phase addition to spectrum of signals and reconstruction

i have a question regarding phase randomisation and its effect on the
signal. i took the fft of a sound file. to its phase part i added a
random phase. and from the magnitude part i subtracted the magnitude of
the spectrum of noise which in magnitude was very less compared to the
original sound (simple spectral subtraction). i then reconstructed the
sound file thus edited by taking ifft. all this processing was done in
matlab. now after taking ifft i was expecting a real signal which i
should ideally get. but i am getting a complex signal. please explain
this irregularity to me. thanks

in article 1119355225.421761.167410@o13g2000cwo.googlegroups.com, adj at
arshdeepjindal@gmail.com wrote on 06/21/2005 08:00:

> i have a question regarding phase randomisation and its effect on the
> signal. i took the fft of a sound file. to its phase part i added a
> random phase.

if your input signal was real, the phase in the FFT was odd-symmetric about
0 (or about N/2).  if the random phase you added was not also odd-symmetric,
then you break that property and that will be the FFT of a not entirely real
signal.

> and from the magnitude part i subtracted the magnitude of
> the spectrum of noise which in magnitude was very less compared to the
> original sound (simple spectral subtraction). i then reconstructed the
> sound file thus edited by taking ifft. all this processing was done in
> matlab. now after taking ifft i was expecting a real signal which i
> should ideally get. but i am getting a complex signal. please explain
> this irregularity to me. thanks

make sure the real part (or magnitude) is even symmetry and the imag part
(or phase) is odd symmetry.  then you'll get a real result.


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

please could you explain in a little more detail. i would very much
appreciate it. also could you tell me some sources where i can read
more on even symmetry and odd symmetry of magnitude and phase parts.
thank you very much in advance.

Hi,

I would recommend using a real FFT ( an FFT, which is designed for real 
input data ). Its  IFFT assumes the right symmetry properties by default, so 
you will get real output data from it, whatever you do with the Fourier
spectrum ;-)
And as a side effect, the Real FFT will be faster than the usual complex 
FFT.

Unfortunately I don't know if there is any Matlab code around ( well, it 
surely is, but I don't know where to find it.) Maybe you can write a wrapper 
for the C++ code from Laurent de Soras' webpage: 
http://ldesoras.free.fr/prod.html ( look for FFTReal ).

Good luck!
Karin

ps: of course this is not an explanation of the irregularity you found -
maybe you try a Google search on the keywords r b-j  was using in his email 
;-)

Hi,

I would recommend using a real FFT ( an FFT, which is designed for real 
input data ). Its  IFFT assumes the right symmetry properties by default, so 
you will get real output data from it, whatever you do with the 
Fourierspectrum ;-)
And as a side effect, the Real FFT will be faster than the usual complex 
FFT.

Unfortunately I don't know if there is any Matlab code around ( well, it 
surely is, but I don't know where to find it.) Maybe you can write a wrapper 
for the C++ code from Laurent de Soras' webpage:
http://ldesoras.free.fr/prod.html ( look for FFTReal ).

Good luck!
Karin

ps: of course this is not an explanation of the irregularity you found -
maybe you try a Google search on the keywords r b-j  was using in his email 
;-)

adj wrote:
> please could you explain in a little more detail. i would very much
> appreciate it. also could you tell me some sources where i can read
> more on even symmetry and odd symmetry of magnitude and phase parts.
> thank you very much in advance.

Try to look for a chapter named "Properties of the Fourier
Transform" in whatever textbook on DSP you have available.

Rune

thank you karin. i'll surely look this up

adj wrote:
> please could you explain in a little more detail. i would very much
> appreciate it. also could you tell me some sources where i can read
> more on even symmetry and odd symmetry of magnitude and phase parts.
> thank you very much in advance.

Your original signal was real, and its FFT was the Fourier transform of 
a real signal. The noise you added was not the FT of real noise, so the 
sum of the two FTs is not the FT of a real signal. To add random noise 
to a real signal and be sure that the result is real, either do it in 
the time domain, or add the FT of real time-domain noise to the FT of 
the signal.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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