How autocorrelation is related to psd and fourier transform?

autocorrelation

How autocorrelation is related to psd and fourier transform of signal?

Re: autocorrelation

hi

PSD(f)=4*Integral[cos(2*pi*f*t)*Autocorrelation from -inf, +inf]

The PSD is the Fourier transform of the autocorrelation sequence.




hope it helped u
-helios

Re: autocorrelation

FT of the ACF of x(t) is the PSD.

PSD = |FT [x(t)]|^2;

so FT of ACF is |FT[x(t)]|^2;

hope u got it

purna

Re: autocorrelation

ok i am assuming that you are totally new to dsp and as such those two answers that you have already received probably mean nothing to you. Anyway the only relation that there is between autocorrelation and the fourier transfrom is actually the similarity between the DFT (discrete fourier transform) and auto correlation i.e. if you are learning DSP in your book it will give you a hand method of calculating the DFT, cross correlation (between two signals) and the autocorrelation. the calculation of these three items by hand is quite similar (and no i won't get into the technical details for now). the only relation between autocorrelation and psd is the fact that if you take a signal and get the autocorrelation of that signal, then if you apply the fourier transform to the result you will get the psd.
hope this helps,
sincere regards,
t

autocorrelation

PDS = F(R(x))
F() = Fourier transofrm
R(x) = Autocorrelation function

Thanks
Animesh

Re: autocorrelation

I asked the same question a while ago, but everyone kept giving me mathematical equations, can't anybody give us a paper that describes this physically?:idea:

Re: autocorrelation

Hi azaz104,

I dont know the exact paper which describe the mathematical equation physically, but I am attaching a paper which gives you the usage of above mathematical equation in audio/speech codec applications.
I think this paper helps you to understand it physcially.

Thanks
Animesh

Re: autocorrelation

Is this the one by J_lrgen Herre and James Johnston?

Re: autocorrelation

Hi aza101

yes.

Thanks
Animesh