# Find impulse response and frequency response through given filter [duplicate]

I cannot find anything truly helpful in my book, and I find mostly theoretical answers and not practical. So I am posting the exact exercise I want to solve, and through it I hope I'll work some things out.

Our data is that we filter voice/speech signals with this filter: $y(n) = x(n) - 0.8 x(n-1)$

a. What's the impulse response of the filter
b. What's the measure of the frequency response of the filter, in dB, on the frequency $2000 Hz$. The sampling frequency is $Fs = 16000 Hz$.

I started doing this:

$y(n) = x(n) - 0.8x(n-1)$

$Y(z) = X(z) - 0.8X(z^{−1})$

$Y(z) = X(z) [1 -0.8z^{-1}]$

$H(z) = Y(z) / X(z) = 1 - 0.8z^{-1} / 1 = 1 - 0.8z^{-1}$

But I think I'm not there at all. And I actually don't get the first step where $y(n)$ becomes $Y(z)$ etc. Why do this?
And how do I now if I have a FIR or an IIR? [and what does this affect?]

• i don't know how else to tell you this, but you need to either take a course in Signals and Systems (or similarly titled) or you need to curl up with a good book or textbook about it. these are the first topics that would be covered. Jan 28 '15 at 23:02
• Taking same course as these two, huh? click, click. You even got the solution (x2)! What else can I say, @robertbristow-johnson is right - simply study!
– jojek
Jan 28 '15 at 23:47
• oh too bad I work at the same time and didn't have the time to attend class. Thought to give it a shot with the exams, but oh well. EDIT: Oh and did a bad search too
– gkri
Jan 28 '15 at 23:47
• study about z-transform and its properties.. Jan 29 '15 at 12:21