# Homework Help: Finding whether a filter is low/high/band pass

1. Apr 25, 2017

### t.kirschner99

1. The problem statement, all variables and given/known data
Consider the IIR filter yn = xn - yn-2

State whether the filter is low, high, or band pass.

2. Relevant equations
The Z-transform: $$H(z) = \frac {1} {1+z^2},$$

Subbing $z = e^{2πiw}$ : $$H(w) = \frac {1} {1+e^{4πiw}},$$

Amplitude response: $$|H(w)| = \sqrt{{(\frac {1} {1 + cos{(4πw)}})}^2 + {(\frac {1} {sin{(4πw)}})}^2},$$

3. The attempt at a solution
I set up the domain $w = [0,1]$

$w = 0$

Amplitude response would equal $\frac {1} {2}$

$w = \frac {1} {2}$

Amplitude response would equal $\frac {1} {2}$

$w = 1$

Amplitude response would equal $\frac {1} {2}$

Doesn't this not prove anything? I know the answer is band pass, but I would expect zeroes on both ends and a number greater than zero in the middle.

2. Apr 26, 2017