a)

clc;

clear all;

close all;

t=0:0.0001:(5/6)

f=5*sin(8*pi*t)+6*sin(16*pi*t)

figure

plot(t,f)

xlabel('t')

ylabel('f(t)')

grid on

b)

clc;

clear all;

close all;

t=0:(1/24):(5/6)

n=0:1:20

Ts=1/24

fn=5*sin(8*pi*n*Ts)+6*sin(16*n*Ts)

fs=24

fftSignal = fft(fn);

figure;

stem(abs(fftSignal));

title('amplitude of f(t)');

xlabel('Frequency (Hz)');

ylabel('magnitude');

c) time period of given signal is LCM(1/4,1/8) or GCD (4,8)

fundamental time period=4

frequency of the signal =1/4 = 0.25

sampling freuency >=(1/4)*2=0.5 to reconstruct the signal from samples

code:

clc;

clear all;

close all;

t=0:(1/24):(5/6)

n=0:1:20

Ts=2

fn=5*sin(8*pi*n*Ts)+6*sin(16*n*Ts)

figure;

stem(n,fn);

title('sampled signal');

xlabel('n');

ylabel('f(n)');