Solved ECE113: DSP Homework 8

Description

Problem 1: Problem 3.45 in R1
Problem 2: Problem 4.22 in R1 ((c) and (e) only)
Problem 3: Problem 5.27 in R1
Problem 4: Problem 5.68 in R1 (𝑟!”(𝑙) only)
Problem 5: Problem 5.84 in R1
MATLAB:
Hints:
1) Use “fir1” function with proper arguments.
2) Note that the stopband attenuation As and the passband ripple Rp are defined as
follows:
3) But, remember that in most window-based designs, our only design parameters are the
window type and the number of taps in the filter (or the filter order). We already know
that the Hann window will meet ~44dB stopband attenuation, and as such, will meet
our As spec above. Therefore, for this problem, you will NOT use the As and Rp specs
above in your design explicitly. You will just need to find the minimum number of taps
for your filter, as described below, and then once you have the filter, just confirm that it
does meet your specs for both passband ripple and stopband attenuation.
4) Also remember that in window-based FIR design, we always get 𝛿# = 𝛿$ . So from As
and Rp specs, you would have to find 𝛿# and 𝛿$, and then once you have the filter, just
confirm that it will indeed meet the minimum of the two.
5) The exact value of the main-lobe width, and therefore the filter transition bandwidth,
associated with Hann window is 6.2𝜋⁄𝑀 where 𝑀 is the length of the window, or
equivalently the number of taps in your FIR filter. So, given the specs, you can find the
narrowest transition bandwidth you need to achieve, and based on that, find the
minimum number of taps for your filter. Use an odd number so you end up with a Type I
linear-phase FIR filter.
6) Use the center points of the transition bands as the edges of your passband, as passed
to “fir1” function (i.e., [w1 w2]).