《DSP using MATLAB》Problem 7.31
作者:互联网
参照Example7.27,因为0.1π=2πf1 f1=0.05,0.9π=2πf2 f2=0.45
所以0.1π≤ω≤0.9π,0.05≤|H|≤0.45
代码:
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ %% Output Info about this m-file fprintf('\n***********************************************************\n'); fprintf(' <DSP using MATLAB> Problem 7.31 \n\n'); banner(); %% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ f = [0 0.1 0.9 1]; % in w/pi units m = [0 0.05 0.45 0]; % Magnitude values M = 25; % length of filter N = M - 1; % Nth-order h = firpm(N, f, m, 'differentiator'); %h [db, mag, pha, grd, w] = freqz_m(h, [1]); [Hr, ww, c, L] = Hr_Type3(h); %[Hr,omega,P,L] = ampl_res(h); l = 0:M-1; %% ------------------------------------------------- %% Plot %% ------------------------------------------------- figure('NumberTitle', 'off', 'Name', 'Problem 7.31') set(gcf,'Color','white'); subplot(2,2,1); plot(w/pi, db); grid on; axis([0 2 -90 10]); set(gca,'YTickMode','manual','YTick',[-60,-40,-20,0]) set(gca,'YTickLabelMode','manual','YTickLabel',['60';'40';'20';' 0']); set(gca,'XTickMode','manual','XTick',[0,0.1,0.9,1,1.1,1.9,2]); xlabel('frequency in \pi units'); ylabel('Decibels'); title('Magnitude Response in dB'); subplot(2,2,3); plot(w/pi, mag); grid on; %axis([0 1 -100 10]); xlabel('frequency in \pi units'); ylabel('Absolute'); title('Magnitude Response in absolute'); set(gca,'XTickMode','manual','XTick',[0,0.1,0.9,1,1.1,1.9,2]); set(gca,'YTickMode','manual','YTick',[0,1.0,2.0]); subplot(2,2,2); plot(w/pi, pha); grid on; %axis([0 1 -100 10]); xlabel('frequency in \pi units'); ylabel('Rad'); title('Phase Response in Radians'); subplot(2,2,4); plot(w/pi, grd*pi/180); grid on; %axis([0 1 -100 10]); xlabel('frequency in \pi units'); ylabel('Rad'); title('Group Delay'); figure('NumberTitle', 'off', 'Name', 'Problem 7.31') set(gcf,'Color','white'); subplot(2,2,1); stem(l, h); axis([-1, M, -0.6, 0.5]); grid on; xlabel('n'); ylabel('h(n)'); title('Actual Impulse Response, M=25'); set(gca, 'XTickMode', 'manual', 'XTick', [0,12,25]); set(gca, 'YTickMode', 'manual', 'YTick', [-0.6:0.2:0.6]); subplot(2,2,3); 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,-40,-20,0]); set(gca,'YTickLabelMode','manual','YTickLabel',['60';'40';'20';' 0']); subplot(2,2,4); plot(ww/pi, Hr); axis([0, 1, -0.2, 1.5]); grid on; xlabel('frequency in \pi nuits'); ylabel('Hr(w)'); title('Amplitude Response'); n = [0:1:100]; x = 3*sin(0.25*pi*n); y = filter(h,1,x); y_chk = 0.75*cos(0.25*pi*n); figure('NumberTitle', 'off', 'Name', 'Problem 7.31 x(n)') set(gcf,'Color','white'); subplot(2,1,1); stem([0:M-1], h); axis([0 M-1 -0.5 0.5]); grid on; xlabel('n'); ylabel('h(n)'); title('Actual Impulse Response, M=25'); subplot(2,1,2); stem(n, x); axis([0 100 0 3]); grid on; xlabel('n'); ylabel('x(n)'); title('Input sequence'); figure('NumberTitle', 'off', 'Name', 'Problem 7.31 y(n) and y_chk(n)') set(gcf,'Color','white'); subplot(2,1,1); stem(n, y); axis([0 100 -1 1]); grid on; xlabel('n'); ylabel('y(n)'); title('Output sequence'); subplot(2,1,2); stem(n, y_chk); axis([0 100 -1 1]); grid on; xlabel('n'); ylabel('y\_chk(n)'); title('Output sequence'); % --------------------------- % DTFT of x % --------------------------- MM = 500; [X, w1] = dtft1(x, n, MM); [Y, w1] = dtft1(y, n, 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 7.31 DTFT of 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 7.31 DTFT of 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 7.31 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:
根据线性相位FIR性质,differentiator为第3类线性相位FIR,下图为脉冲响应、幅度谱和振幅谱。
脉冲响应和输入序列
下图分别用卷积法和数学求导数方法得到的输出,
各自求其离散时间傅氏变换DTFT,得
两种求微分结果幅度谱对比,可以看出:
1、设计滤波器卷积输入,输出的0.5π频率附近出现能量,数学求法没有;
2、设计滤波器卷积输入,幅度较数学求法小(能量有损失?);
标签:subplot,7.31,title,grid,ylabel,using,Problem,pi,xlabel 来源: https://www.cnblogs.com/ky027wh-sx/p/10849165.html