ECE 330
Homework Set 3A
Section 4.1
t
1. Using the denition of the Fourier transform, determine X(j) if x(t) = et rect( 2 ).
2. Using the denition of the Fourier transform, determine X(ej ) if x[n] =
bn
= eb .
Hint: For all b, even if complex-valued,
n!
n
ECE 330
Homework Set 4A
Section 5.1
1. Consider a linear time-invariant system with input x(t) = 4e6t u(t) e3t u(t) and impulse
1
response h(t) = 2 (t) + 2e2t u(t). Determine the output y(t).
2. Consider a linear time-invariant system for which an input o
ECE 330
Homework Set 4B
Section 5.4
1. Suppose two ideal bandstop lters are placed in series. One has cuto frequencies = 2000
and = 8000 and the other has cuto frequencies = 4000 and = 9000. Characterize the composite lter as lowpass, highpass, bandpass,
ECE 330
Homework Set 5
6.2.1. Use the properties and the table of transforms to determine the Laplace transforms of the
following signals, including the regions of convergence.
(a) x(t) = 2e3t u(t) + 5e4t u(t).
(b) x(t) = (2et t)u(t).
(c) x(t) = (tet 3e2t
ECE 330
Homework Set 4
5.1.1. Consider a linear time-invariant system for which an input of x(t) = (5e2t 4e4t )u(t)
gives output y(t) = (3e2t 3e4t )u(t).
(a) Determine the impulse response h(t).
(b) Determine the output y(t) if the input is x(t) = 8te12t
ECE 330
Homework Set 2B
Section 3.5
1. Consider a linear time-invariant system with input x(t) = 2te2t u(t) and impulse response
h(t) = e2t (u(t) u(t 2). Determine the output y(t). Check your answer using Checks
#1 and #2.
2. Consider a linear time-invari
ECE 330
Homework Set 2A
Section 3.1
1. Consider a system with input x() and output y(t) = t2 x(t 3). Determine the impulse
response h(t) and the step response g(t).
2. Consider a system with input x[] and output y[n] = cos( x[n]). Determine the impulse
2
ECE 330
Homework Set 1B
Section 2.5
1. Suppose x(t) is as shown and suppose w(t) = (t + 1) 2(t 1) + (t 2). Plot y(t) =
x(t) + w(t) and z(t) = x(t)w(t) and give the sum-of-impulses representation of z(t).
x(t)
2
-4 -2
4
t
-1
if 2 n 3
2
1 if 2 n 1 and y[n]
ECE 330
Homework Set 2
3.1.1. Consider a system with input x() and output y(t) = t(x(t 1) x(t 2).
(a) Determine and plot the impulse response h(t).
(b) Determine and plot the step response g(t).
(c) Determine and plot the output due to input x(t) = u(t) u
ECE 330
Homework Set 1A
Section 2.1
2t 3 if 1 < t
1
if 4 < t 5
1. Suppose x(t) =
0
otherwise
5
2
.
Determine the absolute time duration of this signal and plot it.
2
n 1 if 2 n < 2
1
if n 3
2. Suppose x[n] =
.
0
otherwise
Classify this signal as left-
ECE 330
Homework Set 1
2.1.1. For each signal below, (i) plot the signal, (ii) determine the time duration, and (iii) classify
the signal as left-sided, right-sided, two-sided, or time-limited.
1 t if 0 < t 2
n 2 if 1 n 4
1
if t < 1
2
if n = 2
(a) x(t)
Subject Area: Circuits
Open Book Question Number:
Student ID Number:
In the circuit shown below, ig = 1021(1) A There is no initing stored in the circuit
(3.) Find the s-domain expression for i(t), for t>O
(b) Use your result obtained in part (a) together