Assignment 1 1) Determine whether the following discrete time sinusoids are periodic or not. If periodic, find their fundamental period. i. 24 () cos 2 72 xn n π = ii. 13 () cos 2 36 xn n π = 2) What is the difference between the following two discrete time sinusoids 4 cos 2 3 n π ; 1 cos 2 3 n π 3) Which of the following two sinusoids has lower frequency i. cos( ) n π ii. ( ) cos ( )n π ε + where 0 ε > is very small increment 4) Check the following impulse response of an LTI system for stability and causality. 1 () () 2 n hn un = Simplify the convolution sum for this h(n). 5) Consider the signal that is sampled at 1000 samples/second. () 3cos600 2cos1800 xt t t π π = + 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 () () () yn xn hn = ∗ for { } () 1,1, 0,1,1 xn ↑ = ; { } () 1, 2, 3, 4 hn ↑ = − − 7) Check the following impulse response of an LTI system for stability and causality. () ( 1) () hn n un δ = + −
