Hello,

How can I calculate the Fourier transform of impulse response ^h(w) and phase function psi(w) of the given impulse response h= (kh) is defined by: h0= 1/2, h1= 1, h2= 1/2, otherwise= 0 ?

Thanks for your help.

- Dec 3rd 2010, 05:17 PMnasil122002Pulse response and Phase function (image processing-Wavelets)?
Hello,

How can I calculate the Fourier transform of impulse response ^h(w) and phase function psi(w) of the given impulse response h= (kh) is defined by: h0= 1/2, h1= 1, h2= 1/2, otherwise= 0 ?

Thanks for your help. - Dec 3rd 2010, 11:09 PMchisigma
The [discrete] 3-points Fourier Tranform of h(n) is given by...

$\displaystyle \displaystyle H(k)= \sum_{n=0}^{2} h(n)\ e^{- j 2 \pi \frac{k n}{3}$ , $\displaystyle k=0,1,2$ (1)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - Dec 4th 2010, 01:59 AMnasil122002
Thanks for the answer, how can I now calculate the pulse response h^(w) and psi (w) on this formula? I need really a complete solution.

- Dec 6th 2010, 02:14 AMchisigma
The Z-Transform os the finite 3-points sequence h(n) by definition is given by...

$\displaystyle \displaystyle H(z)= \sum_{n=0}^{2} h(n)\ z^{-n}$ (1)

The complex transfer function [FIR filter...] is easily obtained from (1) setting $\displaystyle z=e^{j \omega}$. A more complex alternative is the derivation of the H(z) fron the H(k) I have defined in my previous post using the inverse discrete Fourier transform...

$\displaystyle \displaystyle H(z)= \frac{1}{3}\ \sum_{k=0}^{2} H(k)\ \frac{1-z^{-3}}{1- e^{-j 2 \pi \frac{k}{3}}\ z^{-1}}$ (2)

... and again You can find the complex transfer function setting in (2) $\displaystyle z=e^{j \omega}$...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$