FFT 窗函数及其对频谱带功率的影响
如果我对时域瞬态信号应用一个窗口，我会将时间信号频谱与窗口函数的频谱进行卷积。如果我不使用窗口，我会将信号与矩形窗口的频谱进行卷积。
我拥有的是具有不同时间频谱带功率的瞬态信号，这意味着高频位于信号的开头，低频位于信号的中间和结尾。但这也可以改变。现在，如果我将时域信号与汉恩窗相乘，则由于该窗，开始和结束的振幅将大幅衰减，但如果我不使用窗（矩形），则频谱将被展宽，我的能量也会出错。
我想要的是最准确的频带功率，哪个窗口最适合此应用？ 
If i apply a window to my time domain transient signal i convoulte the temporal signal spectrum with the spectrum of the window function. If i use no window i convolute the signal with the spectrum of a rectangular window.
What i have is a transient signal with differing temporal spectral bandpower, meaning high frequencies are at the beginning of the signal and low frequencies are at the middle and end. But this can also change. Now if i multiply my time domain signal with a hann window the amplutide of the beginning and the end will be substantially damped due to the window but if i use no window (rectangular) the spektrum will be broadend and my energies will be wrong too.
What i want to have is the most accurate band powers, which window is the best for this application?
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如果您正在处理真实的数据流，FFT 应该有某种重叠（以帮助解决您对丢失某些内容的担忧）。对于我目前正在进行的音频分析，我喜欢使用至少 15% 的重叠。
根据原始描述，如果给您一个数据快照并要求对其进行分析，您可以使用一些技术来绕过你所描述的真正问题。您可以添加自己的填充或（我最喜欢）在更大的 FFT 中复制数据（如果您的主要兴趣是幅度而不是相位，您可以实施镜像方法来解决边缘不连续性）。
If you are working with a real data flow, the FFT should have some sort of overlap (to help address your concerns about missing something). For the audio analysis I'm currently working on, I like to use a minimum overlap of 15%
Based on the original description, if you are given one snapshot of data and asked to analyze it, there are techniques you use to get around the real problem you described. You can add your own padding or (my favorite) replicate the data within a larger FFT (if your primary interest is magnitude and not phase, you can implement a mirroring approach to address edge discontinuities).
正如您所说，当您将信号乘以窗口时，您将信号的 FFT 与窗口的 FFT 进行卷积。
然而，这两种 FFT 都很复杂，并且上述陈述忽略的是，由于窗口和信号之间的相位关系，这种卷积会衰减窗口末端附近出现的频率。
窗口程序似乎不适合您正在做的事情。您基本上有两种选择：
您可以使用多个重叠窗口，正如 JR 在他的回答中所说。重叠 50% 并平均功率谱。
您可以用零将信号填充到其原始长度的 4 倍或 8 倍，而不是加窗，然后对整个信号进行 FFT。这将为您的 FFT 提供更高的分辨率，并且由于时间有限的信号具有带限傅里叶变换，因此 FFT 将非常平滑，您可以使用三次插值来为您提供实际连续信号的良好近似值 信号的傅里叶变换。
As you say, when you multiply the signal by the window, you convolve the signal's FFT with the window's FFT.
Both of these FFTs are complex, however, and what the above statement neglects is that, because of the phase relationship between the window and the signal, this convolution will attenuate the frequencies that occur near the window ends.
The windowing procedure doesn't seem to be appropriate for what you're doing. You basically have two choices:
You can use multiple overlapping windows, as J.R. says in his answer. Overlap by 50% and average the power spectra.
Instead of windowing, you can pad your signal out with zeros to 4x or 8x its original length, and then do an FFT of the whole thing. This will give you more resolution in your FFT and, because a time-limited signal has a band-limited Fourier transform, the FFT will be pretty smooth and you can use cubic interpolation to give you a good approximation of the actual continuous Fourier transform of your signal.