改变频域信号的相位（MatLab） [英] Change phase of a signal in frequency domain (MatLab)

问题描述

我在dsp.stackexchange上发布了这个问题，并且被告知它与stackoverflow更相关，因为它主要是一个编程问题：

我试图写一个代码，它允许我改变频域信号的相位。但是，我的输出不完全正确，所以一定是错的。举一个简单的例子，假设我们有函数y = sin（2 * pi * t）并且想实现-pi / 2的相移。我的代码如下所示：

 清除所有
关闭所有
 
 N = 64; ％样本数量
 fs = 10; ％采样频率
 ts = 1 / fs; ％采样间隔
 tmax =（N-1）* ts; 
 t = 0：ts：tmax; 
 y = sin（2 * pi * t）; 
 
 figure 
 plot（t，y）
 
％我们做FT 
f = -fs / 2：fs /（N-1）： fs / 2的; 
 Y = fftshift（fft（y））; 
 
％幅度
 figure 
 plot（f，abs（Y））; 
 
 phase = angle（Y）; 
 
相谱
图
图（f，阶段）
 
 Y = ifftshift（Y）
 
％尝试相移
 Y = Y. * exp（-i * 2 * pi * f * pi / 2）; 
 
％逆FT 
 u = ifft（Y）; 
 
 figure 
 plot（t，real（u））
  

除了最后的情节外，所有情节都看起来不错：

这看起来几乎正确，但并不完全。如果任何人都可以给我一些关于如何纠正我的代码，以解决这个问题的指针，我将不胜感激！我有一种感觉，我的错误与行 Y = Y. * exp（-i * 2 * pi * f * pi / 2）; 有关，但是我我不知道如何解决这个问题。
解决方案

我不能真正进入傅里叶分析的细节（因为我没有真的知道他们），但我可以提供一个工作解决方案，提供一些提示：首先，你应该用虚构的术语来表达你的浪潮，例如：

  y = exp（1i * 2 * pi * t）; 
  

更重要的是，您必须真正地转换阶段，而不要混淆整个频谱：

 ％尝试相移
 Y = abs（Y）。* exp（1i * angle（Y） -1i * PI / 4）; ％-pi / 4 shift 
  

您应该注意，这个转换与频率无关，我猜是有道理的
最后你可以画出结果：

$ p $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ k'）
持有
图（t，real（y），'r'）

real（y）实际上是一个余弦函数，并且您以正弦开始，但是希望您能理解。
对于pi / 4 shift我得到了这样的东西（用红色开始，用黑色结束）：

I posted this question on dsp.stackexchange, and was informed that it was more relevant for stackoverflow as it is primarily a programming question:

I am attempting to write a code which allows me to change the phase of a signal in the frequency domain. However, my output isn't exactly correct, so something must be wrong. For a simple example assume that we have the function y = sin(2*pi*t) and want to implement a phase shift of -pi/2. My code looks as follows:

clear all
close all

N = 64; %number of samples
fs = 10; %sampling frequency
ts = 1/fs; %sample interval
tmax = (N-1)*ts;
t = 0:ts:tmax;
y = sin(2*pi*t);

figure
plot(t,y)

% We do the FT
f = -fs/2:fs/(N-1):fs/2;
Y = fftshift(fft(y));

% Magnitude spectrum
figure
plot(f,abs(Y));

phase = angle(Y);

% Phase spectrum
figure
plot(f,phase)

Y = ifftshift(Y)

% Attempt at phase shift
Y = Y.*exp(-i*2*pi*f*pi/2);

% Inverse FT
u = ifft(Y);

figure
plot(t,real(u))

All plots look OK except for the final plot which looks as follows:

This looks almost correct but not quite. If anyone can give me some pointers as to how my code can be corrected in order to fix this, I would greatly appreciate it! I have a feeling my mistake has something to do with the line Y = Y.*exp(-i*2*pi*f*pi/2);, but I'm not sure how to fix it.

解决方案

I can't really get into the Fourier analysis details (because I do not really know them), but I can offer a working solution with some hints:

First of all, You should express Your wave in imaginary terms, i.e.:

y = exp(1i*2*pi*t);

And what's even more crucial, You have to truly shift only the phase, without messing with the whole spectrum:

% Attempt at phase shift
Y = abs(Y).*exp(1i*angle(Y)-1i*pi/4); % -pi/4 shift

You should note that the shift isn't related to frequency anymore, which I guess makes sense. Finally You can plot the results:

figure
plot(t,real(u),'k')
hold on
plot(t,real(y),'r')

real(y) is actually a cosine function, and You started with sine, but hopefully You get the idea. For pi/4 shift i got something like this (started with red, finished with black):

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