EE422

Homework #1

Due Tuesday, January 19

1a) Write an expression for the signal below using u(t) and r(t):

b) Find the derivative of x(t) for the above signal.

c) Determine if the following signals are periodic, then find the fundamental period:

i) x(t) = 10 sin(100p t)

ii) x(t) = 2 cos(15p t) + 4sin(10p t)

iii) cos(100p t) + sin(422t)

d) Classify the following as power or energy signals:

i) u(t)

ii) cos(2t)

iii) e^-5t u(t)

e) Find the fundamental period and average power (P_ave) of the following power signals:

i) 10sin(2t)

ii) 5+10cos(2t) +10sin(3t)+20cos(4t)+40sin(5t) Hint: Think Parseval!

iii)

2a) Show that the following RL circuit BIBO stable for L and R > 0:

b) For the following periodic signal, find three different Fourier series representations:

c) Find the Fourier transform of x(t) = 5e^-8t u(t)

d) What is the energy spectal density for the signal in part 2c)?

e) Using your answer to part d) how much energy would remain if we passed x(t) through an ideal lowpass filter which only allowed the following frequencies to pass: i) |f| £ 1 Hz ii) |f| £ 100 Hz