CN107729288A - A kind of Polynomial Phase Signals time-frequency conversion method based on particle group optimizing - Google Patents
A kind of Polynomial Phase Signals time-frequency conversion method based on particle group optimizing Download PDFInfo
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Abstract
The present invention provides a kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing, the Time-frequency Decomposition of Polynomial Phase Signals can be completed, each component of signal for wherein decomposing to obtain only corresponds to the simple component of a frequency for any instant, then each component of signal is utilized, the instantaneous frequency value at each moment, the Sinc functions responded by only retaining main lobe directly calculate signal frequency distribution corresponding to the generation corresponding moment, overcome the non-simple component that a moment corresponds to multiple frequencies in traditional time-frequency conversion and the defects of cross term be present, final output is without any cross term interference and time-frequency combination resolution ratio preferably time-frequency distributions；The principle of the invention is simple, easy to operate, can effectively overcome the loss of the adverse effect and time-frequency combination resolution ratio of classical Time-Frequency Analysis Method cross term interference, can effectively lift the quality and benefits of non-stationary Polynomial Phase Signals time frequency analysis.
Description
Technical field
The invention belongs to field of signal processing, more particularly to a kind of Polynomial Phase Signals based on particle group optimizing are adaptive
Answer time-frequency transform method.
Background technology
Many natural and artificial signals, for example voice, biomedicine signals, the ripple propagated in dispersive medium, machinery
Vibration, animal cry, music, radar, sonar signal etc., are all typical non-stationary signals, are characterized in limited duration,
And frequency is time-varying, have non-stationary, it is non-linear, non-homogeneous, non-structural, non-determined, non-accumulate, be non-reversible, amorphous state,
Irregular, discontinuous, Non-smooth surface, it is aperiodic, asymmetric the features such as.Time-frequency combination analyzes (joint time-frequency
Analysis, abbreviation time frequency analysis) it is exactly the time varying characteristic for being conceived to actual signal constituent, an one-dimensional time is believed
Number by two dimension T/F density function in the form of show, it is intended to disclose how many frequency component are contained in signal, and
How each component changes over time.
1948, French scholar J.Ville existed the American physicist E.P.Wigner that Budapest, HUN is born
The Wigner distributions proposed for 1932 introduce field of signal processing, are referred to as " Wigner-Ville distribution " (Wigner-
Ville distribution, WVD).Follow-up scholar rises and imitated, it is proposed that some new time-frequency distributions.Frequency division when whole
The history of analysis, almost exactly one history struggled with WVD deficiency., can will be varied according to the substantive characteristics of each group
Time-frequency distributions be included into following several classes：(1) linear time-frequency representation；(2) Cohen classes bilinearity time-frequency distributions；(3) affine class two-wire
Property time-frequency distributions；(4) class bilinearity time-frequency distributions are reset；(5) self-adaptive kernel function class time-frequency distributions；(6) frequency division when parameterizing
Cloth.
Wherein, linear time-frequency conversion Gabor transformation, STFT time frequency resolution are limited by the shape and width of window function.
Wavelet analysis m- dimensional analysis when being substantially a kind of, being more suitable for analysis has the signal (such as point shape) of self-similar structure and dashes forward
Become (transient state) signal, and in terms of the Time variable structure angle for portraying signal, the result of wavelet transformation is often difficult to explain.
The essence of Cohen class bilinearity time-frequency distributions, it is to be distributed in the energy (certain quadratic form of signal) of signal
In time-frequency plane, its basis is then WVD.But WVD is not linear, i.e. the WVD of two signal sums is not the WVD of each signal
Sum, wherein having more an addition Item.Cross term influences strong on WVD, it is seen that one spot.Cross term is real, is unworthily moved in from item
Between composition, and amplitude is larger；In addition, cross term is oscillation mode, each two component of signal will produce a cross term.If
Signal has N number of component, then can produceIndividual cross term.Explanation of the people to WVD is seriously disturbed in the presence of cross term；When
When the constituent of signal becomes complexity, the time-frequency distributions that WVD is provided even become meaningless.
In order to solve the influence of cross term interference, people propose several different Time-Frequency Analysis Method in succession, wherein
Cohen class kernel function Time-Frequency Analysis Methods by designing two-dimentional kernel function (two dimensional filter), produce with required characteristic when
Frequency division cloth.But the smooth method suppressing crossterms of such time-frequency distributions, be using sacrifice the time frequency resolution that is entirely distributed as
Cost.
Previously described various distributions (except wavelet transformation) are logical to the time of signal and portraying for frequency local characteristicses
Cross time shift and frequency displacement converts what is realized；In contrast, the distribution of affine class is realized by time shift and stretching.
Foremost distribution, which is worked as, in affine class pushes away scalogram (Scale gram), i.e. square of wavelet transformation.Due to this
The basis of class distribution is still WVD, and therefore, WVD turns into one of its member naturally.In fact, WVD be exactly connect Cohen classes and
The tie of affine class.The former is smooth (time-frequency smoothing) based on the time-frequency carried out to WVD, and the latter Ze Ji
In affine smooth (affine smoothing).
Cohen classes and affine class time-frequency distributions, by carrying out the smooth m- yardstick smoothing processing in time of time-frequency to WVD, such as scheme
It shown in 6, can greatly disturb suppressing crossterms, but still there are many cross terms to remain, and some distributions can also introduce
New cross term.It is proposed to enter rearrangement to time-frequency plane first further to improve the performance, K.Kdoera etc. of this two class distribution
Thought, hereafter F.Auger and P.Flandrin are expanded and the perfect method reset.
