% (a)
t=0:0.01:11;
x=1-exp(-0.3662*t);
plot(t,x);
xlabel('t');
ylabel('x(t)');
title('Step response of RC lowpass filter');
grid

% (b)
n=-2:19;
x=[9 10 9 10 11.5 11.5 11.5 12 14 12.5 13 13.5 13.5 14.5 15.5 14.5 14.5 15 16 15.5 17 17.5];
stem(n,x);
xlabel('n');
ylabel('x[n]');
title('Weekly average temperature');
xlim([-5 22])

% (c)
t=-2:0.01:15;
% two partial answers and an attempt
x=cos(2*pi*t);
x=cos(2*pi/8*(t-6));
x=cos(2*pi*t).*cos(2*pi/8*(t-6));
% pretty good
x=cos(2*pi*t).*(1+5/6*cos(2*pi/8*(t-6)))/(1+5/6);
plot(t,x);
xlabel('t');
ylabel('x(t)');
title('Amplitude-modulated carrier in a communication system');
grid

% (d)
n=-2:19;
x=-cos(3*pi/10*(n-1)).*exp(-n/5);
stem(n,x);
xlabel('n');
ylabel('x[n]');
title('Samples from an exponentially damped sinusoid');
xlim([-5 22])