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标题: MATLAB ------- 用 MATLAB 得到高密度谱和高分辨率谱的方式比对（附MATLAB脚本） [打印本页]

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作者: ulppknot    时间: 2019-12-9 11:11
标题: MATLAB ------- 用 MATLAB 得到高密度谱和高分辨率谱的方式比对（附MATLAB脚本）
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）
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。

. S' B$ b3 s# z! p9 P5 [8 c7 I2 t& ?这篇就是为此而写。

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* a% O8 L: R7 _; q/ S想要基于有限样本数来确定他的频谱。
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& P; T% L5 j# v* G# g7 E, `下面我们分如下几种情况来分别讨论：
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+ k/ e1 W- x+ Q6 j4 ta. 求出并画出   ，N = 10 的DFT以及DTFT；

  y# h0 x4 S) r* ~1 M2 [b. 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；

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；

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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那就干呗！

题解：

a.
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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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b.

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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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7 ]& Z. J6 `* H7 Uc.

• 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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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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  K6 E+ c, D9 Z5 d$ D# Y

5 P8 {( [. Y  [4 {e.

• 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：



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作者: angern    时间: 2019-12-9 20:00
谢谢分享

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