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EDA365电子论坛网»电子社区 › 研发技术版块 › MATLAB论坛 › MATLAB ------- 用 MATLAB 得到高密度谱和高分辨率谱的 ...
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MATLAB ------- 用 MATLAB 得到高密度谱和高分辨率谱的方式比对（附MATLAB脚本）

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发表于 2019-12-9 11:11 | 只看该作者 |只看大图 回帖奖励 |倒序浏览 |阅读模式

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MATLAB ------- 使用 MATLAB 得到高密度谱（补零得到DFT）和高分辨率谱（获得更多的数据得到DFT）的方式对比（附MATLAB脚本）
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* N/ x2 y: f- ^- e% T6 B1 J2 R% W上篇分析了同一有限长序列在不同的N下的DFT之间的不同： MATLAB ------- 用 MATLAB 作图讨论有限长序列的 N 点 DFT（含MATLAB脚本）- a2 k3 @* G* ]+ ~; k' }
那篇中，我们通过补零的方式来增加N，这样最后的结论是随着N的不断增大，我们只会得到DTFT上的更多的采样点，也就是说频率采样率增加了。通过补零，得到高密度谱（DFT），但不能得到高分辨率谱，因为补零并没有任何新的信息附加到这个信号上，要想得到高分辨率谱，我们就得通过获得更多的数据来进行求解DFT。
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6 I! q1 y% ^: @( e这篇就是为此而写。
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$ K" Q6 |2 x8 L2 }" a案例：
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5 Z4 Y. z, B; l: O/ @/ i/ t想要基于有限样本数来确定他的频谱。8 l9 @% h. R% S- j# i0 d
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下面我们分如下几种情况来分别讨论：
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/ P& {( H7 V6 b, r6 Wa. 求出并画出   ，N = 10 的DFT以及DTFT；
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' v6 V; x4 \; q( {# Q$ y; kb. 对上一问的x(n)通过补零的方式获得区间[0,99]上的x(n)，画出 N = 100点的DFT，并画出DTFT作为对比；$ g" R% ^% Z$ b! P0 c
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c.求出并画出   ，N = 100 的DFT以及DTFT；- y2 x: c$ u2 l" v" m* L
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d.对c问中的x(n)补零到N = 500，画出 N = 500点的DFT，并画出DTFT作为对比；
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e. 比较c和d这两个序列的序列的DFT以及DTFT的异同。0 w1 L4 a  q& y3 v4 q! q
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那就干呗！. z( r0 B3 k: u: m
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题解：8 `5 n7 Z! G$ m- w: Q
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  • clc;clear;close all;
  • n = 0:99;
  • x = cos(0.48*pi*n) + cos(0.52*pi*n);
  • n1 = 0:9;
  • y1 = x(1:10);
  • subplot(2,1,1)
  • stem(n1,y1);
  • title('signal x(n), 0 <= n <= 9');
  • xlabel('n');ylabel('x(n) over n in [0,9]');
  • Y1 = dft(y1,10);
  • magY1 = abs(Y1);
  • k1 = 0:1:9;
  • N = 10;
  • w1 = (2*pi/N)*k1;
  • subplot(2,1,2);
  • stem(w1/pi,magY1);
  • title('DFT of x(n) in [0,9]');
  • xlabel('frequency in pi units');
  • %In order to clearly see the relationship between DTFT and DFT, we draw DTFT on the same picture.
  • %Discrete-time Fourier Transform
  • K = 500;
  • k = 0:1:K;
  • w = 2*pi*k/K; %plot DTFT in [0,2pi];
  • X = y1*exp(-j*n1'*w);
  • magX = abs(X);
  • hold on
  • plot(w/pi,magX);
  • hold off% ^5 ]- R4 @) _( U
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  • clc;clear;close all;
  • n = 0:99;
  • x = cos(0.48*pi*n) + cos(0.52*pi*n);
  • % zero padding into N = 100
  • n1 = 0:99;
  • y1 = [x(1:10),zeros(1,90)];
  • subplot(2,1,1)
  • stem(n1,y1);
  • title('signal x(n), 0 <= n <= 99');
  • xlabel('n');ylabel('x(n) over n in [0,99]');
  • Y1 = dft(y1,100);
  • magY1 = abs(Y1);
  • k1 = 0:1:99;
  • N = 100;
  • w1 = (2*pi/N)*k1;
  • subplot(2,1,2);
  • stem(w1/pi,magY1);
  • title('DFT of x(n) in [0,9]');
  • xlabel('frequency in pi units');
  • %In order to clearly see the relationship between DTFT and DFT, we draw DTFT on the same picture.