In the bilinearity time-frequency distributions of Cohen classes, affine class and rearrangement class, core letter of each distribution with a fixation
Number is corresponding, is exactly that the kernel function determines the cross term rejection characteristic being accordingly distributed.Self-evident, a kind of kernel function is only to one
Class signal is effective, thus the bilinearity time-frequency distributions in all above-mentioned three classes lack the adaptability to signal.
Previously described various Time-Frequency Analysis Methods, it is the method for imparametrization, they are without a priori hypothesis letter
Which kind of number it is made up of model signals.And Parametric Time-frequency Analysis (parametric time frequency analysis)
Method, then according to the analysis to signal hierarchical structure, construct the signal model with signal hierarchical structure best match, thus energy
The information of signal is concentrated, simplifies the expression of signal, and thus obtains the time-frequency distributions of signal.
In linear time-frequency representation (Atomic Decomposition) method, if the atom selected is similar to the main component of signal, only
The linear combination of a small number of atoms is needed, just can relatively accurately represent signal, the result of decomposition will be sparse (sparse).Instead
It, if the character of atom and the primary structure of signal greatly differ from each other or totally different, then just need with substantial amounts of or even infinite more
Atom, could precisely enough be assembled into original signal, disperse on too many atom, is unfavorable for effectively by the information of signal
Represent signal.So when using Atomic Decomposition method, it is necessary to according to the partial structurtes feature of signal, be adaptive selected atom
Combination, to atom as few as possible come decomposed signal.Frequency division when S.Qian and D.Chen had started parametrization in 1994
The beginning of analysis (its inventive concept can trace back to 1988), it is proposed that " adaptive expansion ', (adaptive expansion)
Algorithm；S.Mallat and Z.Zhang in 1993 proposes the sisters' algorithm-" matching pursuit " calculations adaptively deployed
Method.It is substantially of equal value substantially without implacable dissimilarity although both algorithm titles are different.
The essence of Adaptive matching pursuit pyramidal algorithm algorithm, be with the time-frequency Energy distribution of atom approach original signal when
Frequency Energy distribution.Because S.Qian and S.Mallat is using the constant Gabor atoms of frequency, therefore iterative algorithm is to time-frequency
The division of plane is a kind of lattice segmentation.Constant frequency component effect is fine during this algorithm pair, but works as signal to be analyzed
When being Chirp signals, this matching approaches equivalent to Zero order curve, certainly will cause decomposable process exist many block with component it
Between mixing distortion.To overcome this defect, S.Mann and S.Haykin et al. almost propose to use simultaneously through flexible, time shift,
" chirplet " is used as atom one by one for frequency displacement and the inclined Gauss functions of frequency, to substitute the constant Gabor atoms of frequency
(S.Mann separately adds time tilt operation), and obtained so-called " chirplet conversion " with Law of Inner Product.
Chirplet conversion based on Adaptive matching pursuit pyramidal algorithm algorithm, inherently on time-frequency plane
Any one energy curve carries out linear approximation with one group of arbitrarily inclined line segment.Obviously, single order approaches that approached than zeroth order can be more
Compactly express chirp class signals.Although scholars have deep love for linearly always, but the Nature is typically nonlinear.Work as signal
Frequency content when non-linearly changing with the time, for example a kind of naturally occurring or artificially generated Doppler signals, with frequency
Rate characterizes with the atom of time work linear (zeroth order or single order) change, the increase of atom number certainly will be caused, so as to both influence
Understanding and way to decomposition result are released, and influence the data compression capability of decomposition result again.
But above-mentioned adaptive time-frequency Decomposition is based on known signal hierarchical structure or signal model, in signal parameter
On be adaptive decomposition, but be non-blind on signal type.Further to improve above-mentioned parameter Time-Frequency Analysis Method also
Need to carry out new trial.
Time frequency analysis is in speech recognition, Radar Signal Processing and image procossing, seismic data processing, signal reconstruction and expansion
AF panel in frequency communication etc., existing many successful applications.All things considered, the application field of time frequency analysis substantially just like
Lower four classes：First, time varying spectrum is analyzed；Second, calculate some physical quantitys indirectly by time-frequency distributions；Third, by the use of time-frequency distributions as
The carrier (whether can very represent energy density without concern for it) of information entrained by signal；Fourth, the reconstruct of signal, compression and
Coding etc..
From investigating for evolution properties angle of the frequency content of signal with the time, the result of wavelet transformation is puzzling,
Although this field is very powerful and exceedingly arrogant.Wavelet transformation be using time and yardstick as parameter, when m- yardstick plane diverse location on
With different resolution ratio, thus it is a kind of multiresolution analysis method.Wavelet analysis have benefited from small echo atom completeness, from
Similitude and multi-resolution analysis, two most important reasons that it can succeed, it is that it possesses turriform fast algorithm and good
Time-frequency Local Characteristic；Shortcoming is then that application effect can be greatly affected once morther wavelet selection is improper.From Signal Compression and eliminate friendship
Fork item interference angle sees that the Time-Frequency Analysis Method of parametrization is preferable, seeks only the parameter of its atom model, nor easy thing.WVD and institute
There are other Cohen classes time-frequency distributions, can be used in analyzing narrow band signal, but they are not particularly suitable for analyzing multicomponent width
Band signal and radar and sonar signal, according to the distribution of affine class, then the problem of resolution ratio space-variant be present.To be objective,
Difficult point of quality of various time-frequency analysis technologies, it is important to which it is adapted to what type of signal.One time-tested experience is, can be with
The spectrogram of STFT first with arithmetic speed quickly is attempted, as shown in Figure 5；If desired higher time frequency resolution, can use
Parametric Time-frequency Analysis method.
But existing various Time-Frequency Analysis Methods still difficulty, which is completely suitable for phase-modulation, is represented by finite term multinomial level
Several Polynomial Phase Signals.
