Can't apply FFT on a simple cosine wave

Question

I've already read quite a few posts about the Discrete Fourier transform, but I find myself struggling to apply it on a simple cosine wave. I'm using the kiss_fft library to calculate the DFT of a set of data and a bitmap library to visualize the result.

Here's the C++ code:

#define FIXED_POINT 32
#include "kiss_fft.h"

int main()
{    
    const int width = 512;
    const int height = 512;
    const int align_center = 256;
    const int fft_siz = width;
    const int is_inverse = 0;

    Bitmap bmp_t("fft_time.bmp", width, height);
    Bitmap bmp_f("fft_frq.bmp", width, height);

    kiss_fft_cpx* in = (kiss_fft_cpx*)malloc(sizeof(kiss_fft_cpx) * fft_siz);
    kiss_fft_cpx* out= (kiss_fft_cpx*)malloc(sizeof(kiss_fft_cpx) * fft_siz);
    kiss_fft_cfg cfg = kiss_fft_alloc(fft_siz, is_inverse, NULL, NULL);

    // initialize input data
    for(int i = 0; i < fft_siz; i++)
    {
        // I think I shouldn't add align_center to in[i].r
        // but should wait till line (1*)
        in[i].r = align_center + 128 * cos(0.128f * i);
        in[i].i = 0;

        // line (1*)
        bmp_t.setPixel(i, in[i].r, 255, 255, 255);
    }

    kiss_fft(cfg, in, out);

    // visualize output
    for(int i = 1; i < fft_siz; i ++)
        bmp_f.setPixel(out[i].r, out[i].i, 255, 255, 255);

    free(in);
    free(out);
    free(cfg);

    kiss_fft_cleanup();

    bmp_t.write();
    bmp_f.write();

    return 0;
}

Here is the input:

enter image description here

and what I'm getting as output:

enter image description here

The result doesn't feel right at all. What is that I'm doing wrong ?

[Don't cast the return value of `malloc()` in C](http://stackoverflow.com/a/605858/28169). — unwind, Jun 28 '13 at 12:21

score 3 · Accepted Answer · answered Jun 28 '13 at 12:07

3

Plotting just the real component of the FFT output is not very meaningful - plot the magnitude instead (sqrt(re*re+im*im)). Even better, plot the log magnitude in dB (10*log10(re*re+im*im))

answered Jun 28 '13 at 12:07

Paul R

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Ok. [ouput](http://farm8.staticflickr.com/7377/9159266730_04148f7b37_o.jpg) `sqrt(re*re+im*im)` is in white and `10*log10(re*re+im*im)` in red. I googled fft for cos, and it seems right. – Jonas Jun 28 '13 at 12:32
1

Yes - note also that if you add a window function prior to the FFT you'll get a sharper peak. You should also only plot the first N/2 points. – Paul R Jun 28 '13 at 13:48

Can't apply FFT on a simple cosine wave

1 Answers1