DSP - Frequency Response of an FIR Filter

[Lightning19]

Homework Statement

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.

 

[dlgoff]

Here's a Wiki page on http://en.wikipedia.org/wiki/Complex_number#Notation_of_the_polar_form" that might help.

 

[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?

 

[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 explanation on page 147.

We can replot the data by separating the plots for magnitude and
phase making two plots versus frequency...

"www.ece.clemson.edu/crb/ece409/PlettNotes/PlettDawson.pdf"[/URL]

Regards