利用matlab/octave中的fft和ifft实现信号频率的增减

Question

我正在尝试使用fft和IFFT来增加/减少信号的频率。第一个曲线图是1Hz，第二个曲线图是2Hz，我试图通过改变fft和ifft值来获得。

我可以在频域和时域之间转换，但如何使用fft/IFFT来增加或减少信号的频率呢？

注意：是的，我知道我可以通过改变公式的频率值来改变频率，但我只是将其用作测试信号。我将使用的信号不会有方程，它们将被导入。

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')

Answer 1

很抱歉，下面的内容有点乱。我做每件事都是手动的，因为我不知道还能怎么做。

首先，您需要了解MATLAB如何存储频域数据。举下面的例子：

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)是恒定失调（有时称为直流失调）
• y(2:n/2+1)是正频率的集合
• y(n/2+2:end)是负频率的集合...通常情况下，我们会在垂直轴左侧绘制此图。

null

在你的情况下，你需要做的是...

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

就这样吧：