Question

我正在尝试在我的一个项目中实现FFT。不幸的是，我觉得我去的每个网站都在解释我的想法。我已经查看了许多不同的网站进行澄清，但到目前为止我还没有找到它。

到目前为止，我所拥有的每个网站都要么编写好的代码，没有对变量或其他解释的评论，要么已经解释了一些我无法理解的事情。

如果有人能够以最具描述性的方式分解此代码的每个部分和过程，我将不胜感激。

首先，我知道FFT的输入是[1.0,1.0,1.0,1.0,0.0,0.0,0.0,0.0]。这些数字代表什么？它们是赫兹还是伏特？

最后，我知道FFT的输出是4.000 2.613 0.000 1.082 0.000 1.082 0.000 2.613。这些数字代表什么？单位是什么？它们如何用于从数据集中获得幅度或频率？

同样，我正在寻找要解释的每一步，因此评论以下FFT代码也会非常有帮助。如果你能够很好地解释这个5岁的孩子会理解的话，我将永远感激不尽。（有时候看文章的时候我觉得这个年龄。）

提前感谢所有帮助。你们这里的人帮了我一个TON。

代码来源：http://rosettacode.org/wiki/Fast_Fourier_transform#Python

CODE：

from cmath import exp, pi

def fft(x):
    # I understand that we are taking the length of the array sent
    #   into the function and assigning it to N. But I do not get why.
    N = len(x)
    # I get that we are returning itself if it is the only item. 
    # What does x represent at this point?
    if N <= 1: return x
    # We are creating an even variable and assigning it to the fft of 
    #   the even terms of x. This is possibly because we can use this 
    #   to take advantage of the symmetry? 
    even = fft(x[0::2])
    # We are now doing the same thing with the odd variable. It is 
    #   going to be the fft of the odd terms of x. Why would we need
    #   both if we are using it to take advantage of the symmetry?
    odd =  fft(x[1::2])
    T= [exp(-2j*pi*k/N)*odd[k] for k in range(N//2)]
    return [even[k] + T[k] for k in range(N//2)] + \
           [even[k] - T[k] for k in range(N//2)]
# I understand that we are printing a join formatted as a float
# I get that the float will have 3 numbers after the decimal place and
#    will take up a total of 5 spots
# I also understand that the abs(f) is what is being formatted and
#    that the absolute value is getting rid of the imaginary portion
#    that is often seen returned by the FFT
print( ' '.join("%5.3f" % abs(f) 
            for f in fft([1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0])) )

返回值：

4.000 2.613 0.000 1.082 0.000 1.082 0.000 2.613

Answer 1

FFT只是计算DFT的一种快速方法（使用分解技巧）。

也许首先要了解DFT的作用，因为FFT因子技巧可能会混淆DFT的作用。 DFT只是基础变换（一种矩阵乘法）。单位可以是完全任意的（毫伏，英寸，加仑，美元等）。任何一组频率结果都取决于输入数据的采样率。

FFT代码分解

1 个答案: