates and filters, the signal component being closer on separation frequency domain is able to suppress and makes an uproar in combination with modal overlap suppression module is used
Acoustic jamming generate time-frequency domain discontinuous point, and then solve the problems, such as simultaneously frequency resolution be and modal overlap.The present invention passes through
Instant bandwidth analysis, and then time varing filter is constructed, IMF is obtained by iterative filtering, the amplitude of time varing filter of the invention,
Frequency can change over time and change, and obtain the amplitude of signal, frequency can also change over time and change.Therefore the present invention is right
There is good discomposing effect in stationary signal (such as sine wave signal) and non-stationary signal (such as FM signal).
In conjunction with the explanation and practice of the invention disclosed here, the other embodiment of the present invention is for those skilled in the art
It all will be readily apparent and understand.Illustrate and embodiment is regarded only as being exemplary, true scope of the invention and purport are equal
It is defined in the claims.
Claims (8)
1. a kind of signal time based on instant bandwidth-frequency decomposition method, comprising the following steps:
Step 1: empirical mode decomposition is carried out to signal using signal decomposition method, is a series of intrinsic mode by signal decomposition
The combination of function；
Step 2: time-frequency characteristics extraction is carried out using Hilbert transform pairs intrinsic mode function, is asked in Hilbert transform domain
Solution obtains local cutoff frequency；
Step 3: time varing filter is constructed using the local cutoff frequency, is filtered using the time varing filter；
Step 4: repeating step 2 and step 3, obtains meeting the signal part bandwidth of termination condition until filtering, obtains part
The intrinsic mode function of bandwidth.
2. signal time according to claim 1-frequency decomposition method, which is characterized in that in step 1, signal decomposition
The detailed process of method are as follows: input signal x (t) extracts an intrinsic mode function imf (t) by method for sieving, and calculates surplus
R (t) is otherwise carried out new one as new x (t) when the extreme point number of r (t) stops decomposing less than 3 by remaining signal r (t)
Take turns decomposable process；After algorithm, the result of output is a series of set of imf (t).
3. signal time according to claim 2-frequency decomposition method, which is characterized in that the method for sieving includes: wink
When amplitude and instant bandwidth module, local cutoff frequency estimation block, modal overlap suppression module, time-variable filtering module and office
Portion's bandwidth judges module；The part cutoff frequency estimation block and the time-variable filtering module are used on separation frequency domain more
Close signal component；The modal overlap suppression module, the time-frequency domain discontinuous point for inhibiting noise jamming to generate.
4. signal time according to claim 3-frequency decomposition method, which is characterized in that the instantaneous amplitude and instantaneous
Bandwidth module is for calculating instantaneous amplitude A (t) and instant bandwidthThe following steps are included:
1) Hilbert transform of input signal x (t) is asked
2) the analytic signal z (t) for seeking input signal x (t), obtain A (t) and
Wherein,
5. signal time according to claim 4-frequency decomposition method, which is characterized in that the part cutoff frequency is estimated
Module is calculated for estimating local cutoff frequencyThe following steps are included:
1) all maximum points of instant bandwidth A (t) and the time of minimum point appearance are asked, are denoted as { t respectivelymaxAnd { tmin}；
2) to point A ({ tmin) cubic spline interpolation is done, obtained curve is denoted as β1(t)；To point A ({ tmax) do three
Secondary spline interpolation, obtained curve are denoted as β2(t)；
3) a is calculated according to the following formula1(t) and a2(t):
a1(t)=[β1(t)+β2(t)]/2
a2(t)=[β2(t)-β1(t)]/2
Wherein, a1(t)、a2(t) it is respectively the pre- index contour that the instantaneous envelope of two signals is obtained after decomposing:
4) to pointCubic spline interpolation is done, curve η is obtained1(t), to pointCubic spline interpolation is done, curve η is obtained2(t)；
5) it calculates according to the following formulaWith
Wherein,WithThe pre- index contour of the instantaneous frequency of two signals is obtained after respectively decomposing；
6) local cutoff frequency is calculated
6. signal time according to claim 5-frequency decomposition method, which is characterized in that the modal overlap inhibits mould
Block is for being calculated new local cutoff frequencyThe following steps are included:
1) time of occurrence for seeking input signal x (t) maximum, is denoted as ui, i=1,2,3...；
2) discontinuous point is found according to the following formula, is denoted as ej: meet
Wherein, ρ is preset constant, such as sets ρ=0.25；It is equal to
uiAt the time of, that is, discontinuous point, i.e. ej=ui；
3) to each discontinuous point ej, judge its classification, if there isejIt is in
Rising edge；If there isejIt is inFailing edge；
4) to each discontinuous point ejIf be inRising edge, thenIt is marked as non-interpolative point；Such as
Fruit is inFailing edge, thenIt is marked as non-interpolative point；
5) rightIn all interpolation points carry out interpolation, obtain new
7. signal time according to claim 6-frequency decomposition method, which is characterized in that inhibit mould according to modal overlap
Block obtainsAfterwards, the time-variable filtering module input signal x (t) is fitted, and obtains fitting result as time-variable filtering
The output of device, specifically includes the following steps:
1) h (t) is calculated according to the following formula:
H (t) is filter cutoff frequency reference signal；
2) all extreme value point moments for calculating h (t), are denoted as ki, i=1,2,3...；
3) with kiFor node, B-spline fitting is carried out to input signal x (t), fitting result is obtained and is denoted as mean value signal m (t), as
The output of time varing filter.
8. signal time according to claim 7-frequency decomposition method, which is characterized in that calculated according to above-mentioned module
To m (t), a1(t) and a2(t)、WithThe part bandwidth judges module, comprises the following steps that
1) Instantaneous mean frequency of input signal is calculated
2) the Loughlin instant bandwidth of input signal is calculated:
3) instant bandwidth displacement factor θ (t) is calculated:
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| CN114714157B (en) * | 2022-03-23 | 2023-05-30 | 大连大学 | Grinding chatter monitoring method based on time-varying filtering empirical mode decomposition and instantaneous energy ratio |
| CN115687862A (en) * | 2022-10-19 | 2023-02-03 | 北京科技大学 | Rotating machinery signal time-frequency analysis method based on time-varying filtering |
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