只放第1小题。
代码:
%% ------------------------------------------------------------------------ %% Output Info about this m-file fprintf(‘\n***********************************************************\n‘); fprintf(‘ <DSP using MATLAB> Problem 9.4.1 \n\n‘); banner(); %% ------------------------------------------------------------------------ % ------------------------------------------------------------ % PART 1 % ------------------------------------------------------------ % Discrete time signal n1_start = 0; n1_end = 100; n1 = [n1_start:1:n1_end]; xn1 = cos(0.15*pi*n1); % digital signal D = 4; % downsample by factor D OFFSET = 0; y = downsample(xn1, D, OFFSET); ny = [n1_start:n1_end/D]; % ny = [n1_start:n1_end/D-1]; % OFFSET=2 figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 9.4.1 xn1 and y‘) set(gcf,‘Color‘,‘white‘); subplot(2,1,1); stem(n1, xn1, ‘b‘); xlabel(‘n‘); ylabel(‘x(n)‘); title(‘xn1 original sequence‘); grid on; subplot(2,1,2); stem(ny, y, ‘r‘); xlabel(‘ny‘); ylabel(‘y(n)‘); title(sprintf(‘y sequence, downsample by D=%d offset=%d‘, D, OFFSET)); grid on; % ---------------------------- % DTFT of xn1 % ---------------------------- M = 500; [X1, w] = dtft1(xn1, n1, M); magX1 = abs(X1); angX1 = angle(X1); realX1 = real(X1); imagX1 = imag(X1); max(magX1) %% -------------------------------------------------------------------- %% START X(w)‘s mag ang real imag %% -------------------------------------------------------------------- figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 9.4.1 X1 DTFT‘); set(gcf,‘Color‘,‘white‘); subplot(2,1,1); plot(w/pi,magX1); grid on; %axis([-2, -1, -0.5, 0, 0.15, 0.5, 1, 2]); title(‘Magnitude Response‘); xlabel(‘digital frequency in \pi units‘); ylabel(‘Magnitude |H|‘); set(gca, ‘xtick‘, [-2,-1.85,-1.5,-1,-0.15,0,0.15,0.5,1,1.5,1.85,2]); subplot(2,1,2); plot(w/pi, angX1/pi); grid on; %axis([-1,1,-1.05,1.05]); title(‘Phase Response‘); xlabel(‘digital frequency in \pi units‘); ylabel(‘Radians/\pi‘); figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 9.4.1 X1 DTFT‘); set(gcf,‘Color‘,‘white‘); subplot(2,1,1); plot(w/pi, realX1); grid on; title(‘Real Part‘); xlabel(‘digital frequency in \pi units‘); ylabel(‘Real‘); subplot(2,1,2); plot(w/pi, imagX1); grid on; title(‘Imaginary Part‘); xlabel(‘digital frequency in \pi units‘); ylabel(‘Imaginary‘); %% ------------------------------------------------------------------- %% END X‘s mag ang real imag %% ------------------------------------------------------------------- % ---------------------------- % DTFT of y % ---------------------------- M = 500; [Y, w] = dtft1(y, ny, M); magY_DTFT = abs(Y); angY_DTFT = angle(Y); realY_DTFT = real(Y); imagY_DTFT = imag(Y); max(magY_DTFT) ratio = max(magX1)/max(magY_DTFT) %% -------------------------------------------------------------------- %% START Y(w)‘s mag ang real imag %% -------------------------------------------------------------------- figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 9.4.1 Y DTFT‘); set(gcf,‘Color‘,‘white‘); subplot(2,1,1); plot(w/pi, magY_DTFT); grid on; %axis([-2,2, -1, 2]); title(‘Magnitude Response‘); xlabel(‘digital frequency in \pi units‘); ylabel(‘Magnitude |H|‘); set(gca, ‘xtick‘, [-2,-1.4,-1,-0.6,0,0.6,1,1.4,2]); subplot(2,1,2); plot(w/pi, angY_DTFT/pi); grid on; %axis([-1,1,-1.05,1.05]); title(‘Phase Response‘); xlabel(‘digital frequency in \pi units‘); ylabel(‘Radians/\pi‘); figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 9.4.1 Y DTFT‘); set(gcf,‘Color‘,‘white‘); subplot(2,1,1); plot(w/pi, realY_DTFT); grid on; title(‘Real Part‘); xlabel(‘digital frequency in \pi units‘); ylabel(‘Real‘); subplot(2,1,2); plot(w/pi, imagY_DTFT); grid on; title(‘Imaginary Part‘); xlabel(‘digital frequency in \pi units‘); ylabel(‘Imaginary‘); %% ------------------------------------------------------------------- %% END Y‘s mag ang real imag %% ------------------------------------------------------------------- figure(‘NumberTitle‘, ‘off‘, ‘Name‘, sprintf(‘Problem 9.4.1 X1 & Y--DTFT of x and y, D=%d offset=%d‘, D,OFFSET)); set(gcf,‘Color‘,‘white‘); subplot(2,1,1); plot(w/pi,magX1); grid on; %axis([-1,1,0,1.05]); title(‘Magnitude Response‘); xlabel(‘digital frequency in \pi units‘); ylabel(‘Magnitude |H|‘); set(gca, ‘xtick‘, [-2,-1.85,-1.4,-1,-0.6,-0.5,-0.15,0,0.15,0.5,0.6,1,1.4,1.85,2]); set(gca, ‘ytick‘, [-0.2, 0, 13.5, 20, 40, 51, 60]); hold on; plot(w/pi, magY_DTFT, ‘r‘); gtext(‘magY(\omega)‘, ‘Color‘, ‘r‘); hold off; subplot(2,1,2); plot(w/pi, angX1/pi); grid on; %axis([-1,1,-1.05,1.05]); title(‘Phase Response‘); xlabel(‘digital frequency in \pi units‘); ylabel(‘Radians/\pi‘); hold on; plot(w/pi, angY_DTFT/pi, ‘r‘); gtext(‘AngY(\omega)‘, ‘Color‘, ‘r‘); hold off;
运行结果:
分两种情况
1、按照D=4抽取,offset=0
原始序列,抽取序列
原始序列的谱
抽取序列的谱
二者的DTFT混叠到一起,红颜色曲线是抽取序列的DTFT,可看出,其幅度大致为原始序列的谱幅度的1/4(精确值是1/3.7778)。
2、按照D=4抽取,offset=2
二者的DTFT混叠到一起,红颜色曲线是抽取序列的DTFT,可看出,其幅度大致为原始序列的谱幅度的1/4(精确值是1/4.0699)。
原文地址:https://www.cnblogs.com/ky027wh-sx/p/12003290.html
时间: 2024-11-08 23:48:28