%%% Matlab exploration for Pulses with Interfering Sinusoid

p=[ones(1,9) zeros(1,6)];   %%% Create one pulse and zeros
p=[p p p p p];   %%% stack 5 of them together
p=0.25*p;   %%% adjust its amplitude to be 0.25
subplot(3,1,1)
stem(0:74,p)   %%% look at the sequence of pulses
xlabel('Sample Index, n')
ylabel('Pulsed Signal p[n]')
x=p+cos((pi/2)*(0:74));  % add in an interfering sinusoid
subplot(3,1,2)
stem(0:74,x)
xlabel('Sample Index, n')
ylabel('x[n] Input = pulse + sinusoid')
h = ones(1,4);   %%% define impulse response of filter
y=conv(x,h);   %% filter out sinusoid with DT conv
subplot(3,1,3)
stem(0:77,y)
xlabel('Sample Index, n')
ylabel('y[n] = Output')
%%%  Note that pulses are free of sinusoidal interference but have been "smoothed"

w=-pi:0.001:pi;
H=freqz(h,1,w);
figure
subplot(2,1,1)
plot(w/pi,abs(H))
xlabel('\Omega/\pi (normalized radians/sample)')
ylabel('|H(\Omega)|')
subplot(2,1,2)
plot(w/pi,angle(H))
xlabel('\Omega/\pi (normalized radians/sample)')
ylabel('<H(\Omega) (rad)')

figure
zplane(h,1)