# Homework Help: Phase shift and amplitude change when put through FIR filter

1. May 1, 2013

### Jd303

Hey all,
I am having trouble with this problem:

A sampled sinusoidal signal having a normalized frequency of 0.30π is sent through an FIR filter. The filter impulse response is,

h[n] = 1/3δ[n] + 1/3δ[n-1] + 1/3δ[n-2]

From this I must find out by what factor the input signal is multiplied by and what the phase shift is, (if there is in fact a phase shift).

my current theory is:
Let z = e^(jω) (j = i for those not in an electrical field)

H(z) = 1/3 + 1/3*z^(n-1) + 1/3*z^(n-2)

y[n] = H(z)*z^n

Then I am lost from here assuming my above theory is even correct. Any help would be greatly appreciated as I have been stuck on this one for a while. :)

2. May 2, 2013

### rude man

Do you know what "normalized frequency" means? I sure don't. It must be related to the sample time T. So assuming T = 1 then f = 0.3pi/T?

3. May 2, 2013

### Jd303

Not to worry, figured it out you can obtain phase and magnitude directly from H(z), also normalised frequency is just omega divided by the sampling rate