如何对傅立叶复数值降采样? [英] How to downsample Fourier complex values?

问题描述

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我正在编写一个函数，该函数采用一维数组并对其执行快速傅立叶变换.运作方式如下:

I'm writing a function that takes a 1D array and performs Fast Fourier Transform on it. Here's how it works:

1. 如果数组的大小不是2的幂，则在末尾加0，以使其大小成为2的幂.
2. 对填充数组执行FFT并将结果存储在数组x中.
3. 对复杂数组x进行下采样以匹配原始非填充数组的长度.
4. 返回x.

1. If the array's size is not a power of two, pad it with 0s at the end so that its size becomes a power of two.
2. Perform FFT on the padded array and store the results in an array x.
3. Downsample the complex array x to match the length of the original non-padded array.
4. Return x.

我在执行第3步时遇到问题.如果我省略第3步，并对函数调用的结果执行逆FFT，则会得到初始填充数组，这意味着该函数成功执行了第1步和第2步.

I'm having trouble with step 3. If I omit step 3 and perform inverse FFT on the result of the function call, I get the initial padded array which means the function successfully performs steps 1 and 2.

我尝试通过使用线性插值进行下采样来实现第3步，但是当我使用MatLab对最终结果执行傅立叶逆变换时，得到的结果不等于原始数组.我需要使用的编程语言不是 MatLab，我仅使用MatLab来验证结果的正确性.

I tried implementing step 3 by downsampling using linear interpolation, but when I perform inverse fourier transform on the final result using MatLab, the results I got were not equivalent to the original array. The programming language I need to use is not MatLab, I'm only using MatLab to verify correctness of the results.

我可以使用哪些技术执行第3步，同时在进行逆FFT后仍然能够取回原始的未填充数组?

推荐答案

使用循环Sinc核插值计算向下采样的点.对于新的较低的下采样采样率，Sinc宽度将为低通滤波器的截止宽度，该截止值适合于抗混叠.

Use circular Sinc kernel interpolation to compute the down sampled points. The Sinc width will that of a low-pass filter with a cut-off appropriate to anti-alias for the new lower down-sampled sample rate.

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