使用scipy.signal在Python中进行卷积和反卷积 [英] Convolution and Deconvolution in Python using scipy.signal

问题描述

我正在尝试对音频样本进行（反）卷积。
我有一个示例 s ，并且同一示例带有 s_f 并添加了一些过滤器。两个样本都表示为numpy数组。
我想对它们进行反卷积，以获得代表孤立过滤器 f 的数组。一旦这样做，我应该能够使用 s 和 f 的卷积来再现 s_f 。

I am trying to do some (de)convolution with audio samples. I have one sample s and the same sample with some filters added on top of it s_f. Both samples are represented as numpy arrays. I want to deconvolve them in order to get an array that represents the isolated filter f. Once I do that I should be able to reproduce s_f using convolution of s and f.

这是代码：

f = signal.deconvolve(s, s_f)
convolved = signal.convolve(s, f)

但是，第二行出现以下错误：

However, I get the following error on the second line:

ValueError: in1 and in2 should have the same rank

有人知道我在做什么错吗？

Does anyone know what am I doing wrong here?

非常感谢，
omer

Thanks much, omer

推荐答案

deconvolve 返回两个数组，即商和余数。因此，尝试：

deconvolve returns two arrays, the quotient and the remainder. So try:

f, r = signal.deconvolve(s, s_f)

长期以来， deconvolve 尚无适当的文档字符串，但其中有一个文档字符串。 github上的master分支： https://github.com/ scipy / scipy / blob / master / scipy / signal / signaltools.py＃L731

For a long time, deconvolve has not had a proper docstring, but it has one in the master branch on github: https://github.com/scipy/scipy/blob/master/scipy/signal/signaltools.py#L731

文档字符串显示了反卷积。这是另一个（ sig 是 scipy.signal 和 np numpy ）：

The docstring shows an example of the use of deconvolve. Here's another (sig is scipy.signal and np is numpy):

要进行反卷积的信号是 z ，并且滤波器系数在 filter 中：

The signal to be deconvolved is z, and the filter coefficients are in filter:

In [9]: z
Out[9]: 
array([  0.5,   2.5,   6. ,   9.5,  11. ,  10. ,   9.5,  11.5,  10.5,
         5.5,   2.5,   1. ])

In [10]: filter = np.array([0.5, 1.0, 0.5])

应用解卷积：

In [11]: q, r = sig.deconvolve(z, filter)

In [12]: q
Out[12]: array([ 1.,  3.,  5.,  6.,  5.,  4.,  6.,  7.,  1.,  2.])

将过滤器应用于 q 以验证我们是否返回了 z ：

Apply the filter to q to verify that we get back z:

In [13]: sig.convolve(q, filter)
Out[13]: 
array([  0.5,   2.5,   6. ,   9.5,  11. ,  10. ,   9.5,  11.5,  10.5,
         5.5,   2.5,   1. ])

通过构造，这是一个非常干净的示例。其余为零：

By construction, this is a very clean example. The remainder is zero:

In [14]: r
Out[14]: array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])

当然，您不会总是得到如此出色的结果。

Of course, you won't always get such nice results.

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