Problem 1: Topics: Energy Signals.

a) Sketch x(t) = u(t) + 3u(t-2) - 4u(t-4)

b) Find the energy in the signal.

Problem 2: Topics: Power Signals

a) Sketch x(t) = u(t) + 2u(t-2) - u(t-4)

b) Find the Power in the signal.     

Problem 3: Topics: Double Sided Amplitude and Phase Spectra. Power Spectral Density

Given x(t) = 3cos(6πt - π/3) + 5cos(10πt + π/3)

a) Sketch double sided amplitude spectra.

b) Sketch double sided phase spectra.

c) Sketch Power Spectral Density.

Problem 4: Topics: Double Sided Amplitude and Phase Spectra. Power Spectral Density

A system is defined

Is this system causal? Justify your answer.

Problem 5: Topics: System Response, Delay Filters

Given the system:

a) Use any method to find the system output.      

Problem 6: Topics: Convolution

Given x1(t) =  e^-t u(t) and x2(t) =  u(t) - u(t-3)  

a) Use the convolution integral to find x3(t)                   

Clearly sketch the cases and regions related to no overlap, partial overlap and full overlap.

b) Corroborate your answer in a) by finding x3(t) using Laplace.      

Problem 7: Topics: System Response, Impulse Response

Given the following system:

a) Find the impulse response in terms of C and R.

b) Find the step response (find vo(t) when vi(t) = u(t)) in terms of C and R using any method.

Book: Linear Dynamic Systems and Signals by Zoran Gajic.