Patent " a kind of adaptive time-frequency conversion method of the Polynomial Phase Signals of model-driven " is directed to above-mentioned realistic problem,
A kind of feasible new approaches and new method are proposed, but do not specifically give the specific practicality of wherein various modern optimization algorithms
Operation and calculating process.The present invention is directed to this problem, gives a kind of for the adaptive of non-stationary Polynomial Phase Signals
Time-frequency conversion algorithm, the algorithm are that the one kind of " the adaptive Time-frequency Decomposition new method of Polynomial Phase Signals of model-driven " is specific
Implementation and practical calculating process and calculation process, the Time-frequency Decomposition of completion Polynomial Phase Signals that can be adaptively, and
Output is without any cross term interference and time-frequency combination resolution ratio preferably time-frequency distributions.
The content of the invention
To solve the above problems, the present invention provides a kind of adaptive time-frequency of Polynomial Phase Signals based on particle group optimizing
Transform method, it is direct by the Sinc functions for only retaining main lobe response using each component of signal, the instantaneous frequency value at each moment
Calculate and generate signal frequency distribution corresponding to corresponding moment, overcoming a moment in traditional time-frequency conversion corresponds to multiple frequencies
Non- simple component the defects of cross term be present, final output is without any cross term interference and time-frequency combination resolution ratio preferably time-frequency
Distribution.
A kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing, comprises the following steps：
Step 1：The original polynomial phase signal s (t) that radar receives repeatedly is divided using particle swarm optimization algorithm
Solution, the optimal models exponent number of one component of signal of determination and optimal undetermined coefficient collection is decomposed every time, specifically：
Step 11：According to polynomial-phase model, reference function h corresponding to generation original polynomial phase signal s (t)p,
And initialized reference function hpModel order N1=1, and calculate original polynomial phase signal s (t) ENERGY E0, it is random raw
Into reference function hpAt least two undetermined coefficient collection { an, n=0,1,2 ..., N1, wherein undetermined coefficient collection { anNumber
Use NParticlesRepresent；By undetermined coefficient collection { anLocation parameter as primary in particle swarm optimization algorithm, NParticles
Individual primary forms predecessor group IParticles；
Step 12：By each undetermined coefficient collection { anCorresponding to reference function hpConjugation respectively with original polynomial phase
Signal s (t), which is multiplied, obtains Hybrid-modulated Signal x (t), implements Fourier Tranform to Hybrid-modulated Signal x (t), obtains conversion knot
Fruit X (f), the characteristic value of transformation results X (f) one of frequency domain character is calculated, and using this feature value as evaluation transformation results X
(f) fitness, it is good and bad according to the fitness of each transformation results X (f), obtain each particle in local of current optimization cycle
Location parameter ParticleL, the location parameter ParticleG of global optimum's particle corresponding to current optimal transformation result X (f),
Wherein ParticleG is the location parameter of the optimal particle in all optimization cycles, and in first time optimization cycle,
ParticleL is the location parameter of primary；
Step 13：The location parameter of the local each particle of renewal, obtains new particle group；
Step 14：Using undetermined coefficient collection { a corresponding to each particle position parameter in the new particle groupnBy step 12
Method, recalculate and evaluate the fitness of transformation results X (f) corresponding to each particle position parameter in new particle group, Ran Hougeng
The location parameter ParticleL of local optimal particle and the location parameter of current global optimum's particle of new current optimization cycle
ParticleG；
Step 15：Update the location parameter of each particle of new particle group, and it is each after the renewal obtained using this step
Undetermined coefficient collection { a corresponding to individual particle position parameternRepeat step 14, by that analogy, until the cycle of particle group optimizing reaches
To the maximum Cycles of setting, the location parameter ParticleG of final global optimum's particle is obtained；
Step 16：Make model order N1Maximum possible exponent number order_max is got from 2, after each value, repeat to walk successively
Rapid 11 to step 15, so as to obtain the fitness index after Cycles cycle particle group optimizing under different model orders
Optimal location parameter ParticleG；
Step 17：Obtain selecting the optimal position ginseng of fitness index in all location parameter ParticleG from step 16
Number, so that it is determined that the optimal models exponent number N of original polynomial phase signal s (t) current demand signal componentspAnd NpIt is corresponding optimal
Undetermined coefficient collection { an}max；
Step 2：Utilize optimal models exponent number NpWith optimal undetermined coefficient collection { an}maxThe conjugation of the component of signal of determination and original
Beginning Polynomial Phase Signals s (t) is multiplied and implements Fourier Tranform, obtains frequency spectrum X'(f), by frequency spectrum X'(f) envelope maximum
After the intensity complex valued zero setting at place, implement inverse Fourier transform, so as to obtain time-domain signal y (t)；
Step 3：It is N using model orderpWith optimal undetermined coefficient collection { an}maxThe component of signal of determination and time-domain signal y
(t) it is multiplied and obtains residual signals z (t), this decomposition terminates；
Step 4：Calculate residual signals z (t) ENERGY Ed, with original polynomial phase signal s (t) ENERGY Es0Take ratio R,
If ratio R is less than setting thresholding γ or decomposes the upper limit quantity N that number reaches settingmax, then stop decomposing, obtain each component
The optimal models exponent number N of signalpWith optimal undetermined coefficient collection { an}max；Otherwise, the residual signals z (t) calculated using step 3 is replaced
The original polynomial phase signal s (t) changed in step 1 recalculates Hybrid-modulated Signal x (t), repeat step 1 to step 3, directly
It is less than setting thresholding γ to ratio R or decomposes the upper limit quantity N that number reaches settingmax；
Step 5：By optimal models exponent number NpWith optimal undetermined coefficient collection { an}maxCorresponding each component of signal is suitable by decomposing
Sequence numbering is hc, wherein c=1,2 ..., C, wherein C are the number of adaptive decomposition；
Step 6：By the physical definition of simple component signal transient frequency, each component of signal h is obtainedcCorresponding instantaneous frequency is bent
Line fc(t), and according to instantaneous frequency profile fc(t) original polynomial phase signal s (t) frequency distribution scope is determined, it is finally right
After the frequency distribution scope carries out discretization, the response of reservation main lobe and overlap-add operation successively, original polynomial phase is obtained
Signal s (t) time-frequency combination distribution f (t).
