Question

The MATLAB program below designs a lowpass filter for a passband edge frequency of 250Hz and a stopband edge of 350Hz. The sampling frequency is 2kHz. A Hamming window is used. (a) The program is on Webcampus. Run it and copy and paste the wvtool plots into Word. % FIR Filter Design (using wvtool) % Lowpass Design clear fpass 250; fstop 350; fs 2000; wp 2*pi* fpass/ fs; ws 2* pi fstop / fs; M=ceil(6.6 * pi / (ws-wp)) + 1;wc = (wp + ws) / 2; no-(M-1) / 2; n-0:M-1;hLP = sin(wc * (n-no),J(wc * (n-n0)); hLP(n0 + 1)=1; w = 0.54-0.46 * cos(2 * pi * n/ (M-1)); wvtool(hLP.* w) (b) Repeat (a) for a highpass filter. Recall the conversion hHP (1) hLP (c) Repeat for a bandpass filter with a center frequency of 300 Hz. and a bandwidth of SO H To implement this, you can recalculate hL.P with a cutoff of 50 Hz. and convert using hBP = 2 cos(n wo) hLP where wo is the normalized bandwidth.

Answer 1

MATLAB code is given below in bold letters.

clear;close all;
fpass = 250;
fstop = 350;
fs = 2000;
wp = 2*pi* fpass/fs;
ws = 2*pi* fstop/fs;
M = ceil(6.6*pi/(ws-wp))+1;
wc = (ws+wp)/2;
n0 = (M-1)/2;
n = 0:M-1;
hLP = sin(wc*(n-n0))./(wc*(n-n0));
hLP(n0+1) = 1;
w = 0.54-0.46*cos(2*pi*n/(M-1));
wvtool(hLP.*w);

% part b
hHP = (-1).^n .* hLP;
wvtool(hHP.*w);

% part c
w0 = 2*pi*50/fs;
hBP = (2*cos(n*w0)) .* hLP;
wvtool(hBP.*w);

Frequency domain Time domain 20 0.8 -20 0.6 -40 fhi" 0.4 -60 哎0.2 -80 -100 0.2 -120 -140 0.4 10 20 30 40 50 60 Samples 0 0.2 0.4 0.6 0.8 Normalized Frequency (×π rad/sample)

Frequency domain Time domain 20 0.8 0ii -20 0.4 -40 fhi" 0.2 시 N 0 -60 0.2 -80 0.4 -0.6 0.8 -100 -120 -140 10 20 30 40 50 60 Samples 0 0.2 0.4 0.6 0.8 Normalized Frequency (×π rad/sample)

Frequency domain Time domain 1.2 20 10 -10 0.6 命-20 0.4 3-30 Σ-40 :EA) 0.2 -50 -60 0.2 70 0.4 -80 10 20 30 40 50 60 Samples 0 0.2 0.4 0.6 0.8 Normalized Frequency (×π rad/sample)