本文借鉴 小墨学FPGA 的文章 《零基础学FPGA( 三十二) 写在京城,多级FIR半带滤波器的FPGA实现 》
地址是: http://bbs.elecfans.com/forum.php?mod=viewthread&tid=509022
假设我们的合成信号是由100,300和600hz的正弦波相加而成的信号,并将其进行8bit量化,初始采样频率为6400hz,现在我需要将采样信号降为800hz,并要求获得100hz有用信号,要求滤波器的通阻带容限为0.1,设计这样一个FIR半带滤波器。
clear all clc close all
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 通带截止频率近似3KHz,阻带截止频率近似5KHz fp = 100; % 要求最后一级滤波器的通带截止频率 fc = 300; % 要求最后一级滤波器的阻带截止频率 fs = 6400; %原始采样频率 fs_out = 800; % 要求降频后的采样频率 dev=0.1; %要求的滤波器通阻带容限 D=fs/fs_out; %求总抽取倍数 N=log2(D) ; %求滤波器级数 devi=dev/N; % 求每级滤波器通阻带容限
% 设计前2级半带滤波器 hin1 = firhalfband('minorder',fp/(fs/2),dev); %designs a lowpass minimum-order filter, % with passband edge fp. The peak ripple is constrained by the scalar dev. % This design uses the equiripple method.
hin2 = firhalfband('minorder',fp/(fs/4),dev); fid=fopen('E:\WORK\DRS6000_Q\MATLAB CODE\hin1.txt','wt'); fprintf(fid, '%d\n', hin1); fclose(fid);
fid=fopen('E:\WORK\DRS6000_Q\MATLAB CODE\hin2.txt','wt'); fprintf(fid, '%d\n', hin2); fclose(fid);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 设计最后一级最优低通滤波器 f = [fp,fc]; % 最优低通滤波器带宽 a = [1 0]; % 最优低通滤波器幅频特性,低通滤波器 devk = [devi,dev] ; % 要求的滤波器通阻带容限 mag = [1 1 0 0]; %最优滤波器幅度特性 fpm = [0 fp/((fs_out*2)/2) fc/((fs_out*2)/2) 1]; [n,wn,beta,firtype] = kaiserord(f,a,devk,fs_out*2); %调用函数求滤波器最小阶数 hin3 =firpm(n,fpm,mag); %调用函数设计最优滤波器 % freqz(hin3);
fid=fopen('E:\WORK\DRS6000_Q\MATLAB CODE\hin3.txt','wt'); fprintf(fid, '%d\n', hin3); fclose(fid);
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f1 = 100; % 信号频率 f2 = 300; % 信号频率 f3 = 600; % 信号频率 lengthy = 1024; n = 0:1:lengthy-1; t = n/fs; si = sin(2*pi*f1*t)+sin(2*pi*f2*t)+sin(2*pi*f3*t); figure plot(t,si); freq=linspace(-fs/2,fs/2,lengthy); figure plot(freq,fftshift( abs(fft(si)) )); xlim( [ 0, 1000 ] ); %设置横轴范围0~1000 xlabel('Frequency '); title('Magnitude spectrum of chirp signal'); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %滤波与抽取过程 F1_out = filter (hin1,1,si); %第一级半带滤波器 s1 = F1_out (1:2:length(F1_out)); %2倍抽取 F1_max = max (abs(F1_out));
F2_out = filter (hin2,1,s1); %第二级半带滤波器 s2 = F2_out (1:2:length(F2_out)); %2倍抽取
F3_out = filter (hin3,1,s2); %第二级半带滤波器 sout = F3_out (1:2:length(F3_out)); %2倍抽取 sout = sout/max(sout); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% lengths = lengthy/8; n1 = 0:1:lengths-1; t1=n1/fs; figure plot(t1,sout); freq=linspace(-fs/16,fs/16,lengths); figure plot(freq,fftshift( abs(fft(sout)) )); xlim( [ 0, 1000 ] ); %设置横轴范围0~1000 xlabel('Frequency '); title('Magnitude spectrum of chirp signal'); figure subplot(211) stem(si); subplot(212) stem(sout);
% % 前2级半带滤波器的幅频相应 % figure % impz(hin1); % figure % impz(hin2); % % h1 = mfilt.firdecim(2,hin1); % Create a polyphase decimator % h2 = mfilt.firdecim(2,hin2); % Create a polyphase decimator % freqz(h1); % freqz(h2);
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