Further, reference function h corresponding to the original polynomial phase signal s (t)pSpecially：
Wherein, order_max is original polynomial phase signal s (t) maximum possible exponent number.
Further, the frequency distribution scope of the original polynomial phase signal s (t) is specially：
All component of signal hcInstantaneous frequency profile fc(t) the instantaneous frequency minimum value in is believed for original polynomial phase
Number s (t) minimum frequency fimin, instantaneous frequency maximum is original polynomial phase signal s (t) peak frequency fimax。
Further, the undetermined coefficient collection { anIt is specially vectorWherein N1Represent current excellent
The model order of change, a0For fixed value, original polynomial phase signal s (t) directly Fourier Tranform gained peak values are set to
The position number of place sampled point；For undetermined coefficient to be optimized, produced by random function Rand, span
For [- M, M], wherein M is original polynomial phase signal s (t) sampled point number, specifically：
Wherein rand (NParticles,N1) represent to randomly generate NParticlesIndividual dimension is N1Be distributed in the random of [0,1]
Number, is N so as to obtain model order1Primary group IParticles。
Further, the frequency domain character described in step 12 is in the spectrum shape entropy of spectrum peak, the contrast of frequency spectrum or frequency spectrum
Any one, wherein the characteristic value spectrum peak X of each frequency domain characterp, frequency spectrum contrast XcAnd the spectrum shape entropy X of frequency spectrumePoint
It is not：
Xp=max { abs [X (f)] }
Xe=sum (- pS·logpS)
Wherein
The sum operation of sum () representation vector, abs () are to take absolute value；
As selection spectrum peak XpOr spectrum contrast XcDuring as fitness, the value is bigger, and evaluation result is more excellent, is elected to
Select the spectrum shape entropy X of frequency spectrumeDuring as fitness, the value is smaller, and evaluation result is more excellent.
Further, the specific update method of the location parameter is：
Step 131：The speed parameter V of each particle is updated first, the speed parameter V after being updatednext, specifically：
Wherein, K be velocity inertia constraint factor, speed parameter V={ Vn, n=0,1,2 ..., N1The value of initial value
Scope is [- Vmax,Vmax], and V0=0, VmaxEqual to original polynomial phase signal s (t) sample sequence sampling numbers M integer
Times, rand (NParticles,N1) represent to randomly generate NParticlesIndividual dimension is N1The random number for being distributed in [0,1],
Respectively local optimal particle and the attracting factor of global optimum's particle, if requiring the particle after renewal by local optimal particle
Attraction it is bigger, thenIf it is required that renewal after particle it is bigger by the attraction of global optimum's particle,Such as
Fruit does not consider the particle taxis after renewal, then
Step 132：Utilize the speed parameter V after renewalnextRemove to update the location parameter of each particle：
Particles'=Particles+Vnext
Wherein Particles' is the location parameter after renewal.
Further, the location parameter of each particle carries out error correction after being updated to step 13, completes the location parameter of error correction again
Into step 14, wall is regular, stealthy wall is regular or reflecting wall rule to absorb for the rule that wherein error correction specifically uses.
Further, discretization is carried out successively to the frequency distribution scope it is specially described in step 6：
fis=[fimin fimin+Δf fimin+2Δf fimin+3Δf ... fimax]T
Wherein, fisFor the instantaneous frequency values of discrete frequency vector, Δ f is the frequency resolution of setting, specifically：
Wherein, fiminFor original polynomial phase signal s (t) minimum frequency, fimaxFor original polynomial phase signal s
(t) peak frequency, L are the discrete frequency dimension of setting, and i is imaginary part unit.
Further, the reservation main lobe response circular that carried out to the frequency distribution scope described in step 6 is：
Wherein, AcFor c-th of component of signal hcSpectrum envelope maximum at intensity complex valued, i is imaginary part unit,
Δ f be setting frequency resolution, fisFor discrete frequency vector fsInstantaneous frequency values, fic(t) it is each component of signal hcIt is corresponding
Instantaneous frequency profile fc(t) instantaneous frequency values.
Beneficial effect：
The present invention provides a kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing, can be complete
Into the Time-frequency Decomposition of Polynomial Phase Signals, wherein each component of signal for decomposing to obtain only corresponds to one for any instant
The simple component of individual frequency, then using each component of signal, the instantaneous frequency value at each moment, by only retaining main lobe response
Sinc functions directly calculate signal frequency distribution corresponding to the generation corresponding moment, overcome a moment in traditional time-frequency conversion
There is the defects of cross term in the non-simple component of corresponding multiple frequencies, final output is differentiated without any cross term interference and time-frequency combination
Rate preferably time-frequency distributions；
The principle of the invention is simple, easy to operate, can effectively overcome the unfavorable shadow of classical Time-Frequency Analysis Method cross term interference
The loss of sound and time-frequency combination resolution ratio, it can effectively lift the quality and effect of non-stationary Polynomial Phase Signals time frequency analysis
Benefit.
