CN104820786B - A kind of instantaneous weighting is synchronous to squeeze small echo double-spectrum analysis method - Google Patents
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Abstract
A kind of instantaneous weighting is synchronous to squeeze small echo double-spectrum analysis method, including six steps：Step 1 determines the minimum division number of signal, step 2 calculates separately the weight coefficient corresponding to each segmentation, step 3 forms the weight matrix of signal with the corresponding weight coefficient of each signal subsection calculated, calculate the frequency sequence corresponding to each row weight coefficient, step 4 calculates the synchronous of signal and squeezes wavelet coefficient, it obtains and is distributed more compact time-frequency domain representation, step 5 is weighted synchronous extruding wavelet conversion coefficient by frequency separation to obtain modified wavelet coefficient, and step 6, which calculates to weight to synchronize, squeezes small echo bispectrum extruding small echo bispectrum synchronous with instantaneously weighting；The present invention is using the higher synchronous extruding wavelet transformation of frequency resolution, the frequency content of signal can be accurately distinguished, according to the information that signal overall frequency is distributed, temporally it is segmented plus weights to the synchronous wavelet coefficient that squeezes calculated, avoids the low disadvantage of conventional method accuracy.
Description
Technical field
The invention belongs to processing of biomedical signals technical fields, more particularly to detect the instantaneous phase between non-stationary signal
The instantaneous weighting of one kind of coupled relation is synchronous to squeeze small echo double-spectrum analysis method.
Background technology
Double-spectrum analysis is a kind of effective technology of abnormal characteristic that capableing of quantitative study response of nonlinear system, extensive
Applied to econometrics, Underwater acoustic signal processing, the fields such as mechanical fault diagnosis and biomedicine signals feature extraction.In biology
In medical signals process field, since significantly non-linear behavior is all presented in almost all of physiology system, the life generated
Signal of science has significant non-stationary, abnormal characteristic.This kind of signal is mostly generated by the phase harmonic processes of a phase coupling estimation, institute
The analysis and processing of this kind of signal are often used with double-spectrum analysis.Traditional double-spectrum analysis method is based on time averaging fast
Fast Fourier transformation, to the temporal properties recognition capability existing defects of signal.In order to solve this problem, Janez et al. is proposed
Small echo bispectrum this analytical technology with instantaneous phase coupled relation recognition capability, this signal processing technology will have two
The bispectrum of secondary phase coupling estimation and Non-Gaussian Distribution recognition capability and the wavelet transformation with time frequency analysis ability combine, from
And the concept of instantaneous small echo bispectrum is proposed, this makes the instantaneous nonlinearity phase coupling estimation between in situ study non-stationary signal close
System is possibly realized, thus can obtain more accurate testing result in practical applications.
Due to the band-pass filtering property of wavelet transformation, spectral leakage on different frequency bands can be caused, in adjacent scale
It is interior may band overlapping so that the wavelet coefficient distortion of signal, and then can introduce when carrying out bispectrum calculating dry
It disturbs, therefore there is also defects for the accuracy of the algorithm.In the phase coupling estimation detection applied to frequency time varying signal, the defect is straight
Connect the coupled relation for causing small echo bispectrum mistakenly to reflect between current demand signal.In actual non-stationary system, phase coupling estimation closes
It is increasingly complex.Intermodulation product inside not only being generated during Nonlinear phase coupling, also will produce oneself of non-phase coupling
Body harmonic wave, though these harmonic waves do not have with other compositions Nonlinear phase coupling, as long as but meeting between its frequency double
Spectral condition, and not stringent phase condition, then still will appear peak at the bispectrum respective frequencies coordinate calculated
Value, and then provides error result in Non-linear coupling between studying signal, thus there is an urgent need to a kind of significantly more efficient technology with
Improve the accuracy of detection.
Invention content
In order to overcome the defect of the above-mentioned prior art, it is an object of the invention to propose that it is small that a kind of instantaneous weighting synchronizes extruding
Wave double-spectrum analysis method introduces the higher synchronous extruding wavelet transformation of frequency resolution, Yi Jixin when calculating small echo bispectrum
The information of number overall frequency distribution, avoids the low disadvantage of conventional method accuracy.