  • %Discrete-time Fourier Transform
  • K = 500;
  • k = 0:1:K;
  • w = 2*pi*k/K; %plot DTFT in [0,2pi];
  • X = y1*exp(-j*n1'*w);
  • % w = [-fliplr(w),w(2:K+1)];   %plot DTFT in [-pi,pi]
  • % X = [fliplr(X),X(2:K+1)];    %plot DTFT in [-pi,pi]
  • magX = abs(X);
  • % angX = angle(X)*180/pi;
  • % figure
  • % subplot(2,1,1);
  • hold on
  • plot(w/pi,magX);
  • % title('Discrete-time Fourier Transform in Magnitude Part');
  • % xlabel('w in pi units');ylabel('Magnitude of X');
  • % subplot(2,1,2);
  • % plot(w/pi,angX);
  • % title('Discrete-time Fourier Transform in Phase Part');
  • % xlabel('w in pi units');ylabel('Phase of X ');
  • hold off
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  • clc;clear;close all;
  • n = 0:99;
  • x = cos(0.48*pi*n) + cos(0.52*pi*n);
  • % n1 = 0:99;
  • % y1 = [x(1:10),zeros(1,90)];
  • subplot(2,1,1)
  • stem(n,x);
  • title('signal x(n), 0 <= n <= 99');
  • xlabel('n');ylabel('x(n) over n in [0,99]');
  • Xk = dft(x,100);
  • magXk = abs(Xk);
  • k1 = 0:1:99;
  • N = 100;
  • w1 = (2*pi/N)*k1;
  • subplot(2,1,2);
  • stem(w1/pi,magXk);
  • title('DFT of x(n) in [0,99]');
  • xlabel('frequency in pi units');
  • %In order to clearly see the relationship between DTFT and DFT, we draw DTFT on the same picture.
  • %Discrete-time Fourier Transform
  • K = 500;
  • k = 0:1:K;
  • w = 2*pi*k/K; %plot DTFT in [0,2pi];
  • X = x*exp(-j*n'*w);
  • % w = [-fliplr(w),w(2:K+1)];   %plot DTFT in [-pi,pi]
  • % X = [fliplr(X),X(2:K+1)];    %plot DTFT in [-pi,pi]
  • magX = abs(X);
  • % angX = angle(X)*180/pi;
  • % figure
  • % subplot(2,1,1);
  • hold on
  • plot(w/pi,magX);
  • % title('Discrete-time Fourier Transform in Magnitude Part');
  • % xlabel('w in pi units');ylabel('Magnitude of X');
  • % subplot(2,1,2);
  • % plot(w/pi,angX);
  • % title('Discrete-time Fourier Transform in Phase Part');
  • % xlabel('w in pi units');ylabel('Phase of X ');
  • hold off
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  • clc;clear;close all;
  • n = 0:99;
  • x = cos(0.48*pi*n) + cos(0.52*pi*n);
  • % n1 = 0:99;
  • % y1 = [x(1:10),zeros(1,90)];
  • %zero padding into N = 500
  • n1 = 0:499;
  • x1 = [x,zeros(1,400)];
  • subplot(2,1,1)
  • stem(n1,x1);
  • title('signal x(n), 0 <= n <= 499');
  • xlabel('n');ylabel('x(n) over n in [0,499]');
  • Xk = dft(x1,500);
  • magXk = abs(Xk);
  • k1 = 0:1:499;
  • N = 500;
  • w1 = (2*pi/N)*k1;
  • subplot(2,1,2);
  • % stem(w1/pi,magXk);
  • stem(w1/pi,magXk);
  • title('DFT of x(n) in [0,499]');
  • xlabel('frequency in pi units');
  • %In order to clearly see the relationship between DTFT and DFT, we draw DTFT on the same picture.
