如何在F＃中进行卷积？ [英] How do I do convolution in F#?

问题描述

我希望卷积具有离散滤波器的离散信号。信号和滤波器是F＃中的float序列。

我唯一能弄清楚方法的方法是两个嵌套的for循环和一个可变的数组来存储结果，但是感觉不太实用。 / p>

这是我无法执行的操作：

  conv = double [len（信号）+ len（过滤器）-1] 
 for i = 1到len（信号）
 for j = 1到len（过滤器）
 conv [i + j ] = conv [i + j] + signal（i）* filter（len（filter）-j）
  

解决方案

尝试以下功能：

 让卷积信号滤波器= 
 [ | 0 ..数组长度信号+数组长度过滤器-1 |] |> Array.map（fun i-> 
 [| 0 .. i |] |> Array.sum_by（fun j-> signal。[i] * filter。[Array.length filter-（i- j）-1]））
  

这可能不是最好的函数解决方案，但应该可以完成。我怀疑是否存在一种纯粹的功能性解决方案，但是该解决方案在速度上必须与当务之急相匹配。

希望有所帮助。 p>注意：该函数当前未经测试（尽管我已经确认可以编译）。让我知道它是否未完全应做。另外，请注意 i 和 j 变量所引用的内容与原始帖子所引用的内容不同。

I would like convolve a discrete signal with a discrete filter. The signal and filter is sequences of float in F#.

The only way I can figure out how to do it is with two nested for loops and a mutable array to store the result, but it does not feel very functional.

Here is how I would do it non-functional:

conv = double[len(signal) + len(filter) - 1]
for i = 1 to len(signal)
  for j = 1 to len(filter)
    conv[i + j] = conv[i + j] + signal(i) * filter(len(filter) - j) 

解决方案

Try this function:

let convolute signal filter =
    [|0 .. Array.length signal + Array.length filter - 1|] |> Array.map (fun i ->
        [|0 .. i|] |> Array.sum_by (fun j -> signal.[i] * filter.[Array.length filter - (i - j) - 1]))

It's probably not the nicest function solution, but it should do the job. I doubt there exists a purely functional solution that will match the imperative one for speed however.

Hope that helps.

Note: The function is currently untested (though I've confirmed it compiles). Let me know if it doesn't quite do what it should. Also, observe that the i and j variables do not refer to the same things as is your original post.

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