在MATLAB/octave中使用fft和ifft增加/降低信号的频率

本文介绍了在MATLAB/octave中使用fft和ifft增加/降低信号的频率的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！

问题描述

我正在尝试使用fft和ifft增大/减小信号的频率.第一个图是 1hz，第二个图是2hz，我正在尝试通过更改fft和ifft值来获得.

I'm trying to increase / decrease the frequency of a signal using fft and ifft. The first plot is 1hz and the second plot is 2hz which I'm trying to get by altering the fft and ifft values.

我可以在频域和时域之间切换，但是如何使用fft/ifft增大或减小信号的频率?

I can go between the frequency domain and time domain but how can I increase or decrease the frequency of the signal using fft / ifft?

注意:是的，我知道我可以通过更改方程式的频率值来更改频率，但我只是将其用作测试信号.我将使用的信号将没有方程式将被导入.

Note: Yes I know I could change the frequency by changing the frequency value of the equation but I'm just using that as a test signal. The signals I will be using won't have equations they will be imported.

我试图通过调整fft和ifft值来获得2hz的图

下面的示例代码:

clear all,clf

Fs = 100;% Sampling frequency
t=linspace(0,1,Fs);

%1a create signal
ya = .5*sin(2*pi*1*t);

%2a create frequency domain
ya_fft = fft(ya);

mag = abs(ya_fft);
phase = unwrap(angle(ya_fft));
ya_newifft=ifft(mag.*exp(i*phase));

%3a frequency back to time domain
ya_ifft=real(ifft(ya_fft));

%1b time domain plot
subplot(2,2,1),plot(t,ya)
title('1 Orginal Signal Time domain')
ylabel('amplitude')
xlabel('Seconds')

%2b frequency domain plot.
[xfreq,yamp]=rtplotfft(ya,Fs);
yamp2=(yamp(:,1)/max(abs(yamp(:,1)))*1); %keep at 1, amplitude levels adjustied in loop below
subplot(2,2,2),plot(xfreq,yamp)
title('2 Frequency domain')
xlabel('Frequency (Hz)')
ylabel('amplitude')

Ps:我正在使用与Matlab兼容的八度3.8.1

Ps: I'm using octave 3.8.1 which works with matlab

推荐答案

我很抱歉以下内容有些混乱.我手动完成所有操作，因为我不确定该怎么做.

I apologize that the following is a bit messy. I did everything manually because I'm not sure how else to do it.

首先，您需要了解MATLAB如何存储频域数据.请看以下示例:

First you need to know how MATLAB stores frequency domain data. Take the following example:

N = 100;            % number of samples
Fs = 100;           % sampling frequency
f = 5;              % frequency of the signal
t = 0:1/N:1-1/N;    % time goes from 0 to 1 second
y = cos(2*pi*f*t);  % time signal
Y = fft(y);         % frequency signal

figure(1); plot(y);
figure(2); plot(abs(Y));

Y(1)是恒定偏移量(有时称为DC偏移量)
Y(2:N/2 + 1)是一组正频率
Y(N/2 + 2:end)是一组负频率...通常，我们将绘制垂直轴的左.

Y(1) is the constant offset (sometimes called the DC offset)
Y(2:N/2 + 1) is the set of positive frequencies
Y(N/2 + 2:end) is the set of negative frequencies... normally we would plot this left of the vertical axis.

请注意，因为N=100是偶数，所以会有50正频率分量和49负频率分量.如果N为奇数，则正负频率相等.

Note that because N=100 is even, there will be 50 positive frequency components and 49 negative frequency components. If N is odd, then there will be an equal number of positive and negative frequencies.

如果要增加频率，我们需要做的是:

If we want to increase the frequency, we need to do is:

进行傅立叶变换
保持直流偏移不变
将频谱的正向右移
将频谱的负数向左移动

要降低频率，我们只需反转换档的方向即可.

To decrease the frequency we would just reverse the direction of the shifts.

对于您而言，您需要做的是...

In your case, what you need to do is...

clear all,clf

Fs = 100;% Sampling frequency
t=linspace(0,1,Fs);

%1a create signal
ya = .5*sin(2*pi*1*t);

%2a create frequency domain
ya_fft = fft(ya);

mag = abs(ya_fft);
phase = unwrap(angle(ya_fft));
ya_newifft=ifft(mag.*exp(i*phase));

% ----- changes start here ----- %

shift   = 1;                            % shift amount
N       = length(ya_fft);               % number of points in the fft
mag1    = mag(2:N/2+1);                 % get positive freq. magnitude
phase1  = phase(2:N/2+1);               % get positive freq. phases
mag2    = mag(N/2+2:end);               % get negative freq. magnitude
phase2  = phase(N/2+2:end);             % get negative freq. phases

% pad the positive frequency signals with 'shift' zeros on the left
% remove 'shift' components on the right
mag1s   = [zeros(1,shift) , mag1(1:end-shift)];
phase1s = [zeros(1,shift) , phase1(1:end-shift)];

% pad the negative frequency signals with 'shift' zeros on the right
% remove 'shift' components on the left
mag2s   = [mag2(shift+1:end), zeros(1,shift)];
phase2s = [phase2(shift+1:end), zeros(1,shift) ];

% recreate the frequency spectrum after the shift
%           DC      +ve freq.   -ve freq.
magS    = [mag(1)   , mag1s     , mag2s];
phaseS  = [phase(1) , phase1s   , phase2s];


x = magS.*cos(phaseS);                  % change from polar to rectangular
y = magS.*sin(phaseS);
ya_fft2 = x + i*y;                      % store signal as complex numbers
ya_ifft2 = real(ifft(ya_fft2));         % take inverse fft

plot(t,ya_ifft2);                       % time signal with increased frequency

然后您就去了

这篇关于在MATLAB/octave中使用fft和ifft增加/降低信号的频率的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持！