Assignment 1 1) Determine whether the following discrete time sinusoids are periodic or not. If periodic, find

their fundamental period.

i. 24( ) cos 272

x n n =

ii. 13( ) cos 236

x n n =

2) What is the difference between the following two discrete time sinusoids

4cos 23

n

; 1cos 23

n

3) Which of the following two sinusoids has lower frequency

i. cos( )n ii. ( )cos ( )n + where 0 > is very small increment

4) Check the following impulse response of an LTI system for stability and causality.

1( ) ( )2

n

h n u n =

Simplify the convolution sum for this h(n).

5) Consider the signal that is sampled at 1000 samples/second.

( ) 3cos600 2cos1800x t t t = +

i. What is the Nyquist rate for the signal x(t)? ii. What is the folding frequency?

iii. What are the frequencies in the resulting discrete-time signal x(n)? 6) Compute the convolution ( ) ( ) ( )y n x n h n= for

{ }( ) 1,1,0,1,1x n

= ; { }( ) 1, 2, 3,4h n = 7) Check the following impulse response of an LTI system for stability and causality.

( ) ( 1) ( )h n n u n= +