英文:
Why does the Nyquist frequency of FFT of even length dataset end up on negative side of spectrum?
问题
当计算偶数长度数据集的FFT时，你会得到偶数个频率箱，因此它不对称于零。额外的频率箱，位于奈奎斯特频率处，最终会出现在双边频谱的负侧，而不是正侧 - 我想了解为什么会这样，但一直没有找到答案。
我尝试过在Google上搜索和查看Stack Overflow的其他地方，例如：https://www.mathworks.com/matlabcentral/answers/465242-fftshift-with-even-and-odd-number-of-data-points-scaling-the-positive-and-negative-frequency-axis
然而，我找到的内容都还没有回答我的问题。
英文:
When computing the FFT of an even length dataset, you end up with an even number of frequency bins, and so it is not symmetric about zero. The additional frequency bin, which is at the Nyquist frequency, ends up going in the negative side of the double sided spectrum rather than the positive side - I would like to understand why this is the case, but haven't been able to find an answer.
I've tried Googling and looking elsewhere on Stack Overflow, for example: https://www.mathworks.com/matlabcentral/answers/465242-fftshift-with-even-and-odd-number-of-data-points-scaling-the-positive-and-negative-frequency-axis
However nothing I have found has answered my question yet.
答案1
得分: 1
Bin在奈奎斯特频率处是独特的，它既不是正数也不是负数，它是一个边界，就像零位于正数和负数之间一样。奈奎斯特频率没有它的对应物。
假设我们有N=8的FFT：
[0] -> 直流分量（DC）
[1, 2, 3] -> 正频率分量 f1, f2, f3
[4] -> 奈奎斯特频率
[5, 6, 7] -> 负频率分量 f3, f2, f1
英文:
Bin at Nyquist frequency is unique, it is neither positive or negative, its a margin, just like zero is between positive and negative numbers. Nyquist frequency does not have its counterpart.
Lets say we have N=8 FFT:
[0] -> DC
[1, 2, 3] -> positive f1, f2, f3
[4] -> Nyquist frequency
[5, 6, 7] -> negative f3, f2, f1
答案2
得分: 1
The Nyquist bin “wraps around” because the spectrum is periodic, so the +Fs/2 bin is the same as the -Fs/2 bin. You can also view the spectrum as being at all positive frequencies if you prefer, with the Nyquist bin in the middle at +Fs/2.
英文:
The Nyquist bin “wraps around” because the spectrum is periodic, so the +Fs/2 bin is the same as the -Fs/2 bin. You can also view the spectrum as being at all positive frequencies if you prefer, with the Nyquist bin in the middle at +Fs/2.
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