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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.

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  • $\begingroup$ Posted simultaneously to electronics.SE (and possibly to other SE sites also) where it has received two answers as well as several comments. $\endgroup$ Commented Apr 3, 2013 at 23:01

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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.

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  • $\begingroup$ 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 $\endgroup$ Commented Apr 3, 2013 at 12:12
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    $\begingroup$ 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
    Commented Apr 3, 2013 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
    Commented Apr 3, 2013 at 17:50

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