In order to achieve the above object, the technical solution adopted by the present invention is：
A kind of instantaneous weighting is synchronous to squeeze small echo double-spectrum analysis method, includes the following steps：
Step 1：Given length is the discrete signal sequence g (n) of N, and the minimum of signal needs is calculated using formula (1)
Segments nseg：
Wherein：fs--- signal sampling rate,
f0--- the minimum frequency resolution ratio of needs；
Step 2：After determining signal subsection number, the corresponding weight coefficient of each signal subsection is calculated using formula (2)：
Wherein：M --- weight coefficient serial number,
The serial number of x --- signal subsection,
Gx(m) --- the amplitude absolute value of the Fourier transformation of the xth segmentation of signal g (n) is calculated by formula (3)：
Gmax——Gx(m) maximum value；
Step 3：Using the corresponding weight coefficient of each signal subsection of calculating as column vector, it is ranked sequentially according to the time period
The weight matrix of signal g (n), w=[w can be formed1(m) ... ..., wnseg(m)], each row and frequency in weight matrix
Element in sequence is one-to-one, and corresponding frequency sequence is found out by formula (4)：
Step 4：The wavelet transformation that discrete series g (n) is calculated using formula (5), obtains the time-frequency domain of discrete signal sequence
Expression-form：
Wherein：ψ --- selected mother wavelet function,
U --- time factor,
aj--- the discretization scale parameter of mother wavelet function ψ,
The discretization translation parameters of n --- mother wavelet function ψ,
G (u) --- signal sequence to be analyzed,
* --- expression takes conjugation；
Then it utilizes formula (6) to calculate the synchronous of signal g (n) and squeezes wavelet conversion coefficient：
Wherein：Gn --- determine discretization scale ajNumber constant,
aj--- discretization scale can be determined by formula (7)：
f(aj, n) --- the frequency surface that derivation is obtained is carried out by the time frequency plane to wavelet transformation,
fi--- scale aiCorresponding frequency meets relationship fi=1/ai,
fi +,fi ---- according to fiThe upper bound of determined frequency separation and lower bound can be determined by formula (8)：
N --- time factor,
Cψ--- constant coefficient can be calculated by formula (9)：
Wherein：* --- expression takes conjugation；
Step 5：Synchronous extruding wavelet conversion coefficient is weighted using formula (10) to obtain modified small echo by frequency separation
Coefficient：
WSWg(fl,n0)=SWg(fl,n0)*wx(k)(10)
Wherein：SWg(fl,n0) --- the synchronous of signal g (n) squeezes wavelet conversion coefficient,
wx(k) --- time factor n0The corresponding weight coefficient of segmentation at place,
fl--- the synchronous frequency factor for squeezing the time-frequency domain expression-form that wavelet transformation obtains,
n0--- the synchronous time factor for squeezing the time-frequency domain expression-form that wavelet transformation obtains,
X --- time factor n0To fragment sequence number, can by formula (11) determine：
K --- frequency factor flThe frequency serial number for the frequency separation being located at can be determined by formula (12)：
f(k-1)<fl≤f(k) (12)
Step 6：The result being calculated by formula (10) is substituted into formula (13), the synchronous extruding small echo of weighting is calculated
Bispectrum：
Wherein：Frequency f1、f2、f3Meet relationship f3=f1+f2,
WSWg(f1, n) --- it is f that synchronizing after weighting, which squeezes wavelet coefficient in frequency,1, the time is the value at n,
WSWg(f2, n) --- it is f that synchronizing after weighting, which squeezes wavelet coefficient in frequency,2, the time is the value at n,
WSWg(f3, n) --- it is f that synchronizing after weighting, which squeezes wavelet coefficient in frequency,3, the time is the value at n；
To formula (14) be substituted by the result that formula (10) are calculated, and obtain signal sequence g (n) in n0Moment it is instantaneous
Weighting is synchronous to squeeze small echo bispectrum：
Since the synchronous small echo bispectrum that squeezes of the instantaneous weighting of calculating is plural number, the shape of formula (15) can be expressed as
Formula：
Wherein：A(f1,f,n0) --- in n0Moment, bifrequency (f1,f2) when instantaneous weighting synchronous squeeze small echo bispectrum width
Value,
φ(f1,f2,n0) --- in n0Moment, bifrequency (f1,f2) when instantaneous weighting synchronous squeeze small echo bispectrum phase.
