CN108920418A - Time-frequency converter technique when a kind of adaptive strain window length based on the degree of bias - Google Patents
Time-frequency converter technique when a kind of adaptive strain window length based on the degree of bias Download PDFInfo
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Abstract
The invention belongs to time frequency analysis fields in signal processing, and in particular to time-frequency converter technique when a kind of adaptive strain window length based on the degree of bias, for NLFM signal.The present invention controls the adaptive process of window function length using the degree of bias：It first takes the long starting point of window for start point signal, takes a length of maximum of window, gradually diminution window is long based on degree of bias control, until getting the adaptive of window length as a result, adding window starting point is then moved forward (N1/ 4) a point carries out adding window；Take this adding window starting point (3N backward1/ 4) starting point at a point as adding window next time；After completing all adding windows, each secondary result is aggregated into a time-frequency figure.The present invention solves the problems, such as that existing adaptive time-frequency conversion signal concentration class and resolution ratio when analyzing multi -components FM signal are not high enough.
Description
Technical field
The invention belongs to time frequency analysis fields in signal processing, and in particular to a kind of adaptive strain window length based on the degree of bias
When time-frequency converter technique, mainly for NLFM signal.
Background technique
FM signal refer to continue during frequency consecutive variations signal, be widely used in include radar, sonar and lead to
In various information systems including letter.Form according to signal frequency variation is different, and FM signal can be divided into linear FM signal
And NLFM signal.
Following general expressions can be used to express in linear FM signal：
Wherein s indicates input signal, and t indicates time variable, and K indicates the number of components of signal, AkIndicate signal kth component
Amplitude, e indicate natural logrithm, fkIndicate the centre frequency of signal kth component, γkFor the frequency modulation rate of signal kth component.
Following general expressions can be used to express in NLFM signal：
Wherein θk(t) be signal kth component phase function.It can be seen that formula (1) is a kind of special circumstances of formula (2).
The mode that analysis FM signal generallys use has Short Time Fourier Transform (Short-Time Fourier
Transform, STFT) and Wigner-Willie transformation (Wigner-Ville Distribution, WVD).Both methods is all
There are some defects.The signal energy concentration class of STFT is relatively low, and WVD has very strong cross term.To improve drawbacks described above, people
Propose Lyu be distributed (Lv Distribution, LVD).The existing very high signal energy concentration class of LVD, and friendship can be eliminated
Pitch item.The inverse transformation ILVD (Inverse LVD) of LVD is the Time-Frequency Analysis Method based on time-frequency representation, processing result
For the time-frequency figure of signal.However ILVD is not directly applicable NLFM signal, therefore people use for reference the thought of STFT, uses
The thought of adding window segmentation solves the problems, such as this, proposes Lv Bianhuan (Short-Time Lv Transform, STLVT) in short-term.With
STFT is compared, and the effect that STLVT handles NLFM signal is more preferable.
STFT and STLVT be all using fixed window function length, for it is certain different periods frequency variation difference compared with
The treatment effect of big signal, STFT and STLVT are all undesirable.People have had been incorporated into adaptive thought to realize that change window is long
STFT, according to signal frequency variation, to be adaptively adjusted window long.Due to the performance ratio of STLVT processing NLFM signal
STFT is more preferable, so performance also can be better than the STFT of adaptive strain window length if being able to achieve adaptive strain window long STLVT.
But the long technology of existing adaptive strain window is not directly applicable STLVT, so STLVT still have cannot according to signal frequency
The long defect of the variation adjustment window of rate.
Summary of the invention
For above-mentioned there are problem or deficiency, for long, this hair that solves the problems, such as that STLVT cannot adjust window according to signal characteristic
A kind of bright time-frequency converter technique when providing adaptive strain window length based on the degree of bias, referred to as adaptive windows Lv transformation
(Adaptive Window based Lv Transform, AWLT).
Time-frequency converter technique when the adaptive strain window length, specific technical solution is as shown in Figure 1, include the following steps.
Step 1：The NLFM signal as shown in formula (2) is inputted, selects the starting point of input signal as adding window starting point.
It is arranged and reduces the long ratio Q (0 of window each time<Q<1).
Step 2：Enable N0Equal to the distance of adding window starting point to signaling destination point.