  • %Discrete-time Fourier Transform
  • K = 500;
  • k = 0:1:K;
  • w = 2*pi*k/K; %plot DTFT in [0,2pi];
  • X = x1*exp(-j*n1'*w);
  • % w = [-fliplr(w),w(2:K+1)];   %plot DTFT in [-pi,pi]
  • % X = [fliplr(X),X(2:K+1)];    %plot DTFT in [-pi,pi]
  • magX = abs(X);
  • % angX = angle(X)*180/pi;
  • % figure
  • % subplot(2,1,1);
  • hold on
  • plot(w/pi,magX,'r');
  • % title('Discrete-time Fourier Transform in Magnitude Part');
  • % xlabel('w in pi units');ylabel('Magnitude of X');
  • % subplot(2,1,2);
  • % plot(w/pi,angX);
  • % title('Discrete-time Fourier Transform in Phase Part');
  • % xlabel('w in pi units');ylabel('Phase of X ');
  • hold off

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       % H. S4 S& b, K: F5 C

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  • clc;clear;close all;
  • n = 0:99;
  • x = cos(0.48*pi*n) + cos(0.52*pi*n);
  • subplot(2,1,1)
  • % stem(n,x);
  • % title('signal x(n), 0 <= n <= 99');
  • % xlabel('n');ylabel('x(n) over n in [0,99]');
  • Xk = dft(x,100);
  • magXk = abs(Xk);
  • k1 = 0:1:99;
  • N = 100;
  • w1 = (2*pi/N)*k1;
  • stem(w1/pi,magXk);
  • title('DFT of x(n) in [0,99]');
  • xlabel('frequency in pi units');
  • %In order to clearly see the relationship between DTFT and DFT, we draw DTFT on the same picture.
  • %Discrete-time Fourier Transform
  • K = 500;
  • k = 0:1:K;
  • w = 2*pi*k/K; %plot DTFT in [0,2pi];
  • X = x*exp(-j*n'*w);
  • % w = [-fliplr(w),w(2:K+1)];   %plot DTFT in [-pi,pi]
  • % X = [fliplr(X),X(2:K+1)];    %plot DTFT in [-pi,pi]
  • magX = abs(X);
  • % angX = angle(X)*180/pi;
  • % figure
  • % subplot(2,1,1);
  • hold on
  • plot(w/pi,magX);
  • % title('Discrete-time Fourier Transform in Magnitude Part');
  • % xlabel('w in pi units');ylabel('Magnitude of X');
  • % subplot(2,1,2);
  • % plot(w/pi,angX);
  • % title('Discrete-time Fourier Transform in Phase Part');
  • % xlabel('w in pi units');ylabel('Phase of X ');
  • hold off
  • % clc;clear;close all;
  • %
  • % n = 0:99;
  • % x = cos(0.48*pi*n) + cos(0.52*pi*n);
  • % n1 = 0:99;
  • % y1 = [x(1:10),zeros(1,90)];
  • %zero padding into N = 500
  • n1 = 0:499;
  • x1 = [x,zeros(1,400)];
  • subplot(2,1,2);
  • % subplot(2,1,1)
  • % stem(n1,x1);
  • % title('signal x(n), 0 <= n <= 499');
  • % xlabel('n');ylabel('x(n) over n in [0,499]');
  • Xk = dft(x1,500);
  • magXk = abs(Xk);
  • k1 = 0:1:499;
  • N = 500;
  • w1 = (2*pi/N)*k1;
  • stem(w1/pi,magXk);
  • title('DFT of x(n) in [0,499]');
  • xlabel('frequency in pi units');
  • %In order to clearly see the relationship between DTFT and DFT, we draw DTFT on the same picture.
  • %Discrete-time Fourier Transform
  • K = 500;
  • k = 0:1:K;
  • w = 2*pi*k/K; %plot DTFT in [0,2pi];
  • X = x1*exp(-j*n1'*w);
  • % w = [-fliplr(w),w(2:K+1)];   %plot DTFT in [-pi,pi]
  • % X = [fliplr(X),X(2:K+1)];    %plot DTFT in [-pi,pi]
  • magX = abs(X);
  • % angX = angle(X)*180/pi;
  • % figure
  • % subplot(2,1,1);
  • hold on
  • plot(w/pi,magX,'r');
  • % title('Discrete-time Fourier Transform in Magnitude Part');
  • % xlabel('w in pi units');ylabel('Magnitude of X');
  • % subplot(2,1,2);
  • % plot(w/pi,angX);
  • % title('Discrete-time Fourier Transform in Phase Part');
  • % xlabel('w in pi units');ylabel('Phase of X ');
  • hold off
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局部放大看：; u- I5 {: Z& H
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