CN106208967A - A kind of multi-components real number linear FM signal converter technique based on chockstone fractal transform - Google Patents

Abstract

The invention belongs to time frequency analysis field in signal processing, be specifically related to a kind of multi-components real number linear FM signal converter technique based on chockstone fractal transform.The present invention is directed to multi-components real number LFM signal convert, the thought using chockstone fractal transform improves the distribution of wiener Willie, the time quantum of signal auto-correlation function is carried out time dimension stretching, make its with both retardations unwrapping, thus reach signal autocorrelation item can coherent accumulation, the purpose of suppressing crossterms.Transformation results to multi-components real number LFM signal is a mid frequency frequency modulation rate combination planar, and signal is distributed as spike on that plane from item energy.This peak amplitude corresponds to Time Domain Amplitude, and this spike place plane coordinates corresponds to mid frequency and frequency modulation rate, is derived from each component parameters value of signal.The present invention is simultaneously achieved that signal is high from item energy accumulating, converts without obvious cross term and real number field, and performance is better than prior art.

Description

A kind of multi-components real number linear FM signal converter technique based on chockstone fractal transform

Technical field

The invention belongs to time frequency analysis field in signal processing, be specifically related to a kind of multi-components based on chockstone fractal transform real Number linear FM signal converter technique.

Background technology

When reception of wireless signals end processes, in order to estimate and detect linear frequency modulation (LFM) signal, usually require that and used Technology possesses high signal energy aggregation, requires that cross term is of a sufficiently low simultaneously, prevents interference from item.And for real number signal, also Require that technology used is real number field conversion, prevent imaginary number territory distracter from occurring.Prior art mainly has fourier cosine transform class Such as discrete cosine transform, time-frequency cosine transform class such as fraction cosine transform.But owing to they are linear transformation, to LFM signal Energy accumulating the most poor.The signal of bilinear transformation is better than linear transformation from item energy accumulating, such as wiener-Willie distribution (WVD), can reach the highest concentration class.But there are two problems in WVD, one is to produce strong cross term, and then interference letter Number from the estimation of item and detection；Two be WVD be complex transform, be not suitable for real number signal.The multiple improvement conversion of WVD is as smooth Pseudo-WVD etc., because it is by window function effects, all cannot take into account from item energy accumulating and cross term problem in perfection.Table 1 is summed up The feature of prior art, it can be seen that current shortage meets three kinds of technology required simultaneously, and the highest signal is from item energy accumulating Property, without cross term, real number field conversion.

Table 1 prior art is for multi-components real number LFM signal processing feature

Summary of the invention

For above-mentioned existing problems or deficiency, for meeting high signal from item energy accumulating, without cross term, real number field simultaneously Conversion these three requirement, the invention provides a kind of multi-components real number based on chockstone fractal transform (keystone transform) Linear frequency modulation LFM signal converter technique.

Being somebody's turn to do multi-components real number LFM signal converter technique based on chockstone fractal transform, concrete technical scheme comprises the steps.

Step 1, input signal is carried out parameter autocorrelation calculation；

Input signal is multi-components real number LFM signal, is expressed as:

$s\left(t\right)=\underset{n=1}{\overset{N}{\Σ}}{A}_{n}cos(2{\mathrm{\πf}}_{n}t+{\mathrm{\π\γ}}_n{t}^2),---\left(1\right)$

Wherein N is this component of signal sum, A_n、f_nAnd γ_nRepresent the amplitude of the n-th component, mid frequency and frequency modulation respectively Rate；Based on wiener-Willie distribution WVD thought, formula (1) being carried out parameter auto-correlation function calculating, its result is:

$R_s=s(t+\frac{\mathrm{\τ}+1}{2})s(t-\frac{\mathrm{\τ}+1}{2})=U+Q+R_c=\frac{1}{2}\underset{n=1}{\overset{N}{\Σ}}{A}_n^{2}cos\left(2{\mathrm{\πf}}_n\right(\mathrm{\τ}+1)+2{\mathrm{\π\γ}}_n(\mathrm{\τ}+1\left)t\right)+Q+R_c,---\left(2\right)$

Wherein τ is retardation, U be the constant in signal autocorrelation item i.e. from item constant, Q is the high-order in auto-correlation item , R_cFor the cross term between different components.