Step 3：With N0As window function length, the adding window since adding window starting point, and the signal after adding window is successively held
The result of line (3), (4), (5), (6), (9), (10), (11), (12), formula (12) is denoted as P0。
The parameter auto-correlation function of signal is expressed as：
Wherein CrFor the cross term between unlike signal component, RzFor the auto-correlation item of each component of signal, expression formula is as follows：
The main thought of LVD is the flexible operation being shown below to the parameter auto-correlation function of signal：
tsFor the time quantum after stretching, referred to as scale time, ts=(τ+1) t.Parameter auto-correlation letter after stretching
Number RsBecome：
Referred to as scale parameter auto-correlation function is scale time quantum tsWith the function of retardation τ.
To the scale parameter auto-correlation function of formula (6)Successively along τ dimension, along tsDimension carries out Fourier transformation twice, energy
LVD is obtained, is shown below：
Wherein Fτ{·}、It respectively indicates along τ dimension, along tsThe Fourier transformation of dimension, formula (7) first item indicate that signal is each
Component energy is gathered in frequency-tune frequency plane (f with δ functional formk,γk) on these aspects, Section 2 is the fortune of cross term
Calculate result.
ILVD is to first carry out to the signal section of LVD obtained from inverse operation executes Fourier transformation again, such as formula (8), (9)
It is shown：
S indicates the region for having input signal in " frequency-frequency modulation rate " domain, i.e. (f in formula (8)k,γk) set.Formula (9)
InIt respectively indicates along f dimension, along the inverse Fourier transform of γ dimension, Γ-1{ } is the operation Γ that stretches in formula (5)
Inverse operation.
In time frequency analysis, signal energy concentration class is an important performance indicator, and usual demand concentration class gets over Gao Yue
It is good.The degree of bias is the concept that one of probability theory can measure whether distribution concentrates, therefore can be applied to measurement time frequency analysis
In signal energy concentration class, the degree of bias is bigger to illustrate that signal energy concentration class is higher.L is calculated firstsThe mean value of (f, γ) modulus value
And standard deviation：
μ=E [| Ls(f,γ)|] (10)
Then the degree of bias for calculating LVD is as follows：
Step 4：Adding window starting point is constant, enablesWith N1As window function length again to signal adding window.
Step 5：Formula (3), (4), (5), (6), (9), (10), (11), (12), formula are successively executed to the signal after adding window
(12) result is denoted as P1.If P0≤1.2P1, then 6 are entered step.Otherwise, 7 are entered step.
Step 6：By N1Value be assigned to N0, adding window starting point is constant.Subsequently into step 3.
Step 7：Adding window starting point is moved forward into N1/ 4 points (are at most only moved to input letter as new adding window starting point
Number starting point, without departing from the range of input signal), with N1Adding window is carried out from new adding window starting point for window function length.N is arranged to remember
Record executes the number of step 8, enables n=0.
Step 8：Enable n value increase by 1, to the signal after step 7 adding window successively execute formula (3), (4), (5), (6), (7),
(8),(9).The result of recording (9) is
Step 9：According to adding window starting point and window function length N new in step 71Determine adding window terminal.
If adding window terminal is not in input signal terminal, the adding window starting point for taking step 7 new 3N backward1For next time at/4 points
Adding window starting point, enters step 2.
If adding window terminal is completed in input signal terminal, all adding windows, 10 are entered step.
Step 10：The result for the formula (9) that each secondary adding window is obtainedIt is aggregated into a time-frequency figure in order, comprising all
The processing result of time sampling point.
The present invention controls the adaptive process of window function length, the bigger expression signal energy concentration class of the degree of bias using the degree of bias
Higher, subsequent processing performance is better.P0It indicates to work as the degree of bias of the long adding window of front window, P1Indicate long (i.e. with the window after reducing once
When long K times of front window) degree of bias of adding window.In steps of 5, if P0> 1.2P1It will lead to partially if then representing and continuing to zoom out window length
It spends and reduces obviously, it is long that this expression should not continue to zoom out window at this time, so choosing when front window is long long as this window
The result of adaptive process.If P0≤1.2P1, then should continue to zoom out that window is long, thus allow reduce it is primary after window be grown to it is new
Window is long, into the process for comparing the degree of bias next time.
