代码:
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ %% Output Info about this m-file fprintf(' *********************************************************** '); fprintf(' <DSP using MATLAB> Problem 7.33 '); banner(); %% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ws1 = 0.44*pi; wp1 = 0.49*pi; wp2 = 0.51*pi; ws2=0.56*pi; As = 30; Rp = 1.0; [delta1, delta2] = db2delta(Rp, As) weights = [1 delta2/delta1 1] deltaH = max([delta1,delta2]); deltaL = min([delta1,delta2]); %Dw = min((wp1-ws1), (ws2-wp2)); %M = ceil((-20*log10((delta1*delta2)^(1/2)) - 13) / (2.285*Dw) + 1) M = 51; f = [ 0 ws1 wp1 wp2 ws2 pi]/pi; m = [ 0 0 1 1 0 0]; h = firpm(M-1, f, m, weights); [db, mag, pha, grd, w] = freqz_m(h, [1]); delta_w = 2*pi/1000; ws1i = floor(ws1/delta_w)+1; wp1i = floor(wp1/delta_w)+1; wp2i = floor(wp2/delta_w)+1; ws2i = floor(ws2/delta_w)+1; Asd = -max(db(1:ws1i)) %[Hr, ww, a, L] = Hr_Type1(h); [Hr,omega,P,L] = ampl_res(h); l = 0:M-1; %% ------------------------------------------------- %% Plot %% ------------------------------------------------- figure('NumberTitle', 'off', 'Name', 'Problem 7.33 Parks-McClellan Method') set(gcf,'Color','white'); subplot(2,2,1); stem(l, h); axis([-1, M, -0.1, 0.1]); grid on; xlabel('n'); ylabel('h(n)'); title('Actual Impulse Response, M=51'); set(gca,'XTickMode','manual','XTick',[0,M-1]) set(gca,'YTickMode','manual','YTick',[-0.3:0.1:0.4]) subplot(2,2,2); plot(w/pi, db); axis([0, 1, -80, 10]); grid on; xlabel('frequency in pi units'); ylabel('Decibels'); title('Magnitude Response in dB '); set(gca,'XTickMode','manual','XTick',f) set(gca,'YTickMode','manual','YTick',[-60,-30,0]); set(gca,'YTickLabelMode','manual','YTickLabel',['60';'30';' 0']); subplot(2,2,3); plot(omega/pi, Hr); axis([0, 1, -0.2, 1.2]); grid on; xlabel('frequency in pi nuits'); ylabel('Hr(w)'); title('Amplitude Response'); set(gca,'XTickMode','manual','XTick',f) set(gca,'YTickMode','manual','YTick',[0,1]); delta_w = 2*pi/1000; subplot(2,2,4); axis([0, 1, -deltaH, deltaH]); sb1w = omega(1:1:ws1i)/pi; sb1e = (Hr(1:1:ws1i)-m(1)); %sb1e = (Hr(1:1:ws1i)-m(1))*weights(1); pbw = omega(wp1i:wp2i)/pi; pbe = (Hr(wp1i:wp2i)-m(3)); %pbe = (Hr(wp1i:wp2i)-m(3))*weights(2); sb2w = omega(ws2i:501)/pi; sb2e = (Hr(ws2i:501)-m(5)); %sb2e = (Hr(ws2i:501)-m(5))*weights(3); plot(sb1w,sb1e,pbw,pbe,sb2w,sb2e); grid on; xlabel('frequency in pi units'); ylabel('Hr(w)'); title('Error Response'); %title('Weighted Error'); set(gca,'XTickMode','manual','XTick',f); %set(gca,'YTickMode','manual','YTick',[-deltaH,0,deltaH]); figure('NumberTitle', 'off', 'Name', 'Problem 7.33 AmpRes of h(n), Parks-McClellan Method') set(gcf,'Color','white'); plot(omega/pi, Hr); grid on; %axis([0 1 -100 10]); xlabel('frequency in pi units'); ylabel('Hr'); title('Amplitude Response'); set(gca,'YTickMode','manual','YTick',[-0.0334,0, 0.0334,1,1.057]); %set(gca,'YTickLabelMode','manual','YTickLabel',['90';'40';' 0']); set(gca,'XTickMode','manual','XTick',[0,0.44,0.49,0.51,0.56,1]); %% ------------------------------------------------------- %% Input is given, and we want the Output %% ------------------------------------------------------- num = 200; mean_val=0; variance=1; x2 = mean_val + sqrt(variance)*randn(num,1); n_x2 = 0:num-1; x_axis = min(x2):0.02:max(x2); figure('NumberTitle', 'off', 'Name', 'Problem 7.33 hist'); set(gcf,'Color','white'); %hist(x1,x_axis); hist(x2,100); title('Gaussian Distributed Random Numbers (using hist)'); xlabel('n'); ylabel('x2(n)'); grid on; figure('NumberTitle', 'off', 'Name', 'Problem 7.33 bar'); set(gcf,'Color','white'); %[counts,binlocal] = hist(x1, x_axis); [counts,binlocal] = hist(x2, 100); counts = counts/num; bar(binlocal, counts, 1); title('Gaussian Distributed Random Numbers (using bar)'); xlabel('n'); ylabel('x2(n)'); grid on; % Input n_x3 = [0:1:num-1]; x3 = 2*cos(n_x3*pi/2); [x,n_x] = sigadd (x2, n_x2, x3, n_x3); y = filter(h, 1, x); n_y = n_x; figure('NumberTitle', 'off', 'Name', 'Problem 7.33 Input[x(n)] and Output[y(n)]'); set(gcf,'Color','white'); subplot(2,1,1); stem(n_x, x); axis([-1, 200, -5, 5]); grid on; xlabel('n'); ylabel('x(n)'); title('Input Response, Length=200'); subplot(2,1,2); stem(n_y, y); axis([-1, 200, -3, 3]); grid on; xlabel('n'); ylabel('y(n)'); title('Output Response'); % --------------------------- % DTFT of x and y % --------------------------- MM = 500; [X, w1] = dtft1(x, n_x, MM); [Y, w1] = dtft1(y, n_y, MM); magX = abs(X); angX = angle(X); realX = real(X); imagX = imag(X); magY = abs(Y); angY = angle(Y); realY = real(Y); imagY = imag(Y); figure('NumberTitle', 'off', 'Name', 'Problem 7.33 DTFT of Input[x(n)]') set(gcf,'Color','white'); subplot(2,2,1); plot(w1/pi,magX); grid on; %axis([0,2,0,15]); title('Magnitude Part'); xlabel('frequency in pi units'); ylabel('Magnitude |X|'); subplot(2,2,3); plot(w1/pi, angX/pi); grid on; axis([0,2,-1,1]); title('Angle Part'); xlabel('frequency in pi units'); ylabel('Radians/pi'); subplot(2,2,2); plot(w1/pi, realX); grid on; title('Real Part'); xlabel('frequency in pi units'); ylabel('Real'); subplot(2,2,4); plot(w1/pi, imagX); grid on; title('Imaginary Part'); xlabel('frequency in pi units'); ylabel('Imaginary'); figure('NumberTitle', 'off', 'Name', 'Problem 7.33 DTFT of Output[y(n)]') set(gcf,'Color','white'); subplot(2,2,1); plot(w1/pi,magY); grid on; %axis([0,2,0,15]); title('Magnitude Part'); xlabel('frequency in pi units'); ylabel('Magnitude |Y|'); subplot(2,2,3); plot(w1/pi, angY/pi); grid on; axis([0,2,-1,1]); title('Angle Part'); xlabel('frequency in pi units'); ylabel('Radians/pi'); subplot(2,2,2); plot(w1/pi, realY); grid on; title('Real Part'); xlabel('frequency in pi units'); ylabel('Real'); subplot(2,2,4); plot(w1/pi, imagY); grid on; title('Imaginary Part'); xlabel('frequency in pi units'); ylabel('Imaginary'); figure('NumberTitle', 'off', 'Name', 'Problem 7.33 Magnitude Response') set(gcf,'Color','white'); subplot(1,2,1); plot(w1/pi,magX); grid on; %axis([0,2,0,15]); title('Magnitude Part of Input'); xlabel('frequency in pi units'); ylabel('Magnitude |X|'); subplot(1,2,2); plot(w1/pi,magY); grid on; %axis([0,2,0,15]); title('Magnitude Part of Output'); xlabel('frequency in pi units'); ylabel('Magnitude |Y|');
运行结果:
设计一个50阶(即长度M=51)的线性相位FIR,通带宽度不超过0.02π,阻带衰减达到30dB,
最后要把输入中的高斯噪声过滤掉。
As=33dB,满足设计要求。
用P-M方法设计的脉冲响应幅度谱,
振幅谱
输入信号
滤波前后,输入数出对比
输入输出的谱:
右下图可见,随即噪声分量已滤除,仅留0.5π频率分量,效果良好。