CN101610066A - A kind of white noise amplitude compensation method - Google Patents

Abstract

A kind of white noise amplitude compensation method belongs to the random signal source domain, has solved the smooth problem of insufficient amplitude in the white noise vocal cords.The step of this compensation method: step 1, the power spectral density of the digital white noise that calculating m sequencer produces.Step 2, the power spectral density of white noise are exported the simulating the white noise frequency spectrum by FIR filter, digital to analog converter and filter, and the inverse of this frequency spectrum is exactly the penalty function of white noise at frequency domain.Step 3 changes to time domain with the penalty function of frequency domain.Step 4 with the time-domain function of the penalty function of time domain and FIR filter convolution mutually, obtains final white noise penalty function.This method can compensate the white noise power spectrum amplitude 3dB that the m sequence produces.White noise is widely used in fields such as communication, navigation, radar, communication channel test and electronic countermeasures.

Description

A kind of white noise amplitude compensation method

Technical field

The present invention relates to a kind of white noise amplitude compensation method, belong to the random signal source domain.

Background technology

White noise has a wide range of applications in fields such as communication, navigation, radar, communication channel test and electronic countermeasures.Many at present employing m sequences produce digital white noise sequence, the m sequence is a kind of of pseudo random sequence, it is the abbreviation of maximum length linear shift register sequence, it has and the similarly sharp-pointed autocorrelation of random signal, and has a not available regularity of random signal, and simple in structure, it is convenient to realize.Existing white noise generator comprises: m sequencer, FIR filter, digital to analog converter and filter.The output amplitude of the white noise that existing white noise generator produces has the decline of about 9dB, and this decline has influenced the flatness of output noise.

Summary of the invention

In order to overcome deficiency of the prior art, the invention provides a kind of compensation method of white noise amplitude, this method can compensate the white noise power spectrum amplitude 3dB that the m sequence produces.

The technical scheme of a kind of white noise amplitude compensation method provided by the invention:

The step of this compensation method:

Step 1, the power spectral density of the digital white noise that the m sequencer produces:

$H_0\left(\mathrm{\ω}\right)=\frac{{\left(\sin \frac{{\mathrm{\ωT}}_0}{2}\right)}^2}{{\left(\frac{{\mathrm{\ωT}}_0}{2}\right)}^2}$

In the formula: T ₀Be the sampling period, ω is the frequency of m sequence;

Step 2, the power spectral density of white noise are exported the simulating the white noise frequency spectrum by FIR filter, digital to analog converter and filter, and the inverse of this frequency spectrum is exactly the penalty function of white noise at frequency domain:

$H\left(\mathrm{\ω}\right)=\frac{{\left(\frac{{\mathrm{\ωT}}_0}{2}\right)}^3}{{\left(\sin \frac{{\mathrm{\ωT}}_0}{2}\right)}^3}$

Step 3 changes to time domain with H (ω) $h\left(n\right)=\frac{1}{2\mathrm{\π}}{\∫}_{-\mathrm{\π}}^{\mathrm{\π}}H\left(\mathrm{\ω}\right)e^{\mathrm{j\ωn}}\mathrm{d\ω},$ H (n) is exactly the time domain compensation function of white noise;

Step 4 is with the time domain impulse response h of h (n) and FIR filter _FIR(n) phase convolution obtains the white noise penalty function unit in conjunction with the FIR filter;

Step 5, this white noise penalty function unit is realized by FPGA.

FPGA: be used to produce digital white noise sequence.

Digital to analog converter: convert the white noise sequence after the compensation of FPGA output to the simulating the white noise sequence, its output is the simulating the white noise sequence.

Filter: the simulating the white noise of digital to analog converter output is carried out filtering, remove the unwanted frequency component, output is final simulating the white noise.

Beneficial effect of the present invention: solved the smooth problem of insufficient amplitude in the white noise vocal cords, compensation magnitude is 3dB.

Description of drawings

Fig. 1 is the schematic block diagram of white noise amplitude compensation method of the present invention.

Embodiment

The present invention is described in detail below in conjunction with the drawings and specific embodiments.

Fig. 1 is the device schematic block diagram that white noise compensation method of the present invention is used.

As shown in Figure 1, the device that the white noise compensation method is used comprises: FPGA is field programmable gate array, or uses DSP (Digital Signal Processing) to realize digital to analog converter, filter.Wherein, FPGA comprises m sequence generating unit, penalty function unit and FIR filter.