Step 2, based on chockstone fractal transform thought, by the time quantum in the phase place of U in formula (2) and retardation unwrapping, right Parameter auto-correlation function R_sCarry out time dimension stretching:

If t_sFor the time quantum after yardstick time i.e. stretching, make t_s=(τ+1) t, parameter auto-correlation function R_sBecome:

${\stackrel{\‾}{R}}_s=\frac{1}{2}\underset{n=1}{\overset{N}{\Σ}}{A}_n^{2}cos\left(2{\mathrm{\πf}}_n\right(\mathrm{\τ}+1)+2{\mathrm{\π\γ}}_n{t}_s)+\stackrel{\‾}{Q}+{\stackrel{\‾}{R}}_c,---\left(3\right)$

WhereinFor scale parameter auto-correlation function；From formula (3) Section 1, the time quantum in phase place is with retardation Through unwrapping；

Described to parameter auto-correlation function R_sCarry out time dimension stretching to pass through: for the interpolation method of time dimension t, from Dissipate Fourier transformation-inverse Fourier transform or yardstick Fourier transformation-inverse Fourier transform completes.

Step 3, carry out twice fourier cosine transform, and seek absolute value:

Fourier cosine transform (FCT) is defined as:

$S_{FCT}\left(f\right)={\∫}_0^{\mathrm{\∞}}s\left(t\right)cos\left(2\mathrm{\π}ft\right)dt.---\left(4\right)$

To scale parameter auto-correlation function i.e. formula (3) successively along τ dimension, along t_sDimension carries out fourier cosine transform, and asks exhausted To value, obtain final result:

$F_s(f,\mathrm{\γ})=|\frac{1}{8}cos\left(2\mathrm{\π}f\right)\underset{n=1}{\overset{N}{\Σ}}{A}_n^2\mathrm{\δ}(f-f_n)\mathrm{\δ}(\mathrm{\γ}-{\mathrm{\γ}}_n)+C_{t_s}\{C_{\mathrm{\τ}}\{\stackrel{\‾}{Q}+{\stackrel{\‾}{R}}_c\}\left\}\right|,---\left(5\right)$

Wherein C_τ{·}、Represent respectively along τ dimension, along t_sDimension fourier cosine transform；Formula (5) Section 1 represents signal Each component energy is gathered in the (f of frequency-tune frequency plane with delta-function form_n,γ_n) point on；Section 2 be from item higher order term and The operation result of cross term.

Formula (5) Section 2 is calculated, because of after step 2 time dimension is flexible, from item higher order term and the phase of cross term Position does not the most possess coherence, it is impossible to being carried out coherent accumulation by fourier cosine transform, compared with Section 1, Section 2 is sufficiently small； Ignoring Section 2, formula (5) is further represented as:

$F_s(f,\mathrm{\γ})\≈\underset{n=1}{\overset{N}{\Σ}}{F}_{s_n}(f,\mathrm{\γ})\≈\frac{1}{8}\left|cos\left(2\mathrm{\π}f\right)\right|\underset{n=1}{\overset{N}{\Σ}}{A}_n^2\mathrm{\δ}(f-f_n)\mathrm{\δ}(\mathrm{\γ}-{\mathrm{\γ}}_n).---\left(6\right)$

The present invention is directed to multi-components real number LFM signal convert.The thought using chockstone fractal transform improves WVD conversion, The time quantum of signal auto-correlation function is carried out time dimension stretching so that it is with both retardations unwrapping, thus reach letter Number auto-correlation item can coherent accumulation (improving from item energy accumulating), cross term cannot the mesh of coherent accumulation (suppressing crossterms) 's.The present invention is a mid frequency-frequency modulation rate combination planar to the transformation results of multi-components real number LFM signal, and signal is from item Energy is distributed as spike on that plane.This peak amplitude corresponds to Time Domain Amplitude, during this spike place plane coordinates corresponds to Frequency of heart and frequency modulation rate, be derived from each component parameters value of signal.Based on the present invention seen from formula (6) have progressive linearly.