It is an advantage of the invention that：In order to solve the problems, such as that coefficient of wavelet decomposition existing for small echo bispectrum is overlapped, frequency is introduced
The higher synchronous extruding wavelet transformation of rate resolution ratio, in order to be able to accurately distinguish the frequency content of signal.Secondly, in order to inhibit
Interference caused by a large amount of harmonic components caused by during non-stationary signal phase coupling estimation, it is small to the synchronous extruding calculated
Wave system number, which is temporally segmented, adds weights.So as to avoid conventional method because accuracy is low, and None- identified non-stationary signal
Between phase coupling estimation relationship defect.The present invention cannot be only used for processing of biomedical signals technical field, can be equally used for
Instantaneous phase coupled relation detects in other nonlinear systems.
Description of the drawings
Fig. 1 is the time domain waveform for emulating signal.
Fig. 2 is the weight coefficient of each block signal.
Fig. 3 is the wavelet transformation time-frequency figure for emulating signal.
Fig. 4 is to emulate the synchronous of signal to squeeze wavelet transformation time-frequency figure.
Fig. 5 is the instantaneous bispectrum graphics based on traditional wavelet.
Fig. 6 is based on the synchronous instantaneous bispectrum graphics for squeezing wavelet transformation.
Fig. 7 is that emulation signal transient small echo bispectrum peak phase and amplitude change over time curve.
Fig. 8 is that the synchronous extruding small echo bispectrum peak phase of emulation signal transient weighting and amplitude change over time curve.
Fig. 9 is the flow chart of the present invention.
Specific embodiment
Below in conjunction with the accompanying drawings and example is described in detail the present invention.
For emulating signal, the expression formula such as formula (16) for emulating signal is shown
X (n)=cos (2 π f1n)+η(cos(2πf1n)-cos(2πf2n))2+ξ(n) (16)
Wherein：The white Gaussian noise that ξ (n) --- mean value is zero；
f1--- time-varying coupling frequency, shown in value such as formula (17)：
f2--- time-varying coupling frequency, shown in value such as formula (18)：
η --- coupling strength factor；
It is 300 seconds, sample rate 10Hz to emulate signal X (n) time span, time-varying coupling frequency f1, f2Respectively by different frequencies
The sinusoidal signal modulation of rate, within 300 second time rising to 0.95,0.25 from 0.85 respectively rises to 0.35.Stiffness of coupling system
Number η values are alternately to change, η=0 (no coupling exists), and η=0.6 (weak coupling presence) alternately changes primary for every 20 seconds.It is imitative
The time domain waveform and its frequency spectrum of true signal are as shown in Figure 1.In order to identify be alternately present between simulation frequency time varying signal it is secondary
Phase coupling estimation analyzes data using the present invention.
A kind of instantaneous weighting is synchronous to squeeze small echo double-spectrum analysis method, includes the following steps：
Step 1：Given emulation signal sequence X (n), takes minimum frequency resolution ratio f0=0.1, fs=10, N=3000 are adopted
The minimum segments nseg=30 of signal needs is calculated with formula (1).
Step 2：After determining signal subsection number, the corresponding weights system of each signal subsection is calculated using formula (2)
Number, calculated weight matrix are as shown in Figure 2.
Step 3：Using the corresponding weight coefficient of each signal subsection of calculating as column vector, it is ranked sequentially according to the time period
The weight matrix of signal X (n), w=[w can be formed1(m) ... ..., w30(m)] it, then calculates corresponding to each row weight coefficient
Frequency sequence.
Step 4：Using the wavelet transformation of formula (5) computer sim- ulation discrete series X (n), obtain discrete signal sequence when
Frequency domain presentation form, the time-frequency figure of signal as shown in figure 3, from figure 3, it can be seen that due to wavelet transformation bandpass characteristics, it is small
Wave system number very evacuation point is distributed in side frequency section, this can cause the overlapping of wavelet coefficient between frequency separation, meanwhile, it can be with
See when square phase-couple occurs (η=0.6), due to the frequency time-varying of signal, a large amount of height is produced in coupling process
Subharmonic, it is frequency distribution wavelet coefficient in extensive range to be reflected on time-frequency figure.
Then it utilizes formula (6) to calculate the synchronous of signal X (n) and squeezes wavelet transformation, the time-frequency figure of acquisition is as shown in Figure 4.
