% Chapter 7: Hamming Window Amplitude Response
%
M = 45; alpha = (M-1)/2;
n = -alpha:alpha;
w = (hamming(M))'; sumw = sum(w);
N = 1000; omega = (2*pi/N)*[-N/2:N/2];
Wr = real(w*(exp(-j*n'*omega)));
db = 20*log10(abs(Wr)/max(Wr));
IntWr = cumsum(Wr);
Intdb = 20*log10(abs(IntWr)/N);
k = (N/2+1) - min(find(Intdb > -53));
tr_width = 2*k*2*M/N, %actual transition width in pi/M units
omega1 = -(tr_width/2)/M; omega2 = (tr_width/2)/M;
%
% plots
subplot(1,1,1)
subplot(2,2,1); stem(n,w);
axis([-(alpha+8),(alpha+8),-0.1,1.1]);
set(gca,'YTickMode','manual','YTick',[0,1])
set(gca,'XTickMode','manual','XTick',[-22,0,22]);
title('Hamming Window : M=45')
xlabel('n'); ylabel('w(n)')
subplot(2,2,3); plot(omega/pi,Wr);
axis([-1,1,-2,sumw+5]);
set(gca,'YTickMode','manual','YTick',[0,sumw])
set(gca,'XTickMode','manual','XTick',[-1,0,1]); grid
set(gca,'XTickLabelMode','manual','XTickLabels',[' 0';'22';'45']);
title('Amplitude Response')
xlabel('frequency in pi units'); ylabel('Wr')
subplot(2,2,2); plot(omega/pi,db);
axis([-1,1,-60,10]);
set(gca,'YTickMode','manual','YTick',[-60,-42,0])
set(gca,'YTickLabelMode','manual','YTickLabels',['60';'43';' 0'])
set(gca,'XTickMode','manual','XTick',[-1,0,1]);grid
title('Amplitude Response in dB')
xlabel('frequency in pi units'); ylabel('Decibels')
subplot(2,2,4); plot(omega/pi,Intdb);
axis([-1,1,-70,10]);
set(gca,'YTickMode','manual','YTick',[-70,-54,0])
set(gca,'YTickLabelMode','manual','YTickLabels',['70';'54';' 0'])
set(gca,'XTickMode','manual','XTick',[-1;omega1;omega2;1]);grid
set(gca,'XTickLabelMode','manual','XTickLabels',['-1';'  ';'  ';' 1'])
title('Accumulated Amplitude Response')
xlabel('frequency in pi units'); ylabel('Decibels')
text(omega2,5,'Width=(6.6)*pi/M')