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Re: [Discuss-gnuradio] Why is fft output complex?

From: Daniel Marlow
Subject: Re: [Discuss-gnuradio] Why is fft output complex?
Date: Sat, 11 Oct 2014 18:02:51 -0400

On Oct 11, 2014, at 5:38 PM, <address@hidden> <address@hidden> wrote:

> I can't wrap my head around why fft transform of complex signal produces a 
> complex output. After all the output reflects the amount of energy per 
> frequency bin and frequency bins and energy are both real numbers, no?
> I'm trying to write a python script to analyze the energy across frequency 
> bins but I don't know where to insert a complex to mag block. I think if I 
> can understand the fft I will know to put the complex to mag. 
> Thanks
> Brad.
> _________

Dear Brad,

    What you write is mostly correct.   But you are thinking of the power 
spectrum, which is the modulus of the FFT and thus entirely real.  An FFT 
contains more information.   For example, a Fourier Transform (the continuous 
version of an FFT) can be "inverted" using an Inverse Fourier Transform to 
exactly reproduce the original time-domain waveform.    That would not be 
possible using the power spectrum alone, since information is lost in going 
from the complex Fourier Transform to the power spectrum.

--Dan Marlow

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