1
$\begingroup$

i got that system $x_n \to x_n-x_{n-1}$, so $h_n=[.....,0,1,-1,0,...]$, with $h_0=1$ and $h_1=-1$, so the transfer function given by:

$$\sum_{i=-\infty}^{\infty} h_ne^{-jwn} = h_0e^{-jw(0)}+h_1e^{-jw(1)}=1-e^{-jw}$$. How to knwo the type of filter, if it is HPF, LPF, etc.

I appreciate your help.

$\endgroup$
  • $\begingroup$ Posted simultaneously to electronics.SE (and possibly to other SE sites also) where it has received two answers as well as several comments. $\endgroup$ – Dilip Sarwate Apr 3 '13 at 23:01
2
$\begingroup$

That is an FIR filter transfer function.

Plot the frequency response to determine if it is HP, BP, LP.

(Hint: compare the magnitude at w=0 and w=pi to get a quick idea)

This seems like a homework problem, so I don't think it is appropriate to supply a complete answer.

$\endgroup$
  • $\begingroup$ Yes, that is a homework problem, but i want to know that if H(0)=0, and H(infinity)=1, then it is a HP $\endgroup$ – Sebastian Valencia Apr 3 '13 at 12:12
  • 1
    $\begingroup$ H(infinity) is not a usful concept in discrete time filters. Your upper frequency is fs/2 --> w=pi. In some transforms of continueous time filters to discrete time versions, infinity actually maps to w=pi (bilnear z transform). The important thing to realize is that in a discrete time system, frequency exists only over a finite range with upper bound at fs/2. $\endgroup$ – user2718 Apr 3 '13 at 17:39
  • $\begingroup$ One other point. Checking at 0 and infinity (or pi) might give you an idea about the filter behavior. If my life depended on getting this right, I would look at the response over the entire frequency range to make such a determination. Maybe this filter has a peak of 10000 at w=pi/2. How would you classify it then? $\endgroup$ – user2718 Apr 3 '13 at 17:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.