[FieldTrip] FFT question

Robert Oostenveld r.oostenveld at donders.ru.nl
Tue Aug 25 12:38:06 CEST 2015

On 25 Aug 2015, at 02:34, Ben Hutchinson <benhut1 at gmail.com> wrote:

> I was looking at your webpage on the FFT here http://www.fieldtriptoolbox.org/tutorial/fourier and noticed that the for an ordinary sinewave, like sin(x), the imaginary component of the FFT actually has a negative spike on the left side and a positive spike on the right side. Why is this? I thought that the left side of an FFT had the coefficient of the sinewave, and the right side of the FFT had the negative of that. So with a regular sinewave, (such as sin(x) which is actually the same as coef*sin(x) where coef=1) the left side of the imaginary part of the FFT is supposed to show that coefficient, meaning that it should have a spike of positive 1. But the FFT on this webpage instead shows a spike of -1 at that location. Why is that?

Hi Ben

from Matlab "help fft"
    For length N input vector x, the DFT is a length N vector X,
    with elements
       X(k) =       sum  x(n)*exp(-j*2*pi*(k-1)*(n-1)/N), 1 <= k <= N.
    The inverse DFT (computed by IFFT) is given by
       x(n) = (1/N) sum  X(k)*exp( j*2*pi*(k-1)*(n-1)/N), 1 <= n <= N.

Note the ā€œ-jā€ in the first equation. 

See page 158 in http://www.dspguide.com/CH8.PDF and specifically equation 8.3 on page 153, which explains it in more detail. I recommend the DSP guide as a general resource to learn more about digital signal processing.

best regards,

PS please address future questions to the email discussion list (CC) so that other people can benefit from it.
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