# DSP - Frequency Response of an FIR Filter

1. Oct 17, 2008

### Lightning19

1. The problem statement, all variables and given/known data
A linear time-invariant filter is described by the difference equation

y[n] = x[n] - x[n-2]

a) Obtain an expresson for the frequency response of this system.

b) Sketch the frequency response (magnitude and angle) as a function of frequency.

2. The attempt at a solution

a) {bk} = {1, 0, -1}
H(e^-jw)= 1-e^-j2w

b) I am not sure how to plot the magnitude.

H(e^-jw)= 1-e^-j2w = (e^-jw)(2*j*sin(w))

where (e^-jw) is the angle and (2*j*sin(w)) is the magnitude.

However, there is an imaginary number, j, in the magnitude...what do I do with this?

Thank you.

2. Oct 17, 2008

### dlgoff

Last edited by a moderator: Apr 23, 2017
3. Oct 18, 2008

### Lightning19

OK... so from the notation is seems like cos w is always 0 since the magnitude is

2jsin(w)

So would it just be an empty set of axis?

4. Oct 20, 2008

### dlgoff

I did a little googling to see if I could find a good reference for plotting complex functions in regards to frequency response. Here's a pdf on FEEDBACK CONTROL that's a bit long but has a good explaination on page 147.
"www.ece.clemson.edu/crb/ece409/PlettNotes/PlettDawson.pdf"[/URL]

Regards

Last edited by a moderator: Apr 23, 2017