% question1 %

n = -20:0.1:20;
figure(2)
y = @(n) 5 * cos((2 * pi * n) / 8); % Define anonymous function
y2 = @(n) -8 * exp(-1 * ((n / 6).^2));

subplot(6, 1, 1)
stem(n, y(n), 'g')
title('Plot of y(n)')

subplot(6, 1, 2)
stem(n, y2(n), 'm')
title('Plot of y2(n)')

subplot(6, 1, 3)
stem(n, y(n) .* y2(n), 'y')
title('Plot of y(n) * y2(n)')

subplot(6, 1, 4)
stem(n, y(2 * n) .* y2(3 * n), 'b')
title('Plot of y(2n) * y2(3n)')

subplot(6, 1, 5)
stem(n, (4 * y(n)) .* (2 * y2(n)), 'r')
title('Plot of (4 * y(n)) * (2 * y2(n))')

subplot(6, 1, 6)
stem(n, (2 * y(n / 2)) .* (4 * y2(n / 3)), 'c')
title('Plot of (2 * y(n/2)) * (4 * y2(n/3))')

xlabel('n')
ylabel('Amplitude')


% question2 %

% first define this function in m-file

function y=gd(n)

a=length(n)

for i=1:a

if n(i)<=-4
y(i)=-2;

elseif -4<=n(i) & n(i)<=1
y(i)=n(i);

elseif 1<=n(i)
y(i)=4/n(i);

else
y(i)=0;

end
end

% in the command window, call function and plot it

n=-20:20;

gdeven=(gd(n)+gd(-1*n))/2;
gdodd=(gd(n)-gd(-1*n))/2;


subplot(6,1,1)
stem(n,gd(n),'g')
subplot(6,1,2)
stem(n,gdeven,'y')
subplot(6,1,3)
stem(n,gdodd,'m')
subplot(6,1,4)
stem(n,gd(2*n),'c')
subplot(6,1,5)
stem(n,gd(n/2),'r')
subplot(6,1,6)
stem(n,gdeven+gdodd,'g')