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Department of Electrical and Computer Engineering

Winter 2022 - EE 242 Signal Processing I

Quiz 1

Problem 1 (20pts)

For each of the following signals, state whether the signal is periodic. If it is periodic, find the fundamental period T0 (continuous time) or N0 (discrete time).

a)   () =  2 (4)

b)   () = sin(6) + cos (5)

c)   [] = cos (  ) + sin(2) + 3(−1)+1

d)     [] (even component of part c)

e)     [] (odd component of part c)

Problem 2 (10pts)

For each of the following signals, calculate the E (Energy) and P (Power) components.

a)   [] = () []

b)   () = 0

Problem 3 (20pts)

For each of the following systems, determine whether its memoryless, causal, stable, invertible,  time invariant, and linear. Mathematical derivations for positive proofs and counter examples for negative proofs.

a)   () = cos(3) ()

b)   () = ()

Bonus Problem (5pts)

Graph the even and odd components of the following continuous signal.