The Window Method of Filter Design is based on choosing
engineering
Description
Problem 1: The Window Method of Filter Design is based on choosing h[n] =
v[n]w[n] where v[n] is impulse response of an ideal filter and w[n] is a window
function.
To get the desired frequency
response, one typically adjusts the cutoff frequency of the ideal filter, the
window type, and the window length. (a) Use this method to design a low-pass
filter with pass band 0 ≤ |Ω| < 1.3, pass-band ripple < 0.5 dB, stop band
π/2 ≤ |Ω| ≤ π, and 50 dB stop-band rejection.
Mathematically, this means
20 log10 |H(e jΩ)| < 0.5 for 0 ≤ |Ω| ≤ 1.3
20 log10 |H(e jΩ)| < −50 for π/2
≤ |Ω| ≤ π.
Design the filter (with fdatool or
filterDesigner) plot the magnitude response, and report the final
specifications you achieve (i.e., pass-band ripple and stop-band rejection with
the filter transfer function plot).
(b) Load and listen to ”singing8.wav”. Now,
try decimating by 2 and listening with soundsc(x(1:2:end),Fs/2). What do you
hear?
(c) Can you use the filter from (a)
to allow down-sampling by 2 without audible distortion? Explain.