Figure 4, it is seen that the synchronous wavelet transformation that squeezes has shown that an extremely compact time frequency plane, the distribution of wavelet coefficient are pressed
Contracting, avoids the wavelet coefficient overlap problem between different frequency section；The time that can occur simultaneously in square phase-couple
In section, the higher hamonic wave being distributed on time frequency plane is observed.These harmonic waves can calculate follow-up bispectrum and mislead, and need to pass through
Weight is added to the wavelet coefficient being distributed in different frequency section, to be inhibited.
Step 5：Synchronous extruding wavelet conversion coefficient is weighted using formula (10) to obtain modified small echo by frequency separation
Coefficient.
Step 6：To formula (13) be substituted by the result that formula (10) are calculated, performance signal entirety coupling is calculated
The weighting for closing characteristic synchronizes extruding small echo bispectrum.To formula (14) be substituted by the result that formula (10) are calculated, be calculated
Signal is emulated in n0The instantaneous weighting at moment is synchronous to squeeze small echo bispectrum.
Fig. 5 is the graphics for emulating signal instantaneous small echo bispectrum of the tradition of (η=0.6) when square phase-couple occurs,
It can be found that since wavelet coefficient overlaps in neighbouring frequency separation, in bispectrum result of calculation, the distribution of peak value is also mutual
It overlaps, making it difficult to which the bifrequency of phase coupling estimation occurs for analysis in real time.Fig. 6 is synchronous crowded with the instantaneous weightings of Fig. 5 in the same time
Small echo bispectrum graphics, peak value is pressed to be independently distributed, graphics is extremely compact, can analyze the double frequency that phase coupling estimation occurs in real time
Rate.
Instantaneous weighting that computation goes out is synchronous squeezes small echo bispectrum, can accurate detection simulation signal change over time
Coupled characteristic.The peak-peak that Fig. 7 gives the instantaneous small echo bispectrum of tradition of emulation signal (generates the main of square phase-couple
Frequency content) amplitude and the curve that changes over time of phase, Fig. 8 give instantaneous weighting the synchronous maximum for squeezing small echo bispectrum
The curve that the amplitude and phase of peak value change over time.Theoretically, when there is square phase-couple generation, the peak value of bispectrum is not
Zero, while phase is a constant.It is synchronized by comparing instantaneous weighting proposed by the present invention and squeezes small echo double-spectrum analysis and traditional
Instantaneous small echo double-spectrum analysis the result shows that, the instantaneous double-spectrum analysis based on traditional wavelet transformation cannot distinguish between emulation signal X (n)
In the phase coupling estimation that occurs of interval between the frequency time varying signal hidden, and instantaneous weighting proposed by the present invention synchronize squeeze it is small
Wave double-spectrum analysis algorithm is in no coupling time section：0-20、40-60、80-100、120-140、160-180、200-220、240-
260,280-300 (unit seconds), phase shows random variation tendency, and amplitude is almost nil.Within the period for having coupling, phase
The trend of linear change is presented in position, is constant, and corresponding amplitude is also greater than zero.It is capable of the emulation of accurately crossover frequency time-varying
The period of square phase-couple occurs in signal X (n).
Traditional small echo bispectrum calculation formula is：
Wherein：Frequency f1, f2, f meets relationship f=f1+f2,
Wg(f, n) --- wavelet transformation.
There are two big defects for it：First, the wavelet transformation used is in processing frequency time varying signal, since small echo becomes
The band-pass filtering property changed can occur wavelet coefficient overlapping in adjacent Scaling interval, therefore multiply calculating tire out three times
When can introduce error, cause study non-stationary signal phase coupling estimation relationship when draw the wrong conclusion, secondly, according to Fu
In leaf bispectrum it is theoretical, if a phase harmonic processes as shown in formula (20)：
Wherein：ω --- angular frequency；
φ --- phase；
Meet condition ω3=ω1+ω2；φ3=φ1+φ2+φ0, wherein φ0For phase delay, then x (n) can be described as one
Square phase-couple phase harmonic processes, bispectrum can be in frequency coordinate (ω1,ω2), (ω2,ω1) at generate impulse value, in reality
Non-stationary signal in, phase coupling estimation relationship is increasingly complex, and internal intermodulation production is not only generated during Nonlinear phase coupling
Object also will produce a large amount of harmonic wave of itself, though these harmonic waves do not have with other compositions Nonlinear phase coupling, still
As long as meeting above-mentioned condition between its frequency, then still will appear peak value at the bispectrum respective frequencies coordinate calculated,
And then upset the result substantially of bispectrum Non-linear coupling between studying signal so that small echo bispectrum is in analysis non-stationary signal
Shi Rongyi does the judgement to make mistake.