In step 9, this adding window starting point (3/4*N backward is taken1) be the starting point of adding window next time at a point, this be in order to
The starting point of adding window next time is allowed to be placed exactly in the time-frequency sink of graph that this adding window obtains.And in step 7, by adding window starting point to
Preceding movement (1/4*N1) a point (starting point of input signal being at most only moved to, without departing from the range of input signal), this be in order to
The time-frequency figure that the time-frequency figure for allowing this adding window to obtain is obtained with last adding window can join end to end.
In conclusion the present invention can change the window for adaptively using different length according to the waveform of signal frequency function
Function, it is longer in the window function that signal frequency function waveform is used closer to linear position.Present invention is generally directed to non-linear
FM signal, but it is applied equally to linear FM signal and simple signal.The present invention solves STLVT cannot be according to signal spy
The long problem of point adjustment window realizes the i.e. AWLT of adaptive windows Lv transformation.Due to the performance of STLVT processing NLFM signal
Better than STFT, so time-frequency converter technique performance is more excellent when the present invention is than existing adaptive strain window length.
Detailed description of the invention
Fig. 1 is specific technical solution flow chart of the present invention；
Fig. 2 (a), (b) are respectively the original time-frequency figure of input signal in example 1 and the time-frequency figure of AWLT.
Fig. 3 (a), (b), (c) are respectively the time-frequency figure and STLVT of the original time-frequency figure of input signal in example 2, AWLT
Time-frequency figure.
Specific embodiment
With reference to the accompanying drawing and specific embodiment the invention will be further described.
Example 1：Under computer MATLAB environment, two components emulation signal is generated according to the following formula：Each parameter of frequency modulation is f1
=-30Hz, f2=20Hz, γ1=0.6Hz/s, γ2=20Hz/s；Sample frequency fs=256Hz, signal sampling points Ns=
8192。
In this example, the long ratio Q of window is reduced each time and is set as 0.5.
Fig. 2 (a) is the original time-frequency figure of input signal.Fig. 2 (b) is the time-frequency figure with the i.e. AWLT of the present invention.Pass through comparison
The time-frequency figure height of original time-frequency figure and AWLT that Fig. 2 (a) and Fig. 2 (b) can be seen that input signal is overlapped, and illustrates the present invention
Such signal can be handled well.
In order to show advantage of the present invention relative to STLVT, below again as one example.
Example 2：Under computer MATLAB environment, simple component is generated according to the following formula and emulates signal：Each parameter of frequency modulation is f1
=-5Hz, γ1=6Hz/s；Sample frequency fs=256Hz, signal sampling points Ns=8192.
In this example, the long ratio Q of window is reduced each time and is set as 0.8.
Fig. 3 (a) is the original time-frequency figure of input signal.Fig. 3 (b) is the time-frequency with the present invention i.e. AWLT processing input signal
Figure.Fig. 3 (c) is the time-frequency figure of STLVT, a length of 1536 points using window.From the figure we can see that the time-frequency figure curve of AWLT
It is more smooth, waveform and original waveform very close to.The time-frequency figure curve of STLVT is then not smooth enough, and waveform and original waveform are not yet
It is enough close.This be the fixation window length that STLVT is used can not accomplish it is everywhere suitable caused by.
We can also attempt to that STLVT is allowed to be compared using shorter window length with AWLT.We calculate Fig. 3
(b) average window that AWLT is used in is long, result 906.We allow STLVT to select 906 similarly to believe as the long processing of fixed window
Number, processing result is compared with AWLT.Comparative approach is：It is flat that an exposure mask is made first with the time-frequency figure of input signal
Face is shown below：
Wherein S(t,f)Indicate the signal domain in the original time-frequency figure of input signal.
With the M of formula (15)(t,f)It is multiplied to obtain two time-frequency figures respectively (to be square in Matlab with the result of AWLT, STLVT
Formation formula, is denoted as H respectivelyAWLTAnd HSTLVT), in matrix for 0 element be exactly input signal and processing result time-frequency figure weight
Then the signal energy of intersection is added up, is shown below by the part of conjunction：
Wherein hAWLT(i,j)Indicate HAWLTIn the i-th row jth column element, hSTLVT(i,j)Representing matrix HSTLVTIn the i-th row jth
The element of column.
Gross energy is bigger to illustrate that processing result and input signal registration are higher, and processing result is more outstanding.By calculating,
Use the gross energy E of 906 STLVT grown as fixation windowSTLVTIt is 42, and the gross energy E of AWLTAWLTIt is 141.Therefore, even if
It first calculates proper average window length and is applied to STLVT, the energy compaction measure of processing result still can not show a candle to AWLT.
