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From: Wei on 19 Jan 2010 11:47
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.
From: Wayne King on 19 Jan 2010 11:59
"Wei " <laiwei(a)egr.msu.edu> wrote in message <hj4nmo$790$1(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.

For real-valued signals, the discrete Fourier transform (DFT) is conjugate symmetric, meaning the value at a positive frequency is the complex conjugate of the DFT at a negative frequency. This does not mean that the phases differ by pi radians, or 180 degrees. Read up on some basics of complex numbers and look at the relationship between the argument (phase) of a complex number and its conjugate.
Wayne
From: Luca Zanotti Fragonara on 19 Jan 2010 13:04
"Wei " <laiwei(a)egr.msu.edu> wrote in message <hj4nmo$790$1(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.


It's not just in Matlab, is in the Fourier Transform... To plot the real spectrum, you have to switch the second half of the array before the first half. In this case you obtain before the spectrum for negative frequencies, and later the spectrum for positive frequencies.

By the way the real part of the FFT and the phase of the FFT have no difference in the rappresentation...
From: Wei on 19 Jan 2010 13:28
"Wei " <laiwei(a)egr.msu.edu> wrote in message <hj4nmo$790$1(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. 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?
From: Matt J on 19 Jan 2010 13:40
"Wei " <laiwei(a)egr.msu.edu> wrote in message <hj4tjj$34j$1(a)fred.mathworks.com>...
> "Wei " <laiwei(a)egr.msu.edu> wrote in message <hj4nmo$790$1(a)fred.mathworks.com>...

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?
===============

Like you just said: "In MATLAB, you get both"
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