理解 Matlab FFT 示例 [英] Understanding Matlab FFT example

问题描述

我是 matlab 和 FFT 的新手，想了解 .查看 Mathworks 示例中的这一行:

f = Fs/2*linspace(0,1,NFFT/2+1);

第二个图的频率轴从 0 到 Fs/2，或采样频率的一半.奈奎斯特频率总是采样频率的一半，因为在此之上，混叠发生:

信号会折叠"回自身，并且似乎的某个频率等于或低于 500Hz.

<块引用>

2) 我怎么知道频率在 0 到 500 之间?FFT 不应该告诉我，频率在哪个限制中?

由于上述折叠"(奈奎斯特频率也俗称折叠频率")，500Hz以上的频率在物理上不可能出现在FFT中；较高的频率会折叠"回来并显示为较低的频率.

<块引用>

FFT 是否只返回幅度值而没有频率?

是的，MATLAB FFT 函数仅返回一个幅度向量.但是，它们会映射到您传递给它的频率点.

让我知道什么需要澄清，以便我可以进一步帮助您.

I am new to matlab and FFT and want to understand the Matlab FFT example. For now I have two main questions:

1) Why does the x-axis (frequency) end at 500? How do I know that there aren't more frequencies or are they just ignored?

2) How do I know the frequencies are between 0 and 500? Shouldn't the FFT tell me, in which limits the frequencies are? Does the FFT only return the amplitude value without the frequency?

Thanks for any hint!

---

Example in question:

Consider data sampled at 1000 Hz. Form a signal containing a 50 Hz sinusoid of amplitude 0.7 and 120 Hz sinusoid of amplitude 1 and corrupt it with some zero-mean random noise:

Fs = 1000;                    % Sampling frequency
T = 1/Fs;                     % Sample time
L = 1000;                     % Length of signal
t = (0:L-1)*T;                % Time vector
% Sum of a 50 Hz sinusoid and a 120 Hz sinusoid
x = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t); 
y = x + 2*randn(size(t));     % Sinusoids plus noise
plot(Fs*t(1:50),y(1:50))
title('Signal Corrupted with Zero-Mean Random Noise')
xlabel('time (milliseconds)')

Converting to the frequency domain, the discrete Fourier transform of the noisy signal y is found by taking the fast Fourier transform (FFT):

NFFT = 2^nextpow2(L); % Next power of 2 from length of y
Y = fft(y,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2+1);

% Plot single-sided amplitude spectrum.
plot(f,2*abs(Y(1:NFFT/2+1))) 
title('Single-Sided Amplitude Spectrum of y(t)')
xlabel('Frequency (Hz)')
ylabel('|Y(f)|')

解决方案

1) Why does the x-axis (frequency) end at 500? How do I know that there aren't more frequencies or are they just ignored?

It ends at 500Hz because that is the Nyquist frequency of the signal when sampled at 1000Hz. Look at this line in the Mathworks example:

f = Fs/2*linspace(0,1,NFFT/2+1);

The frequency axis of the second plot goes from 0 to Fs/2, or half the sampling frequency. The Nyquist frequency is always half the sampling frequency, because above that, aliasing occurs:

The signal would "fold" back on itself, and appear to be some frequency at or below 500Hz.

2) How do I know the frequencies are between 0 and 500? Shouldn't the FFT tell me, in which limits the frequencies are?

Due to "folding" described above (the Nyquist frequency is also commonly known as the "folding frequency"), it is physically impossible for frequencies above 500Hz to appear in the FFT; higher frequencies will "fold" back and appear as lower frequencies.

Does the FFT only return the amplitude value without the frequency?

Yes, the MATLAB FFT function only returns one vector of amplitudes. However, they map to the frequency points you pass to it.

Let me know what needs clarification so I can help you further.

这篇关于理解 Matlab FFT 示例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IT屋！