在MATLAB/octave中使用fft和ifft增加/降低信号的频率 [英] increase / decrease the frequency of a signal using fft and ifft in matlab / octave

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

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