Brief description of the drawings
Fig. 1 is the adaptive time-frequency conversion method flow diagram of particle group optimizing of the present invention；
Fig. 2 is the time domain beamformer of the one of multicomponent polynomial phase signal of the present invention；
Fig. 3 optimizes preoperative population distribution map for the present invention；
Fig. 4 is the population distribution map after present invention optimization operation；
Fig. 5 analyzes time-frequency figure for classical STFT in the prior art；
Fig. 6 is classical WVD time-frequencies figure in the prior art；
Fig. 7 is time-frequency figure obtained by the adaptive time-frequency conversion method of particle group optimizing of the present invention.
Embodiment
With reference to the accompanying drawings and examples, the present invention is described in detail.
The present invention estimates Polynomial Phase Signals by some cycles and particle group optimizing of certain scale first
The model order of each component amount and corresponding each rank phase parameter, the thought of " cleaning " is then utilized, extracted corresponding more
Item formula phase signal components, and reject the component of signal from primary signal and obtain residual signals, then with iteration " cleaning "
Mode, recycling particle group optimizing determines rank for residual signals implementation adaptive model and optimal model parameters optimize, and by
Step extracts each component of signal, so repeatedly, until residual signals energy is less than default thresholding or the component of signal extracted
Number reaches default maximum.Then, the phase parameter that each component signal of gained is decomposed using particle group optimizing builds phase
Position-time history, and according to the physical definition of simple component signal transient frequency, it is straight in a manner of parsing to phase history derivation
Connect to obtain the frequency-time history of each component of signal, i.e. time-frequency change curve, according to the time-frequency change curve of each component of signal,
It is determined that the maximum and minimum frequency of whole signal, using the frequency range of the whole signal of its determination, by using required frequency
Rate resolution requirements, discretization is carried out to the frequency range, obtain the discrete frequency vector of required dimension, finally, utilize each point
Amount, the instantaneous frequency value at each moment, it is corresponding that the Sinc functions responded by only retaining main lobe directly calculate the generation corresponding moment
Signal frequency distribution；So repeatedly, until the frequency distribution at all component of signals all moment is generated and finished, by it on time
Between sequencing store and added up by component of signal, you can obtain final Polynomial Phase Signals time-frequency combination distribution.
As shown in figure 1, a kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing, including with
Lower step：
Step 1：The original polynomial phase signal s (t) that radar receives repeatedly is divided using particle swarm optimization algorithm
Solution, the optimal models exponent number of one each component of signal of determination and optimal undetermined coefficient collection is decomposed every time, specifically：
Step 11：According to polynomial-phase model, reference function h corresponding to generation original polynomial phase signal s (t)p,
And initialized reference function hpModel order N1=1, and calculate original polynomial phase signal s (t) ENERGY E0, it is random raw
Into reference function hpAt least two undetermined coefficient collection { an, n=0,1,2 ..., N1, wherein undetermined coefficient collection { anNumber
Use NParticlesRepresent；By wherein undetermined coefficient collection { anLocation parameter as primary in particle swarm optimization algorithm,
NParticlesIndividual primary forms predecessor group IParticles, as shown in Figure 3；
Step 12：By each undetermined coefficient collection { anCorresponding to reference function hpConjugation respectively with original polynomial phase
Signal s (t), which is multiplied, obtains Hybrid-modulated Signal x (t), implements Fourier Tranform to Hybrid-modulated Signal x (t), obtains conversion knot
Fruit X (f), the characteristic value of transformation results X (f) one of frequency domain character is calculated, and using this feature value as evaluation transformation results X
(f) fitness, it is good and bad according to the fitness of each transformation results X (f), obtain each particle in local of current optimization cycle
Location parameter ParticleL, the location parameter ParticleG of global optimum's particle corresponding to current optimal transformation result X (f),
Wherein ParticleG is the location parameter of the optimal particle in all optimization cycles, and in first time optimization cycle,
ParticleL is the location parameter of primary；
Step 13：The location parameter of local each particle in step 12 is updated, obtains new particle group；
Step 14：Using undetermined coefficient collection { a corresponding to each particle position parameter in new particle groupnBy the side of step 12
Method, recalculate and evaluate the fitness of transformation results X (f) corresponding to each particle position parameter in new particle group, then update
The location parameter ParticleL of local optimal particle and the location parameter of current global optimum's particle of current optimization cycle
ParticleG；
Step 15：Update the location parameter of each particle of new particle group, and it is each after the renewal obtained using this step
Undetermined coefficient collection { a corresponding to individual particle position parameternRepeat step 14, by that analogy, until the cycle of particle group optimizing reaches
To the maximum Cycles of setting, the location parameter ParticleG of final global optimum's particle is obtained, as shown in Figure 4；
Step 16：Make model order N1Maximum possible exponent number order_max is got from 2, after each value, repeat to walk successively
Rapid 11 to step 15, so as to obtain the fitness index after Cycles cycle particle group optimizing under different model orders
Optimal location parameter ParticleG；
Step 17：Obtain selecting the optimal position ginseng of fitness index in all location parameter ParticleG from step 16
Number, so that it is determined that the optimal models exponent number N of original polynomial phase signal s (t) current demand signal componentspAnd NpIt is corresponding optimal
Undetermined coefficient collection { an}max；
Step 2：Utilize optimal models exponent number NpWith optimal undetermined coefficient collection { an}maxThe conjugation of the component of signal of determination and original
Beginning Polynomial Phase Signals s (t) is multiplied and implements Fourier Tranform, obtains frequency spectrum X'(f), by frequency spectrum X'(f) envelope maximum
After the intensity complex valued zero setting at place, implement inverse Fourier transform, so as to obtain time-domain signal y (t), as shown in Figure 2；
Step 3：It is N using model orderpWith optimal undetermined coefficient collection { an}maxThe component of signal of determination and time-domain signal y
(t) it is multiplied and obtains residual signals z (t), this decomposition terminates；
Step 4：Calculate residual signals z (t) ENERGY Ed, with original polynomial phase signal s (t) ENERGY Es0Take ratio R,
If ratio R is less than setting thresholding γ or decomposes the upper limit quantity N that number reaches settingmax, then stop decomposing, obtain each component
The optimal models exponent number N of signalpWith optimal undetermined coefficient collection { an}max；Otherwise, the residual signals z (t) calculated using step 3 is replaced
The original polynomial phase signal s (t) changed in step 1 recalculates Hybrid-modulated Signal x (t), repeat step 1 to step 3, directly
It is less than setting thresholding γ to ratio R or decomposes the upper limit quantity N that number reaches settingmax；
Step 5：By optimal models exponent number NpWith optimal undetermined coefficient collection { an}maxCorresponding each component of signal is suitable by decomposing
Sequence numbering is hc, wherein c=1,2 ..., C, wherein C are the number of adaptive decomposition；
Step 6：By the physical definition of simple component signal transient frequency, each component of signal h is obtainedcCorresponding instantaneous frequency is bent
Line fc(t), and according to instantaneous frequency profile fc(t) original polynomial phase signal s (t) frequency distribution scope is determined, it is finally right
After the frequency distribution scope carries out discretization, the response of reservation main lobe and overlap-add operation successively, original polynomial phase is obtained
Signal s (t) time-frequency combination distribution f (t), as shown in Figure 7.