To sum up, from the point of view of the simulation result of two examples, the present invention, that is, AWLT can effectively handle nonlinear frequency modulation letter
Number.It is long that the present invention solves the problems, such as that STLVT cannot adjust window according to signal characteristic.Since STLVT ratio STFT performance is more preferable, institute
Time-frequency converter technique when with performance of the invention better than existing adaptive strain window length.
Claims (1)
1. time-frequency converter technique when a kind of adaptive strain window length based on the degree of bias, specific step is as follows：
Step 1：The NLFM signal as shown in formula (2) is inputted, selects the starting point of input signal as adding window starting point, setting
The long ratio Q (0 of window is reduced each time<Q<1)；
Wherein s indicates input signal, and t indicates time variable, and K indicates the number of components of signal, AkIndicate the amplitude of signal kth component,
E indicates natural logrithm, fkIndicate the centre frequency of signal kth component, γkFor the frequency modulation rate of signal kth component, θkIt (t) is signal
The phase function of kth component；
Step 2：Enable N0Equal to the distance of adding window starting point to signaling destination point；
Step 3：With N0As window function length, the adding window since adding window starting point, and formula is successively executed to the signal after adding window
(3), the result of (4), (5), (6), (9), (10), (11), (12), formula (12) is denoted as P0；
The parameter auto-correlation function of signal is expressed as：
Wherein CrFor the cross term between unlike signal component, RzFor the auto-correlation item for each component of signal, expression formula is as follows：
LVD is the flexible operation being shown below to the parameter auto-correlation function of signal：
tsFor the time quantum after stretching, referred to as scale time, ts=(τ+1) t；Parameter auto-correlation function R after stretchings
Become：
Referred to as scale parameter auto-correlation function is scale time quantum tsWith the function of retardation τ；
To the scale parameter auto-correlation function of formula (6)Successively along τ dimension, along tsDimension carries out Fourier transformation twice, obtains LVD,
It is shown below：
Wherein Fτ{·}、It respectively indicates along τ dimension, along tsThe Fourier transformation of dimension, formula (7) first item indicate each component of signal
Energy is gathered in frequency-tune frequency plane (f with δ functional formk,γk) on these aspects, Section 2 is the operation knot of cross term
Fruit；
ILVD is to first carry out inverse operation to the signal section of LVD and execute Fourier transformation again to obtain, as shown in formula (8), (9)：
S indicates the region for having input signal in frequency-tune frequency domain, i.e. (f in formula (8)k,γk) set；In formula (9) It respectively indicates along f dimension, along the inverse Fourier transform of γ dimension, Γ-1{ } is the inverse of operation Γ that stretch in formula (5)
Operation；
L is calculated firstsThe mean value and standard deviation of (f, γ) modulus value：
μ=E [| Ls(f,γ)|] (10)
Then the degree of bias for calculating LVD is as follows：
Step 4：Adding window starting point is constant, enablesWith N1As window function length again to signal adding window；
Step 5：Formula (3), (4), (5), (6), (9), (10), (11), (12) are successively executed to the signal after adding window, formula (12)
As a result it is denoted as P1；If P0≤1.2P1, then 6 are entered step, otherwise, is directly entered step 7；
Step 6：By N1Value be assigned to N0, adding window starting point is constant, subsequently into step 3；
Step 7：Adding window starting point is moved forward into N1/ 4 points are at most only moved to rising for input signal as new adding window starting point
Point, without departing from the range of input signal；Then with N1It is window function length from new adding window starting point adding window；N record is taken to execute step
Rapid 8 number, enables n=0；
Step 8：Enable n value increase by 1, to the signal after step 7 adding window successively execute formula (3), (4), (5), (6), (7), (8),
(9)；The result of recording (9) is
Step 9：According to the starting point and window function length N of the new adding window of step 71Determine adding window terminal；
If adding window terminal is not in input signal terminal, the adding window starting point for taking step 7 new 3N backward1It is used as at/4 points and adds next time
Window starting point, enters step 2；
If adding window terminal is completed in input signal terminal, all adding windows, 10 are entered step；
Step 10：The result for the formula (9) that each secondary adding window is obtainedIt is aggregated into a time-frequency figure in order, includes institute's having time
The processing result of sampled point.
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