matlab设计多阶MTI滤波器

matlab设计多阶MTI滤波器(equal PRF) 2011-11-22 14:43:59| 分类： 默认分类 | 标签：matlab radar |字号大中小 订阅 （一） 两脉冲对消器由H(z)可以直接得出时域中滤波器系数h(n) = 1 -1其中T就是PRI，fr = PRF，f/fr 是归一化频率fofr1 = 4; % multiplier of PRF is fofr1 fofr = 0:0.01:fofr1;Hf_ = 1 - exp(-1j*2*pi*fofr); % 2 pulses canceler hn = 1 -1max1 = max(Hf_);resp = abs(Hf_ ./ max(Hf_).2; % modular squaring standing for power spectrum density subplot(2,1,1)plot(fofr,abs(resp),k)xlabel (Normalized frequency - f/fr)ylabel( Amplitude response - Volts)gridresp=10.*log10(abs(resp)+eps);subplot(2,1,2)plot(fofr,resp,k);axis tight;grid;xlabel (Normalized frequency - f/fr);ylabel( Amplitude response - dB);（二） 三脉冲对消器fofr1 = 4; % multiplier of PRF is fofr1 fofr = 0:0.01:fofr1;Hf_ = 1 - 2*exp(-1j*2*pi*fofr) + exp(-2*1j*2*pi*fofr); % 3 pulses canceler hn = 1 -2 1resp = abs(Hf_ ./ max(Hf_).2; %modular squaring standing for power spectrum density subplot(2,1,1)plot(fofr,abs(resp),k)xlabel (Normalized frequency - f/fr)ylabel( Amplitude response - Volts)gridresp=10.*log10(abs(resp)+eps);subplot(2,1,2)plot(fofr,resp,k);axis tight;grid;xlabel (Normalized frequency - f/fr);ylabel( Amplitude response - dB);以上代码与MATLAB Simulations for Radar Systems Design - Bassem R. Mahafza提供的一下代码执行结果完全相同,但是该书中没有指出以上等PRF下的MTI滤波器设计的实质。fofr1 = 4;fofr = 0:0.01:fofr1;arg1 = pi .* fofr;resp = 4.0 .* (sin(arg1).2);max1 = max(resp);resp = resp ./ max1;resp2 = resp .* resp;subplot(2,1,1);plot(fofr,resp,k-,fofr, resp2,k);ylabel (Amplitude response - Volts)resp2 = 20. .* log10(resp2+eps);resp1 = 20. .* log10(resp+eps);subplot(2,1,2)plot(fofr,resp1,k-,fofr,resp2,k); axis tight;legend (single canceler,double canceler)xlabel (Normalized frequency f/fr)ylabel (Amplitude response - dB)（三） 4脉冲对消器，hn中有4个抽头系数fofr1 = 4; % multiplier of PRF is fofr1 fofr = 0:0.01:fofr1;Hf_ = 1 - 3*exp(-1j*2*pi*fofr) + 3*exp(-2*1j*2*pi*fofr) - exp(-3*1j*2*pi*fofr); % 4 pulses canceler hn = 1 -3 3 -1resp = abs(Hf_ ./ max(Hf_).2; % modular squaringsubplot(2,1,1)plot(fofr,abs(resp),k)xlabel (Normalized frequency - f/fr)ylabel( Amplitude response - Volts)gridresp=10.*log10(abs(resp)+eps);subplot(2,1,2)plot(fofr,resp,k);axis tight;grid;xlabel (Normalized frequency - f/fr);ylabel( Amplitude response - dB);结论：可见单一PRF雷达的n脉冲MTI滤波器是个FIR滤波器，其hn的元素由 H(z) = ( 1 - z(-1).(n - 1)进行多项式展开得到。以上其实是个二项式展开的系数注意(1+X)a中展开后是X的升幂的，而H(z)中用的是降幂的，依次为z的负幂次，故按上面的二项式系数算的MTI滤波器系数w应该fliplr一下（四） N脉冲对消器，hn中有N个抽头系数close all; clear; fofr1 = 4; % multiplier of PRF is fofr1 fofr = 0:0.01:fofr1;N = 15; % N pulses cancelernegativePwr = -0:N-1;for k = 0:N-1w(k+1) = (-1).(N-1 - k).*nchoosek(N - 1,k);endw = fliplr(w); % change positive power to negative powerHf_ = conj(w)*exp(1j*2*pi*negativePwr*fofr);resp = abs(Hf_ ./ max(Hf_).2; % modular squaring standing for power spectrum density subplot(2,1,1)plot(fofr,abs(resp),k)xlabel (Normalized frequency - f/fr)ylabel( Amplitude response - Volts)gr