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