Further, reference function h corresponding to the original polynomial phase signal s (t)pSpecially：
Wherein, undetermined coefficient collectionIn undetermined coefficient anInitial value generates at random, order_
Max is original polynomial phase signal s (t) maximum possible exponent number.
Further, the frequency distribution scope of the original polynomial phase signal s (t) is specially：
All component of signal hcInstantaneous frequency profile fc(t) the instantaneous frequency minimum value in is believed for original polynomial phase
Number s (t) minimum frequency fimin, instantaneous frequency maximum is original polynomial phase signal s (t) peak frequency fimax。
Further, the undetermined coefficient collection { anIt is specially vectorWherein N1Represent current excellent
The model order of change, a0For fixed value, original polynomial phase signal s (t) directly Fourier Tranform gained peak values are set to
The position number of place sampled point；For undetermined coefficient to be optimized, produced by random function Rand, span
For [- M, M], wherein M is original polynomial phase signal s (t) sampled point number, specifically：
Wherein rand (NParticles,N1) represent to randomly generate NParticlesIndividual dimension is N1Be distributed in the random of [0,1]
Number, is N so as to obtain model order1Primary group IParticles。
Further, the frequency domain character described in step 12 is in the spectrum shape entropy of spectrum peak, the contrast of frequency spectrum or frequency spectrum
Any one, wherein the characteristic value spectrum peak X of each frequency domain characterp, frequency spectrum contrast XcAnd the spectrum shape entropy X of frequency spectrumePoint
It is not：
Xp=max { abs [X (f)] }
Xe=sum (- pS·logpS)
Wherein
The sum operation of sum () representation vector, abs () are to take absolute value；
As selection spectrum peak XpOr spectrum contrast XcDuring as fitness, the value is bigger, and evaluation result is more excellent, is elected to
Select the spectrum shape entropy X of frequency spectrumeDuring as fitness, the value is smaller, and evaluation result is more excellent.
Further, the specific update method of the location parameter is：
Step 131：The speed parameter V of each particle is updated first, the speed parameter V after being updatednext, specifically：
Wherein, K be velocity inertia constraint factor, speed parameter V={ Vn, n=0,1,2 ..., N1The value of initial value
Scope is [- Vmax,Vmax], and V0=0, VmaxEqual to original polynomial phase signal s (t) sample sequence sampling numbers M integer
Times, rand (NParticles,N1) represent to randomly generate NParticlesIndividual dimension is N1The random number for being distributed in [0,1],
Respectively local optimal particle and the attracting factor of global optimum's particle, if requiring the particle after renewal by local optimal particle
Attraction it is bigger, thenIf it is required that renewal after particle it is bigger by the attraction of global optimum's particle,Such as
Fruit does not consider the particle taxis after renewal, then
Step 132：Utilize the speed parameter V after renewalnextRemove to update the location parameter of each particle：
Particles'=Particles+Vnext
Wherein Particles' is the location parameter after renewal.
Further, the location parameter of each particle carries out error correction after being updated to step 13, completes the location parameter of error correction again
Into step 14, wall is regular, stealthy wall is regular or reflecting wall rule to absorb for the rule that wherein error correction specifically uses；
When the location parameter using each particle after absorbing wall rule to renewal carries out error correction, if particle in population
The location parameter of corresponding dimension exceedes the span [- M, M] of setting, then the speed parameter of the corresponding dimension of current particle immediately by
Zero setting, and the location parameter of its corresponding dimension is forced to be set to location boundary value M or-M, particle dimension position ginseng according to symbol
Number will return after particle rapidity parameter during next cycle Particle swarm optimization updates again solves scope；
When the location parameter of each particle after using stealthy wall rule to renewal carries out error correction, if particle in population
The location parameter of corresponding dimension exceedes the span [- M, M] of setting, then the fitness function of current particle is directly zeroed out, and
The particle dimension location parameter will return after particle rapidity parameter during next cycle Particle swarm optimization updates again solves model
Enclose；
When the location parameter of each particle after using reflecting wall rule to renewal carries out error correction, if particle in population
The location parameter of corresponding dimension exceedes the span [- M, M] of setting, and the location parameter of the corresponding dimension of current particle is strong according to symbol
System is set to location boundary value M or-M, and assigns one random velocity of speed parameter that the particle corresponds to dimension, the particle dimension
Location parameter will return after particle rapidity parameter during next cycle Particle swarm optimization updates again solves scope；Wherein, with
Machine speed assigns rule：
Vnext=± 0.1 × rand × Vmax
Wherein rand represents only to produce a random number being distributed in the range of [0,1], is VmaxThe corresponding dimension of current particle
Speed parameter maximum, VnextFor the speed parameter after renewal.