A kind of step of white noise amplitude compensation method:

Step 1, the power spectral density of the digital white noise that the m sequencer produces:

$H_0\left(\mathrm{\ω}\right)=\frac{{\left(\sin \frac{{\mathrm{\ωT}}_0}{2}\right)}^2}{{\left(\frac{{\mathrm{\ωT}}_0}{2}\right)}^2}$

In the formula: T ₀Be the sampling period, ω is the frequency of m sequence;

Step 2, the power spectral density of white noise are exported the simulating the white noise frequency spectrum by FIR filter, digital to analog converter and filter, and the inverse of this frequency spectrum is exactly the penalty function of white noise at frequency domain:

$H\left(\mathrm{\ω}\right)=\frac{{\left(\frac{{\mathrm{\ωT}}_0}{2}\right)}^3}{{\left(\sin \frac{{\mathrm{\ωT}}_0}{2}\right)}^3}$

Step 3 changes to time domain with H (ω) $h\left(n\right)=\frac{1}{2\mathrm{\π}}{\∫}_{-\mathrm{\π}}^{\mathrm{\π}}H\left(\mathrm{\ω}\right)e^{\mathrm{j\ωn}}\mathrm{d\ω},$ H (n) is exactly the time domain compensation function of white noise;

Step 4 is with the time domain impulse response h of h (n) and FIR filter _FIR(n) phase convolution obtains the white noise penalty function in conjunction with the FIR filter;

Step 5, this white noise penalty function is realized by FPGA.

Realize the detailed description of white noise compensation method

In m sequence generating unit of the present invention, produce digital white noise sequence by equation (1) feedback shift register.

$a_n=c_{n-1}{a}_{n-1}\⊕c_{n-2}{a}_{n-2}\⊕c_{n-3}{a}_{n-3}\⊕\·\·\·\⊕c_0{a}_0=\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}{c}_i{a}_i$

Wherein, a _iRepresent i feedback shift register, c _iThe coefficient of representing i feedback shift register, the value of i are from 0 to n-1, and n is the positive integer greater than 2.

The auto-correlation function of m sequence can be expressed as:

$\mathrm{\ρ}\left(\mathrm{\τ}\right)=\mathrm{\ρ}\left({\mathrm{jT}}_0\right)=\left\{\begin{array}{cc}1& j=0\\ -1/m& j\≠0\end{array}\right.$

Wherein m is the cycle of sequence, T ₀Be the sampling interval, j is the number of m sequence.

The auto-correlation function of signal and power spectral density constitute a pair of Fourier transform, so the auto-correlation function of m sequence process Fourier transform, and its power spectral density is:

$P_s\left(\mathrm{\ω}\right)=\frac{m+1}{m^2}\·{\sin c}^2\left(\frac{{\mathrm{\ωT}}_0}{2}\right)\·\underset{n\≠0}{\overset{+\∞}{\underset{n=-\∞}{\mathrm{\Σ}}}}\mathrm{\δ}(\mathrm{\ω}-\frac{2\mathrm{\πn}}{{\mathrm{mT}}_0})+\frac{1}{m^2}\mathrm{\δ}\left(\mathrm{\ω}\right)$

Know by formula (4), when the cycle of m sequence is very big,

Function is minimum at interval, and then its power spectral density can be similar to becomes continuous function, is expressed as:

$H_0\left(\mathrm{\ω}\right)=\frac{{\left(\sin \frac{{\mathrm{\ωT}}_0}{2}\right)}^2}{{\left(\frac{{\mathrm{\ωT}}_0}{2}\right)}^2}$

Wherein, T ₀Be the sampling period, ω is the frequency of m sequence.

