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From: Greg Heath on 19 Jan 2010 18:03
On Jan 19, 1:28 pm, "Wei " <lai...(a)egr.msu.edu> wrote:
> "Wei " <lai...(a)egr.msu.edu> wrote in message <hj4nmo$79...(a)fred.mathworks..com>...
> > I am new to Fast Fourier Transform and have a general question regarding the phase information. I understand for the real-valued data, the FFT is symmetrical. What is the phase relation between the positive and negative frequency domain? In Matlab, the two phases seem to have the same value with opposite signs. Is this conventional or just Matlab thing? I read it somewhere that the phases differ by 180 degrees between the positive and negative frequency domains. Thanks a lot.
>
> Thanks for all the replies. I guess I understand it better now. The phases of the
> positive and negative frequency domain have the same values but opposite signs.

Except in cases where the transform is real and negative.
Theory will give you + pi on one side of zero and -pi on
the other side to maintain the odd function characteristic.

However, the software phase calculation uses the two
argument arctan with principal value defined on (-pi,pi].

> The question is then whether the number in the positive
> or negative frequency domain is reported? In Matlab,
> you get both but in a lot of DSP, only one is reported.
> How do we know which one? What is the convention here?

For real signals the transform is conjugate symmetric.
If software only gives half of the transform it will be
the nonegative half.
It is easy to check. Just recreate the other half and
use the ifft.

Hope this helps.

Greg



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