Time Domain Representation of Continuous and Discrete Signals
91
Example 1.20
Create the script fi le explore_window that returns the plots of the truncated or windowed
function f(t) = cos(2πt) using the following window types:
1. Hamming
2. Hanning
3. Blackman
4. Kaiser (with β = 3.4)
5. Triangular
6. Boxcar
7. Bartlett
Let us defi ne f(t) = cos(2πt) by using 301 points over the range −15 ≤ t ≤ 15, and limit f(t)
using the above-mentioned windows over the range −10 ≤ t ≤ 10.
Display the plots of the windowed function f(t) over the range −15 ≤ t ≤ 15, for the
fi rst three cases and −10 ≤ t ≤ 10, for the remaining four.
MATLAB Solution
% Script file: explore _ window
t = -15:0.1:15;
% returns a vector with 301 elements
f = cos(2*pi*t);
% returns 301 element for f(t)
winpoints = -100:1:100;
% 201 window points
WHam=hamming(201);
WHan= hanning(201);
WBlac= blackman(201);
WKai= kaiser(201, 3.4);
% Beta = 3.4
WTrian= triang(201);
WRect= boxcar(201);
WBar= bartlett(201);
W1Ham= [zeros(1,50) WHam’ zeros(1,50)];
% Hamming window with 301
points
W1Han = [zeros(1,50) WHan’ zeros(1,50)];
% Hanning window with 301
points
W1Blac = [zeros(1,50) WBlac’ zeros(1,50)];
% Blackman window with 301
points
W1Kai = [ zeros(1,50) WKai’ zeros(1,50)] ;
% Kaiser window with 301
points
W1Tria = [ zeros(1,50) WTrian’ zeros(1,50)]; % Triangular window with
301 points
W1Box = [ zeros(1,50) WRect’ zeros(1,50)];
% Boxcar window with 301
points
W1Bar = [ zeros(1,50) WBar’ zeros(1,50)] ;
% Bartlett window with 301
points
Hamwin= W1Ham.*f;
% f(t) is windowed
Hanwin= W1Han.*f;
Blackwin =W1Blac.*f;
Kaiwin=W1Kai.*f;
Triwin=W1Tria.*f;
Boxwin=W1Box.*f;
Barwin=W1Bar.*f;
figure(1)
subplot(3,1,1)
plot(t, Hamwin);ylabel(‘Amplitude’);
title(‘[f(t)*Hamming widow] vs.t’)
CRC_47760_CH001.indd 91
CRC_47760_CH001.indd 91
7/25/2008 4:16:29 PM
7/25/2008 4:16:29 PM