Claims (1)
1. a kind of instantaneous weighting is synchronous to squeeze small echo double-spectrum analysis method, which is characterized in that include the following steps：
Step 1：Given length is the discrete signal sequence g (i) of N, and calculating the minimum of signal needs using formula (1) is segmented
Number nseg：
Wherein：fs--- signal sampling rate,
f0--- the minimum frequency resolution ratio of needs；
Step 2：After determining signal subsection number, the corresponding weight coefficient of each signal subsection is calculated using formula (2)：
Wherein：M --- weight coefficient serial number,
X --- signal subsection serial number,
Gx(m) --- the amplitude absolute value of the Fourier transformation of the xth segmentation of signal sequence g (i) is calculated by formula (3)：
Wherein, gx(q) --- the xth segment data of signal sequence g (i),
Gmax——Gx(m) maximum value；
Step 3：Using the corresponding weight coefficient of each signal subsection of calculating as column vector, being ranked sequentially according to the time period can be with
Form the weight matrix of signal sequence g (i), w=[w1(m) ... ..., wnseg(m)], each row and frequency in weight matrix
Element in sequence is one-to-one, and corresponding frequency sequence is found out by formula (4)：
Step 4：The wavelet transformation that discrete signal sequence g (i) is calculated using formula (5), obtains the time-frequency domain of discrete signal sequence
Expression-form：
Wherein：The selected mother wavelet functions of ψ-,
aj--- the discretization scale parameter of mother wavelet function ψ,
The discretization translation parameters of n --- mother wavelet function ψ,
* --- expression takes conjugation；
Then it utilizes formula (6) to calculate the synchronous of signal sequence g (i) and squeezes wavelet conversion coefficient：
Wherein：Gn --- determine discretization scale ajNumber constant,
ajIt is determined by formula (7)：
f(aj, n) --- the frequency surface that derivation is obtained is carried out by the time frequency plane to wavelet transformation,
fj--- scale ajCorresponding frequency meets relationship fj=1/aj,
fj +,fj ---- according to fjThe upper bound of determined frequency separation and lower bound are determined by formula (8)：
Cψ--- constant coefficient is calculated by formula (9)：
Wherein：ε --- integration variable；
Step 5：Synchronous extruding wavelet conversion coefficient is weighted using formula (10) to obtain modified wavelet systems by frequency separation
Number：
Wherein：SWg(fl,n0) --- the synchronous of signal sequence g (i) squeezes wavelet conversion coefficient,
--- time factor n0The corresponding weight coefficient of segmentation at place,
fl--- the synchronous frequency factor for squeezing the time-frequency domain expression-form that wavelet transformation obtains,
n0--- the synchronous time factor for squeezing the time-frequency domain expression-form that wavelet transformation obtains,
x0--- time factor n0The signal subsection serial number at corresponding moment, is determined by formula (11)：
K --- frequency factor flThe frequency serial number for the frequency separation being located at meets formula (12)：
F (k-1) ＜ fl≤f(k) (12)
Step 6：The result being calculated by formula (10) is substituted into formula (13), the synchronous extruding small echo pair of weighting is calculated
Spectrum：
Wherein：Frequency f1、f2、f3Meet relationship f3=f1+f2,
WSWg(f1,n0) --- synchronizing after weighting squeezes wavelet coefficient in frequency f1, time factor n0The value at place,
WSWg(f2,n0) --- synchronizing after weighting squeezes wavelet coefficient in frequency f2, time factor n0The value at place,
WSWg(f3,n0) --- synchronizing after weighting squeezes wavelet coefficient in frequency f3, time factor n0The value at place；
To formula (14) be substituted by the result that formula (10) are calculated, and obtain discrete signal sequence g (i) in time factor n0Place
Instantaneous weighting synchronous squeeze small echo bispectrum：
Since the synchronous small echo bispectrum that squeezes of the instantaneous weighting of calculating is plural number, the form of formula (15) can be expressed as：
Wherein：A(f1,f,n0) --- in time factor n0Place, bifrequency (f1,f2) when instantaneous weighting synchronous squeeze small echo bispectrum
Amplitude,
φ(f1,f2,n0) --- in time factor n0Place, bifrequency (f1,f2) when instantaneous weighting synchronous squeeze small echo bispectrum phase
Position.
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