Question

ints) A continuous time signal is given below: x(t) = 10 + 3 sin (20t + 3) + 5 cos(40π) This is sampled at t = 0.01 n to get a the discrete-time signal x[n], which is then applied to an ideal DAC to obtain a reconstructed continuous time signal y(t). a. i. Determine x[n] and graph its samples, using Matlab, along with the signal x(t) in one plot, plot a few cycles of x(t). ii. Determine the reconstructed signal, y/(t), as a sinusoidal signal and compare it to x(t). Repeat part a for sampling times oft 0.05n and t-0.1n, what conclusion can you draw b. from these three cases?

Answer 1

MATLAB CODE:

t=0:0.01:2;% sampling the time axis for t=0.01n
x=10+3*sin(2*pi*t+pi/3)+5*cos(40*pi*t);% x(t) is the given function
subplot(2,1,1);
stem(t,x);% discrete plot
title('discrete plot')
subplot(2,1,2);
plot(t,x);% continuos plot
title('continuous plot')

OUTPUT 1:

discrete plot Gnuplot 20_ 15 (10 ) 10 0.5 2 continuous plot 20 15 10 0.5

t=0:0.05:2;% sampling the time axis for t=0.05n
x=10+3*sin(2*pi*t+pi/3)+5*cos(40*pi*t);% x(t) is the given function
subplot(2,1,1);
stem(t,x);% discrete plot
title('discrete plot')
subplot(2,1,2);
plot(t,x);% continuos plot
title('continuous plot')

OUTPUT 2:

discrete plot 20 15 10 0.5 1.5 2 continuous plot 18 16 15 14 一一 13 12 0.5 1.5 2

t=0:0.1:2;% sampling the time axis for t=0.1n
x=10+3*sin(2*pi*t+pi/3)+5*cos(40*pi*t);% x(t) is the given function
subplot(2,1,1);
stem(t,x);% discrete plot
title('discrete plot')
subplot(2,1,2);
plot(t,x);% continuos plot
title('continuous plot')

OUTPUT 3:

discrete plot 20 - 15 - OppoO 10- 0.5 1.5 continuous plot 18 17 15 13 - 12 0.5

By these three cases we can say that to reconstruct the sampled signal ,

ADC should follow nyquist criteria

that is

Fs=2*Fm

Fs= sampling frequency

Fm= maximum signal frequency.