% Name:Kai_Basel.m
clear
clf
%========================================================================
L=input('Type in the length N=');
n=0:L-1;
%========================================================================
alpha=7.865;
beta=alpha*(1-(2*n/(L-1)-1).^2).^0.5;
Ib=1;m=1;Ia=1;
for k=1:50
    m=m*k;
    Ib=Ib+(((beta/2).^k)/m).^2;
    Ia=Ia+(((alpha/2)^k)/m).^2;
end
w=Ib./Ia.*(u(n)-u(n-L));
x=0.4*sin(0.4*pi*(n-ceil(L/2)+eps+1))./(0.4*pi*(n-ceil(L/2)+eps+1)).*w;

%=================================================
N=1024;
H1=fft(w,N);
H2=fliplr(H1);
H=[H2(1:1023),H1];
H=H/max(abs(H));
F1=fft(x,N);
F2=fliplr(F1);
F=[F2(1:1023),F1];
F=F/max(abs(F));           
W=-2*pi+2*pi/N:2*pi/N:2*pi-2*pi/N;
%=======================================================================
figure(1)
subplot(221)
plot(W/pi,abs(F)),title('The magnitude response of FIR filter')
axis([-1,1,0,max(abs(F))])
%=========================================================
subplot(222)
plot(W/pi,abs(H))
axis([-1,1,0,max(abs(H))])
title('The frequency response of the Kai_Basel window'),
%======================================================
subplot(224)
plot(W/pi,20*log10(abs(H)/abs(H1(1))));
axis([0,1,-100,0])
title('The frequency response in dB'),
xlabel('Frequency (*pi)')
%======================================================
subplot(223)
plot(W/pi,20*log10(abs(F)/abs(F1(1))));
axis([0,1,-100,0])
title('The frequency response in dB'),
xlabel('Frequency (*pi)')
%======================================================
figure(2)
subplot(221)
stem(n,w,'.')
title('The Kai_Basel window')
xlabel('Index n')
%=================================================
subplot(222)
stem(n,x,'.')
title('The truncated impulse response')
xlabel('Index n')
%==================================================