Digital to analog converter can equivalence claim a kind of zero-order holder, so digital white noise becomes the process of analog signal by digital to analog converter, can regard that then the impulse response function of this zero-order holder is by a zero-order holding circuit as

$h\left(t\right)=\mathrm{Rect}\left(\frac{t-T_s/2}{T_s}\right)$

Wherein, T _sBe the sampling interval of digital to analog converter, its value equals m sequential sampling period T ₀Therefore, the frequency response function of digital to analog converter is:

$H_{\mathrm{DA}}\left(\mathrm{\ω}\right)=T_0\frac{\sin \left(\frac{{\mathrm{\ωT}}_0}{2}\right)}{\frac{{\mathrm{\ωT}}_0}{2}}{e}^{-\mathrm{j\ω}{T}_0/2}$

The output of then desirable FIR low pass filter by the frequency spectrum of the output analog signal of digital to analog converter is:

$H_{\mathrm{out}}\left(\mathrm{\ω}\right)=H_0\left(\mathrm{\ω}\right)H_{\mathrm{DA}}\left(\mathrm{\ω}\right)=T_0\frac{{\left(\sin \frac{{\mathrm{\ωT}}_0}{2}\right)}^3}{{\left(\frac{{\mathrm{\ωT}}_0}{2}\right)}^3}{e}^{-\mathrm{j\ω}{T}_0/2}$

Here it is by the frequency response of compensating signal, and then penalty function should be:

$H_{\mathrm{offset}}\left(\mathrm{\ω}\right)=\frac{1}{H_{\mathrm{out}}\left(\mathrm{\ω}\right)}=\frac{{\left(\frac{{\mathrm{\ωT}}_0}{2}\right)}^3}{T_0{\left(\sin \frac{{\mathrm{\ωT}}_0}{2}\right)}^3}{e}^{\mathrm{j\ω}{T}_0/2}$

Can ignore the phase factor in the formula

With invariant T ₀, obtain:

$H_{\mathrm{offset}}\left(\mathrm{\ω}\right)=\frac{{\left(\frac{{\mathrm{\ωT}}_0}{2}\right)}^3}{{\left(\sin \frac{{\mathrm{\ωT}}_0}{2}\right)}^3}$

The frequency response of FIR low pass filter is:

H _low＝1，-ω _c≤ω≤ω _c

ω wherein _cIt is cut-off frequency.The penalty function that then carries out after the low-pass filtering is

$H\left(\mathrm{\ω}\right)=H_{\mathrm{offset}}{H}_{\mathrm{low}}=\frac{{\left(\frac{{\mathrm{\ωT}}_0}{2}\right)}^3}{{\left(\sin \frac{{\mathrm{\ωT}}_0}{2}\right)}^3},-{\mathrm{\ω}}_c\≤\mathrm{\ω}\≤{\mathrm{\ω}}_c$

ω is by the scope decision of FIR filter.

Penalty function is regarded a filter as, and it is carried out the impulse response h (n) that Fourier inversion obtains this filter.

FIR low pass filter in the penalty function realizes that with the hamming window its cut-off frequency is with identical by penalty function, and its impulse response can be used h _Ham(n) expression.Time-domain function h with h (n) and FIR filter _FIR(n) phase convolution h (n)=h (n) * h _Ham(n), wherein " * " represents convolution.

Claims (1)

1. a white noise amplitude compensation method is characterized in that, the step of this compensation method:

Step 1, the power spectral density of the digital white noise that the m sequencer produces:

$H_0\left(\mathrm{\ω}\right)=\frac{{\left(\sin \frac{\mathrm{\ω}{T}_0}{2}\right)}^2}{{\left(\frac{\mathrm{\ω}{T}_0}{2}\right)}^2}$

In the formula: T ₀Be the sampling period, ω is the frequency of m sequence;

Step 2, the power spectral density of white noise are exported the simulating the white noise frequency spectrum by FIR filter, digital to analog converter and filter, and the inverse of this frequency spectrum is exactly the penalty function of white noise at frequency domain:

$H\left(\mathrm{\ω}\right)=\frac{{\left(\frac{\mathrm{\ω}{T}_0}{2}\right)}^3}{{\left(\sin \frac{\mathrm{\ω}{T}_0}{2}\right)}^3}$

Step 3 changes to time domain with H (ω) $h\left(n\right)=\frac{1}{2\mathrm{\π}}{\∫}_{-\mathrm{\π}}^{\mathrm{\π}}H\left(\mathrm{\ω}\right)e^{\mathrm{j\ωn}}\mathrm{d\ω},$ H (n) is exactly the time domain compensation function of white noise;

Step 4 is with the time-domain function h of h (n) and FIR filter _FIR(n) phase convolution obtains the white noise penalty function in conjunction with the FIR filter;

Step 5, this white noise penalty function is realized by FPGA.

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