PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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. B a r t l e t t
   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(2pit); % 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’)