Re: [Help-gsl] Quick FFT question

[Nghia Ho]

I was thinking the same thing but written something ambiguous instead. I just 
remembered it was also called taking the "magnitude". Thannks for the 
clarification.


--- On Wed, 7/23/08, Inigo Aldazabal Mensa <address@hidden> wrote:

> From: Inigo Aldazabal Mensa <address@hidden>
> Subject: Re: [Help-gsl] Quick FFT question
> To: address@hidden
> Date: Wednesday, July 23, 2008, 6:06 PM
> El Martes, 22 de Julio de 2008 18:37, Nghia Ho escribió:
> > Hi,
> >
> > I need to implement an algorithm that makes use of the
> FFT to do some
> > basic signal processing. Basically, given an array of
> numbers I would
> > like to extract the coefficients of the N lowest
> frequency components.
> >
> > The GSL document says the results are laid out such
> that index from 0 to
> > N/2 are the positive frequencies and the rest are
> negative. My
> > mathematical knowledge of FFT is limited so please
> bare with me on the
> > next question. I see the real values are the same for
> both
> > positive/negative side, but imaginary values flip.
> 
> This is so because your input signal is Real (I mean, Real
> numbers). In 
> this case the values form the positive/negative frequencies
> are complex 
> conjugate of each other, as you say. See eg[1] for more
> info and 
> references.
> 
> > So if I take the 
> > magnitude (|Re + Imz|) of the first N values of the
> positive side would
> > that give me what I want?
> >
> 
> I don't know what exactly do you mean by |Re + Imz|,  
> but if you take  the 
> modulus of the complex number,   |z|=sqrt(a*a+b*b), being
> z=a+ j b, 
> j=sqrt(-1), this |z| will be equal for each semiaxis, i.e
> |z(w)|=|z(-w)|, 
> and gives you the frequency spectra for your signal. For
> this see 
> e.g. "The Scientist and Engineer's Guide to
> Digital Signal Processing"
> By Steven W. Smith, Ph.D., chapter 8, specifically section
> "Polar Notation" 
> [2]. If you are new to DFT take a look to  the whole
> chapter, and also to 
> the next one "Applications of the DFT", it will
> be worth it.
> 
> [1]http://en.wikipedia.org/wiki/Discrete_Fourier_transform#The_real-input_DFT
> 
> [2]http://www.dspguide.com/ch8/8.htm
> 
> 
> 
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