Answer to Question #268851 in Electrical Engineering for فاطمة

Question

Q1- Consider a continuous time signal x(t)=2cos(21πt+30)+5cos(18 πt)

a) What is the signal frequency and What is the Nyquist rate of the signal?

b) Write a MATLAB M function or a script called sampley4p1 to perform

sampling:

1- Compare the results when the sampling frequencies of 10Hz , and 30 Hz were

used for the time between zero and 0.2sec?

2- determine the sampling frequency which result in the problem of aliasing .2-

Q2- a) suppose that the resulting samples from the Q1 (part a) passed through a 4

bits A/D convertor,

write a MATLAB code to perform the quantization, your MATLAB code and the

report should result in a figure contain the samples and the quantized values in the

same figure for comparison.

Students Tasks for the project1

6

Note: The project materials will be completed at the end of

lecture 4 after interdicting the interpolation technique

Answer 1

1)

signal frequency so 2*pi*f = 21*pi so f= 10.5 Hz

Nyquist rate = 10.5 *2 = 21

Nyquist frequency = 21 Hz

folding frequency = 10.5/2 = 5.25 Hz

3)

a)

we have y= 2cos(21*pi*t) so at fs = 10 Hz

y[n] = 2cos(21*pi*n/10) = 2cos(2.1*pi*n)

and wd = 2.1*pi and fd = 10.5/10 = 1.05

b)

we have y= 2cos(21*pi*t) so at fs = 5 Hz

y[n] = 2cos(21*pi*n/5) = 2cos(10.5*pi*n)

and wd = 10.5*pi and fd = 10.5/5 = 2.1

c)

we have y= 2cos(21*pi*t) so at fs = 20 Hz

y[n] = 2cos(21*pi*n/20) = 2cos(1.05*pi*n)

and wd = 1.05*pi and fd = 10.5/20 = 0.525