Further, discretization is carried out successively to the frequency distribution scope it is specially described in step 6：
fis=[fimin fimin+Δf fimin+2Δf fimin+3Δf ... fimax]T
Wherein, fisFor the instantaneous frequency values of discrete frequency vector, Δ f is the frequency resolution of setting, specifically：
Wherein, fiminFor original polynomial phase signal s (t) minimum frequency, fimaxFor original polynomial phase signal s
(t) peak frequency, K are the discrete frequency dimension of setting, and i is imaginary part unit.
Further, the reservation main lobe response circular that carried out to the frequency distribution scope described in step 6 is：
Wherein, AcFor c-th of component of signal hcSpectrum envelope maximum at intensity complex valued, i is imaginary part unit,
Δ f be setting frequency resolution, fisFor discrete frequency vector fsInstantaneous frequency values, fic(t) it is each component of signal hcIt is corresponding
Instantaneous frequency profile fc(t) instantaneous frequency values.
Certainly, the present invention can also have other various embodiments, ripe in the case of without departing substantially from spirit of the invention and its essence
Know those skilled in the art when can be made according to the present invention it is various it is corresponding change and deformation, but these corresponding change and become
Shape should all belong to the protection domain of appended claims of the invention.
Claims (9)
1. a kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing, it is characterised in that including with
Lower step：
Step 1：The original polynomial phase signal s (t) that radar receives repeatedly is decomposed using particle swarm optimization algorithm, often
Secondary decomposition the optimal models exponent number of one component of signal of determination and optimal undetermined coefficient collection, specifically：
Step 11：According to polynomial-phase model, reference function h corresponding to generation original polynomial phase signal s (t)p, and just
Beginningization reference function hpModel order N1=1, and calculate original polynomial phase signal s (t) ENERGY E0, random generation ginseng
Examine function hpAt least two undetermined coefficient collection { an, n=0,1,2 ..., N1, wherein undetermined coefficient collection { anNumber use
NParticlesRepresent；By undetermined coefficient collection { anLocation parameter as primary in particle swarm optimization algorithm, NParticlesIt is individual
Primary forms predecessor group IParticles；
Step 12：By each undetermined coefficient collection { anCorresponding to reference function hpConjugation respectively with original polynomial phase signal s
(t) it is multiplied and obtains Hybrid-modulated Signal x (t), Fourier Tranform is implemented to Hybrid-modulated Signal x (t), obtains transformation results X
(f) characteristic value of transformation results X (f) one of frequency domain character, is calculated, and using this feature value as evaluation transformation results X (f)
Fitness, it is good and bad according to the fitness of each transformation results X (f), obtain the position of each particle in local of current optimization cycle
Parameter ParticleL is put, the location parameter ParticleG of global optimum's particle corresponding to current optimal transformation result X (f), its
Middle ParticleG is the location parameter of the optimal particle in all optimization cycles, and in first time optimization cycle, ParticleL
For the location parameter of primary；
Step 13：The location parameter of the local each particle of renewal, obtains new particle group；
Step 14：Using undetermined coefficient collection { a corresponding to each particle position parameter in the new particle groupnPress step 12 method,
Recalculate and evaluate the fitness of transformation results X (f) corresponding to each particle position parameter in new particle group, then renewal is current
The location parameter ParticleL of the local optimal particle of optimization cycle and current global optimum's particle location parameter
ParticleG；
Step 15：Update the location parameter of each particle of new particle group, and each grain after the renewal obtained using this step
Undetermined coefficient collection { a corresponding to sub- location parameternRepeat step 14, by that analogy, set until the cycle of particle group optimizing reaches
Fixed maximum Cycles, obtain the location parameter ParticleG of final global optimum's particle；
Step 16：Make model order N1Successively maximum possible exponent number order_max is got from 2, after each value, repeat step 11
It is optimal so as to obtain the fitness index after Cycles cycle particle group optimizing under different model orders to step 15
Location parameter ParticleG；
Step 17：Obtain selecting the optimal location parameter of fitness index in all location parameter ParticleG from step 16, from
And determine the optimal models exponent number N of original polynomial phase signal s (t) current demand signal componentspAnd NpCorresponding optimal system undetermined
Manifold { an}max；
Step 2：Utilize optimal models exponent number NpWith optimal undetermined coefficient collection { an}maxThe conjugation of the component of signal of determination with it is original more
Formula phase signal s (t), which is multiplied, simultaneously implements Fourier Tranform, obtains frequency spectrum X'(f), by frequency spectrum X'(f) at envelope maximum
After intensity complex valued zero setting, implement inverse Fourier transform, so as to obtain time-domain signal y (t)；
Step 3：It is N using model orderpWith optimal undetermined coefficient collection { an}maxThe component of signal of determination and time-domain signal y (t) phases
Multiplied to arrive residual signals z (t), this decomposition terminates；
Step 4：Calculate residual signals z (t) ENERGY Ed, with original polynomial phase signal s (t) ENERGY Es0Ratio R is taken, if
Ratio R is less than setting thresholding γ or decomposes the upper limit quantity N that number reaches settingmax, then stop decomposing, obtain each component signal
Optimal models exponent number NpWith optimal undetermined coefficient collection { an}max；Otherwise, the residual signals z (t) calculated using step 3 replaces step
Original polynomial phase signal s (t) in rapid 1 recalculates Hybrid-modulated Signal x (t), repeat step 1 to step 3, until than
Value R is less than setting thresholding γ or decomposes the upper limit quantity N that number reaches settingmax；
Step 5：By optimal models exponent number NpWith optimal undetermined coefficient collection { an}maxCorresponding each component of signal is compiled by elaborative sequence
Number it is hc, wherein c=1,2 ..., C, wherein C are the number of adaptive decomposition；
Step 6：By the physical definition of simple component signal transient frequency, each component of signal h is obtainedcCorresponding instantaneous frequency profile fc
(t), and according to instantaneous frequency profile fc(t) original polynomial phase signal s (t) frequency distribution scope is determined, finally to institute
State frequency distribution scope carry out successively discretization, retain main lobe response and overlap-add operation after, obtain original polynomial phase letter
Number s (t) time-frequency combination distribution f (t).
