信号处理：FFT重叠处理资源 [英] Signal processing: FFT overlap processing resources

问题描述

有什么好看的（如果可能的科学）关于重叠处理可用资源（网络或书籍）。我不是在分析信号时，因为要求不同使用叠加处理和窗口的作用感兴趣。它更多的是下面的实时情况：（我目前正在处理的音频信号）

Are there any good (if possible scientific) resources available (web or books) about overlap processing. I am not that interested in the effects of using overlap processing and windows when analyzing a signal, since the requirements are different. It is more about the following Real Time situation: (I am currently dealing with audio signals)

• 把一个信号转换成更小的部分。


• 创建重叠的窗口。


• FFTing的窗口块。


• 请在频域处理。


• IFFT的结果。


• 把块一起连续流。

我在上所产生的误差以及重叠长度的效果所使用的窗口的影响特别感兴趣。不过，我无法找到与详细的主题处理任何好的资源。有什么建议？

I am especially interested in the influence of the window used on the resulting error as well as the effect of the overlap length. However I couldn't find any good resources that deal with the subject in detail. Any suggestions?

编辑：

一些讨论，如果使用窗函数是合适的，我发现一个体面的讲义解释重叠和添加/保存方法。的http://www.ece.tamu.edu/~deepa/ecen448/handouts/08c/10_Overlap_Save_Add_handouts.pdf

After some discussions if using a window function is appropriate, I found a decent handout explaining the overlap and add/save method. http://www.ece.tamu.edu/~deepa/ecen448/handouts/08c/10_Overlap_Save_Add_handouts.pdf

不过，做一些测试之后，我注意到，视窗版将执行在大多数情况下比重叠和放大器更准确;添加/保存方法。任何人可以证实这一点？
我不想妄下结论，但有关计算时间......

However, after doing some tests, I noticed that the windowed version would perform more accurate in most cases than the overlap & add/save method. Could anybody confirm this? I don't want to jump to any conclusions regarding computation time though....

EDIT2：

下面是一些图表从我的测试：

Here are some graphs from my tests:

我创建了一个信号，它包括三个余弦波

I created a signal, which consists of three cosine waves

我过滤时域使用该过滤功能。 （这是对称的，因为它被施加到FFT的整个输出，这也是对称的即时输入信号）

I used this filter function in the time domain for filtering. (It's symmetric, as it is applied to the whole output of the FFT, which also is symmetric for real input signals)

在IFFT的输出是这样的：它可以看出，低频衰减比在中期范围内的频率更多。

The output of the IFFT looks like this: It can be seen that low frequencies are attenuated more than frequency in the mid range.

有关的重叠增加/保存，并且加窗处理我除以输入信号转换成256个采样8块。重组后，他们他们看起来像。 （样品490 - 540）

For the overlap add/save and the windowed processing I divided the input signal into 8 chunks of 256 samples. After reassembling them they look like that. (sample 490 - 540)

可以看出，该重叠增加/保存处理从窗口版本在哪里块被放在一起点（样本511）不同。这是比较窗口过程和重叠添加/保存时，这会导致不同的结果的误差。加窗处理是更接近一个在一个大的垃圾进行处理。

It can be seen that the overlap add/save processes differ from the windowed version at the point where chunks are put together (sample 511). This is the error which leads to different results when comparing windowed process and overlap add/save. The windowed process is closer to the one processed in one big junk.

不过，我不知道为什么他们在那里，或者如果他们不应该存在的。

However, I have no idea why they are there or if they shouldn't be there at all.

推荐答案

这是相当知名的信号处理领域，一般来说，如果你是沿着FFT的线路做处理 - >光谱处理 - > IFFT你需要使用重叠，并添加方法。的两个输入端的交叉相关性是一个典型的例子，在比时域中的频谱域更容易地进行。

This is fairly well-known area of signal processing, and generally speaking if you are doing processing along the lines of FFT -> spectral processing -> IFFT you need to use the "overlap and add" approach. Cross-correlation of two inputs is a classic example, done much more easily in the spectral domain than the time domain.

下面是一个简短的论文中，我发现马上通过谷歌（我只是搜索FFT重叠和加法）：的 http://www.coe.montana.edu/ee/rmaher/ee477/ee477_fftlab_sp07.pdf

Here's a short paper I found right away via Google (I just searched for "fft overlap and add"): http://www.coe.montana.edu/ee/rmaher/ee477/ee477_fftlab_sp07.pdf

我会建议你投资在一个良好的信号处理的书，比如经典的Rabiner和放大器;黄金理论和数字信号处理的申请（prentice霍尔ISBN 0-13-914101-4）。应该涵盖重叠和加法运算处理的概念

I would recommend you invest in a good Signal Processing book, such as the classic Rabiner & Gold "Theory and application of digital signal processing" (Prentice-Hall ISBN 0-13-914101-4). That should cover the concept of overlap-and-add processing.

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