The first step of the present invention, based on WVD thought, belongs to bilinear transformation.But final result is approximately without cross term, i.e. simultaneously The advantage possessing linear transformation.Therefore in the process for multi-components real number LFM signal, with bilinear transformation with linear The advantage of conversion.From item energy accumulating and approximate the advantage without cross term owing to the present invention possesses high signal, can be applicable to strong Noise estimated and detects signal, being particularly well-suited to negative signal to noise ratio environment.

In sum, the present invention is simultaneously achieved signal and (reaches approximately the highest gathering of WVD theory from item energy accumulating height Degree), convert without obvious cross term (sufficiently small negligible, also known as progressive linear) and real number field.

Accompanying drawing explanation

Fig. 1 is embodiment concrete technical scheme flow chart；

Fig. 2 (a), (b), (c) are respectively embodiment, fraction cosine transform and discrete cosine transform to comprising three components Real number LFM signal convert after scattergram；

Fig. 3 (a), (b) are respectively embodiment and the signal polluted by white Gaussian noise is become by fraction cosine transform Scattergram (SNR=-2dB) after changing.

Detailed description of the invention

Below in conjunction with the accompanying drawings and detailed description of the invention the invention will be further described.

Under computer MATLAB environment, producing emulation signal according to formula (1) is: component number N=3；Amplitude A_nIt is 1；Mid frequency is f₁=47.5Hz, f₂=27Hz, f₃=26Hz；Frequency modulation rate is γ₁=25Hz/s, γ₂=14Hz/s, γ₃= 32Hz/s；Sample frequency f_s=256Hz, signal sampling points N_s=512.To parameter auto-correlation function R in step 2_sThe time of carrying out Dimension stretching by: yardstick Fourier transformation-inverse Fourier transform completes, such as second dotted line frame in Fig. 1.

Fig. 2 (a), (b), (c) represent that this signal is carried out by the present embodiment, fraction cosine transform, discrete cosine transform respectively Distribution after conversion.Thus figure is visible: 1) signal parameter cannot be estimated by discrete cosine transform, because this signal is LFM Signal, discrete cosine transform is not suitable for the time dependent signal of this frequency；2) fraction cosine transform is by signal three points Amount is all collected as spike, and obtains respective frequency and frequency modulation rate from spike coordinate, but the noise spot outside spike point is stronger；3) Three components are all collected as spike by the present invention equally, obtain frequency and frequency modulation rate from spike coordinate, and assemble performance higher than dividing Number cosine transform (noise spot outside spike point is the most weak).Because the present invention has the advantage aggregation of bilinear transformation Height, and fraction cosine transform is that linear transformation concentration class is medium.

Fig. 3 (a), (b) represent that the present embodiment, the fraction cosine transform signal to being polluted by white Gaussian noise is carried out respectively Distribution after conversion, its input signal-to-noise ratio SNR=-2dB, SNR are defined as 10log₁₀(signal power/noise power), now believes Number power is less than noise power.As seen from the figure: 1) under very noisy (negative signal to noise ratio, i.e. noise power are more than signal power), divide Number cosine transform cannot detect signal peaks；2) present invention remains able to detect the important spike of this signal.

As fully visible: contrasted by simulation result, processing multi-components real number LFM signal, the present invention is at signal energy Amount aggregation aspect is better than fraction cosine transform and discrete cosine transform, and without obvious cross term.Under very noisy, signal is entered During row detection, anti-noise ability of the present invention is better than fraction cosine transform.

