Matlab fft function swapping indices

问题

I've written a simple and very small Matlab code that calculates the Discrete Fourier Transfrom of a given array (or vector).

I worked it out manually and got an answer and my Matlab code also giving the same answer. But fft is giving an answer different from this by swapping indices. Here are the mannual calculations that I've done:

This is the second image:

This is the third image:

From those calculations it is clear that my answer would be {12, -3-3j, -2, -3+3j}

Here is the Matlab code that I've used:

clc;
clear all;
close all;
inp=[1,2,3,4];
j=sqrt(-1);
op=zeros(1,length(inp));
for k=1:length(inp)
    sigma=0;
    for n=1:length(inp)
        sigma=sigma+inp(n)*exp((j*2*pi*(k-1)*(n-1))/length(inp));
    end
    op(k)=sigma;
end
% Checking with fft
fft(inp)

Now I'm getting output as this:

It is very much unexpected that I'm getting values swapped. It is swapping the indices 2 and 4.

回答1:

It looks like you have the wrong sign for your weights (which means you're probably doing an inverse FFT instead of a forward FFT - remember that for the forward transform the weights are exp(-j * theta)).

Change:

    sigma=sigma+inp(n)*exp((j*2*pi*(k-1)*(n-1))/length(inp));

to:

    sigma=sigma+inp(n)*exp(-(j*2*pi*(k-1)*(n-1))/length(inp));

来源：https://stackoverflow.com/questions/45341851/matlab-fft-function-swapping-indices