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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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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）5 P+ U2 C% b- O. V! M8 Z, \1 j
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。7 I6 ^$ d6 u7 I; D
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这篇就是为此而写。7 u+ J$ W6 C. N7 t% O$ O+ E& C

& T5 N- `6 r3 l* G+ k* \3 G案例：# t, `- I/ O: S% N
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想要基于有限样本数来确定他的频谱。
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/ {, i0 Y2 a$ V4 `2 U+ B, F  G下面我们分如下几种情况来分别讨论：3 a! W. M  E0 T8 Z5 P; m) I  ^- P2 C2 z
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a. 求出并画出   ，N = 10 的DFT以及DTFT；% e6 \2 K# Q" W9 v7 p( E

  I# u) }8 X% p2 Tb. 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；6 N% O* Q+ x8 k8 a% S5 L% o- D/ x
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c.求出并画出   ，N = 100 的DFT以及DTFT；
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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；4 r# m: d' n" d2 T4 B1 q
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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。
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题解：$ B( W% Z9 V4 V) N) O

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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
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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

  • 5 x/ F. k- D$ m3 ], t/ ~+ H' j
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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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" p& D% M7 c) L* i太小了，放大看：
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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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e.
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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! l% H7 @+ {9 h
     
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