2. a kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing as claimed in claim 1,
Characterized in that, reference function h corresponding to the original polynomial phase signal s (t)pSpecially：
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Wherein, order_max is original polynomial phase signal s (t) maximum possible exponent number.
3. a kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing as claimed in claim 1,
Characterized in that, the frequency distribution scope of the original polynomial phase signal s (t) is specially：
All component of signal hcInstantaneous frequency profile fc(t) the instantaneous frequency minimum value in is original polynomial phase signal s
(t) minimum frequency fimin, instantaneous frequency maximum is original polynomial phase signal s (t) peak frequency fimax。
4. a kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing as claimed in claim 1,
Characterized in that, the undetermined coefficient collection { anIt is specially vectorWherein N1Represent the mould currently optimized
Type exponent number, a0For fixed value, it is set to adopt where original polynomial phase signal s (t) directly peak values obtained by Fourier Tranform
The position number of sampling point；For undetermined coefficient to be optimized, produced by random function Rand, span for [- M,
M], wherein M is original polynomial phase signal s (t) sampled point number, specifically：
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WhereinExpression randomly generates NParticlesIndividual dimension is N1The random number for being distributed in [0,1], from
And it is N to obtain model order1Primary group IParticles。
5. a kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing as claimed in claim 1,
Characterized in that, the frequency domain character described in step 12 is any in the spectrum shape entropy of spectrum peak, the contrast of frequency spectrum or frequency spectrum
One, wherein the characteristic value spectrum peak X of each frequency domain characterp, frequency spectrum contrast XcAnd the spectrum shape entropy X of frequency spectrumeRespectively：
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Xe=sum (- pS·log pS)
Wherein
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The sum operation of sum () representation vector, abs () are to take absolute value；
As selection spectrum peak XpOr spectrum contrast XcDuring as fitness, the value is bigger, and evaluation result is more excellent, when selection frequency
The spectrum shape entropy X of spectrumeDuring as fitness, the value is smaller, and evaluation result is more excellent.
6. a kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing as claimed in claim 1,
Characterized in that, the specific update method of the location parameter is：
Step 131：The speed parameter V of each particle is updated first, the speed parameter V after being updatednext, specifically：
Wherein, K be velocity inertia constraint factor, speed parameter V={ Vn, n=0,1,2 ..., N1The span of initial value
For [- Vmax,Vmax], and V0=0, VmaxEqual to original polynomial phase signal s (t) sample sequence sampling numbers M integral multiple,
rand(NParticles,N1) represent to randomly generate NParticlesIndividual dimension is N1The random number for being distributed in [0,1],Respectively
For the attracting factor of local optimal particle and global optimum's particle, if requiring that the particle after renewal is inhaled by local optimal particle
Draw more greatly, thenIf it is required that renewal after particle it is bigger by the attraction of global optimum's particle,If no
Consider the particle taxis after renewal, then
Step 132：Utilize the speed parameter V after renewalnextRemove to update the location parameter of each particle：
Particles'=Particles+Vnext
Wherein Particles' is the location parameter after renewal.
7. a kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing as claimed in claim 1,
Characterized in that, the location parameter of each particle carries out error correction after being updated to step 13, the location parameter for completing error correction enters back into step
Rapid 14, wall is regular, stealthy wall is regular or reflecting wall rule to absorb for the rule that wherein error correction specifically uses.
8. a kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing as claimed in claim 1,
Characterized in that, discretization is carried out successively to the frequency distribution scope it is specially described in step 6：
fis=[fimin fimin+Δf fimin+2Δf fimin+3Δf ... fimax]T
Wherein, fisFor the instantaneous frequency values of discrete frequency vector, Δ f is the frequency resolution of setting, specifically：
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Wherein, fiminFor original polynomial phase signal s (t) minimum frequency, fimaxFor original polynomial phase signal s's (t)
Peak frequency, L are the discrete frequency dimension of setting, and i is imaginary part unit.
9. a kind of adaptive time-frequency conversion method of Polynomial Phase Signals based on particle group optimizing as claimed in claim 1,
Characterized in that, the reservation main lobe response circular that carried out to the frequency distribution scope described in step 6 is：
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Wherein, AcFor c-th of component of signal hcSpectrum envelope maximum at intensity complex valued, i is imaginary part unit, and Δ f is
The frequency resolution of setting, fisFor discrete frequency vector fsInstantaneous frequency values, fic(t) it is each component of signal hcIt is corresponding instantaneous
Frequency curve fc(t) instantaneous frequency values.
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| CN108615078A (en) * | 2018-05-11 | 2018-10-02 | 南京师范大学 | Hyperspace code forming method |
| CN109034042A (en) * | 2018-07-20 | 2018-12-18 | 东北大学 | Based on the double synchronous nonstationary random response methods for extracting transformation of generalized chirp |
| CN110441018A (en) * | 2019-08-14 | 2019-11-12 | 清华大学 | Firer's shock response data Time-Frequency Analysis Method |
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