Claims (2)

1. a multi-components real number linear FM signal converter technique based on chockstone fractal transform, specifically includes following steps:

Step 1, input signal is carried out parameter autocorrelation calculation；

Input signal is multi-components real number linear frequency modulation LFM signal, is expressed as:

$s\left(t\right)=\underset{n=1}{\overset{N}{\Σ}}{A}_{n}cos(2{\mathrm{\πf}}_{n}t+{\mathrm{\π\γ}}_n{t}^2),---\left(1\right)$

Wherein N is this component of signal sum, A_n、f_nAnd γ_nRepresent the amplitude of the n-th component, mid frequency and frequency modulation rate respectively； Based on wiener-Willie distribution WVD thought, formula (1) being carried out parameter auto-correlation function calculating, its result is:

$R_s=s(t+\frac{\mathrm{\τ}+1}{2})s(t-\frac{\mathrm{\τ}+1}{2})=U+Q+R_c=\frac{1}{2}\underset{n=1}{\overset{N}{\Σ}}{A}_n^{2}cos\left(2{\mathrm{\πf}}_n\right(\mathrm{\τ}+1)+2{\mathrm{\π\γ}}_n(\mathrm{\τ}+1\left)t\right)+Q+R_c,---\left(2\right)$

Wherein τ is retardation, U be the constant in signal autocorrelation item i.e. from item constant, Q is the higher order term in auto-correlation item, R_cFor Cross term between different components；

Step 2, based on chockstone fractal transform thought, by the time quantum in the phase place of U in formula (2) and retardation unwrapping, to parameter Auto-correlation function R_sCarry out time dimension stretching:

If t_sFor the time quantum after yardstick time i.e. stretching, make t_s=(τ+1) t, parameter auto-correlation function R_sBecome:

${\stackrel{\‾}{R}}_s=\frac{1}{2}\underset{n=1}{\overset{N}{\Σ}}{A}_n^{2}cos\left(2{\mathrm{\πf}}_n\right(\mathrm{\τ}+1)+2{\mathrm{\π\γ}}_n{t}_s)+\stackrel{\‾}{Q}+{\stackrel{\‾}{R}}_c,---\left(3\right)$

WhereinFor scale parameter auto-correlation function；

Step 3, carry out twice fourier cosine transform, and seek absolute value:

Fourier cosine transform FCT is defined as:

$S_{FCT}\left(f\right)={\∫}_0^{\mathrm{\∞}}s\left(t\right)cos\left(2\mathrm{\π}ft\right)dt.---\left(4\right)$

To scale parameter auto-correlation function i.e. formula (3) successively along τ dimension, along t_sDimension carries out fourier cosine transform, and seeks absolute value, Final result:

$F_s(f,\mathrm{\γ})=|\frac{1}{8}cos\left(2\mathrm{\π}f\right)\underset{n=1}{\overset{N}{\Σ}}{A}_n^2\mathrm{\δ}(f-f_n)\mathrm{\δ}(\mathrm{\γ}-{\mathrm{\γ}}_n)+C_{t_s}\{C_{\mathrm{\τ}}\{\stackrel{\‾}{Q}+{\stackrel{\‾}{R}}_c\}\left\}\right|,---\left(5\right)$

Wherein C_τ{·}、Represent respectively along τ dimension, along t_sDimension fourier cosine transform；Formula (5) Section 1 represents each point of signal Energy is gathered in the (f of frequency-tune frequency plane with delta-function form_n,γ_n) point on；Section 2 is from item higher order term and intersection The operation result of item；

Formula (5) Section 2 is calculated, because of after step 2 time dimension is flexible, equal from the phase place of item higher order term and cross term Not possessing coherence, it is impossible to carried out coherent accumulation by fourier cosine transform, compared with Section 1, Section 2 is sufficiently small；Ignore Section 2, formula (5) is further represented as:

$F_s(f,\mathrm{\γ})\≈\underset{n=1}{\overset{N}{\Σ}}{F}_{s_n}(f,\mathrm{\γ})\≈\frac{1}{8}\left|cos\left(2\mathrm{\π}f\right)\right|\underset{n=1}{\overset{N}{\Σ}}{A}_n^2\mathrm{\δ}(f-f_n)\mathrm{\δ}(\mathrm{\γ}-{\mathrm{\γ}}_n)---\left(6\right).$

2. multi-components real number linear FM signal converter technique based on chockstone fractal transform as claimed in claim 1, its feature exists In: to parameter auto-correlation function R in described step 2_sCarrying out time dimension stretching method is: for the interpolation side of time dimension t Method, discrete Fourier transform-inverse Fourier transform or yardstick Fourier transformation-inverse Fourier transform complete.