Question

This is a MATLAB problem.

Part 1. The sample sequence of y[n] = cos(0.25IIn) has a period of___

a. 25     b. 8       c. 20.      d. not enough info

Part 2. The sample sequence y[n] = cos(0.1*pi*n) + 2 sin(0.1*pi*n) is periodic with a period of ___ samples.

a. 10    b. 40.    C. 20   d. 31

Part 3. Following the function shape Y[n] = (2^(-0.5n)) *sin(0.2*pi*n) is a___

a. exponentially increasing sine wave. B. sine wave. C. exponential wave. D. exponentially decreasing sine wave.

Answer 1

Code:

n=1:1:64
y=cos(0.25*pi*n)
subplot(311)
stem(n,y)

y=(cos(0.1*pi*n))+(2*sin(0.1*pi*n))
subplot(312)
stem(n,y)

y = (2.^(-0.5*n)).*(sin(0.2*pi*n))
subplot(313)
stem(n,y)

Plot:

From the plots:

(i) y[n] = cos(0.25IIn) has the period of N=8. After every 8th sample the sequence repeats periodically.

Also N=2pi m/w0 where w0 =0.25pi

N=2pi/0.25pi=8 ===> N=8

(ii)y[n] = cos(0.1*pi*n) + 2 sin(0.1*pi*n) has the period of N=20. After every 20th sample the sequence repeats periodically.

Also N=2pi m/w0 where w0 =0.1pi

N=2pi/0.1pi=20===> N=20

(iii)y[n] = (2^(-0.5n)) *sin(0.2*pi*n) is a   exponentially decreasing sine wave.

Ans: D