DSP实验报告(3)

修改程序后的运行结果为:

100Real part of H(e)j?Amplitude500-50-4-3-2-10? /?1234100j?Imaginary part of H(e)Amplitude500-50-100-4-3-2-10? /?1234

100Magnitude Spectrum |H(e)|j?Amplitude500-4-3-2-10? /?12344Phase Spectrum arg[H(ej?)]Phase in radians20-2-4-4-3-2-10? /?1234

DTFT 是关于 ?的周期函数么？ 答：DTFT 是关于 ?的周期函数。 周期是 - 2?

相位谱中跳变的原因是 - 角度返回到arctan的本值

实验名称：离散傅立叶变换和z变换

实验目的和任务：

掌握离散傅立叶变换（DFT）及逆变换（IDFT）、z变换及逆变换的计算和分析。利用Matlab语言，完成DFT和IDFT的计算及常用性质的验证，用DFT实现线性卷积，实现z变换的零极点分析，求有理逆z变换。

实验内容：

DFT和IDFT计算： Q3.23～3.24

DFT的性质： Q3.26~3.29，Q3.36，Q3.38，Q3.40 z变换分析：Q3.46～3.48 逆z变换：Q3.50

实验过程与结果分析：

Q3.23 编写一个MATLAB程序，计算并画出长度为N的L点离散傅里叶变换X[k]的值，其中L≥N，然后计算并画出L点离散傅里叶变换X[k]。对不同长度N和不同的离散傅里叶变换长度L，运行程序。讨论你的结果。

编写的MATLAB程序：

% Program Q3.23

% Compute and plot the L-point DFT of an N-point signal, L >= N. clf;

%Initialize

N=200; % length of signal L=256; % length of DFT nn = [0:N-1]; kk = [0:L-1]; % the signal x

xR = [0.1*(1:100) zeros(1,N-100)]; % real part xI = [zeros(1,N)]; % imag part x = xR + i*xI; % DFT

XF = fft(x,L); % plot xR and xI subplot(3,2,1);grid; plot(nn,xR);grid; title('Re\\{x[n]\\}'); xlabel('Time index n'); ylabel('Amplitude'); subplot(3,2,2); plot(nn,xI);grid; title('Im\\{x[n]\\}'); xlabel('Time index n'); ylabel('Amplitude');

% plot real and imag parts of DFT subplot(3,2,3);

plot(kk,real(XF));grid; title('Re\\{X[k]\\}');

xlabel('Frequency index k'); ylabel('Amplitude'); subplot(3,2,4);

plot(kk,imag(XF));grid; title('Im\\{X[k]\\}');

xlabel('Frequency index k'); ylabel('Amplitude'); % IDFT

xx = ifft(XF,L);

% plot real and imaginary parts of the IDFT subplot(3,2,5);

plot(kk,real(xx));grid;

title('Real part of IDFT\\{X[k]\\}'); xlabel('Time index n'); ylabel('Amplitude'); subplot(3,2,6);

plot(kk,imag(xx));grid;

title('Imag part of IDFT\\{X[k]\\}'); xlabel('Time index n'); ylabel('Amplitude');

Re{x[n]}Im{x[n]}Amplitude500100Time index nRe{X[k]}200Amplitude1010-10Amplitude0-10000100200300Frequency index kReal part of IDFT{X[k]}Amplitude10005000-5000100Time index nIm{X[k]}200Amplitude0-100100200Time index n300Amplitude1010-10100200300Frequency index kImag part of IDFT{X[k]}100200Time index n300

Q3.24 写一个MATLAB程序，用一个N点复数离散傅里叶计算两个长度为N的实数序列的N点离散傅里叶变换，，并将结果同直接使用两个N点离散傅里叶变换得到的结果进行比较。

编写的MATLAB程序：

% Program Q3.24

% Use a single N-point DFT to compute simultaneously the N-point % DFT's of two real-valued N-point sequences. clf; %Initialize

N=256; % length of signal nn = [0:N-1]; ntime = [-N/2:N/2-1];

g = (0.75).^abs(ntime); % signal g h = (-0.9).^ntime; % signal h % DFT's of g and h GF = fft(g); HF = fft(h);

x = g + i*h; % the composite signal x % DFT of composite signal XF = fft(x);

% DFT of g derived from composite DFT XF XFstar = conj(XF);

XFstarmod = [XFstar(1) fliplr(XFstar(2:N))]; GF2 = 0.5*(XF + XFstarmod); HF2 = -i*0.5*(XF - XFstarmod); abs(max(GF-GF2)) abs(max(HF-HF2))

% plot real and imag parts of direct computation of GF figure(1);clf; subplot(2,2,1);grid; plot(nn,real(GF));grid; title('Two N-point DFT''s'); xlabel('Frequency index k'); ylabel('Re\\{G[k]\\}'); subplot(2,2,2);

plot(nn,imag(GF));grid; title('Two N-point DFT''s'); xlabel('Frequency index k'); ylabel('Im\\{G[k]\\}');

% plot real and imag parts of composite computation of GF subplot(2,2,3);grid; plot(nn,real(GF2));grid; title('Single N-point DFT'); xlabel('Frequency index k');

ylabel('Re\\{G[k]\\}'); subplot(2,2,4);

plot(nn,imag(GF2));grid; title('Single N-point DFT'); xlabel('Frequency index k'); ylabel('Im\\{G[k]\\}');

% plot real and imag parts of direct computation of HF figure(2);clf; subplot(2,2,1);grid; plot(nn,real(HF));grid; title('Two N-point DFT''s'); xlabel('Freq index k'); ylabel('Re\\{H[k]\\}'); subplot(2,2,2);

plot(nn,imag(HF));grid; title('Two N-point DFT''s'); xlabel('Freq index k'); ylabel('Im\\{H[k]\\}');

% plot real and imag parts of composite computation of HF subplot(2,2,3);grid; plot(nn,real(HF2));grid; title('Single N-point DFT'); xlabel('Freq index k'); ylabel('Re\\{H[k]\\}'); subplot(2,2,4);

plot(nn,imag(HF2));grid; title('Single N-point DFT'); xlabel('Freq index k'); ylabel('Im\\{H[k]\\}');

Two N-point DFT's-15x 10Two N-point DFT's102Re{G[k]}0-5-100100200Frequency index kSingle N-point DFT300Im{G[k]}510-10-9100200Frequency index k300101x 10Single N-point DFTRe{G[k]}0-5-100100200Frequency index k300Im{G[k]}50.50-0.5-10100200Frequency index k300

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