Problem 2.3 A thinlm resistor made of germanium is 2 mm in length and its
rectangular cross section is 0.2 mm 1 mm, as shown in Fig. P2.3. Determine the
resistance that an ohmmeter would measure if connected across its:
(a) Top and bottom surfaces
(b) Fr
Problem 5.59 The inputvoltage waveform shown in Fig. P5.59(a) is applied to the
circuit in Fig. P5.59(b). Determine and plot the corresponding out (t).
i
12 V
(a) Waveform of i(t)
2
4
6
8 10 12
t (s)
12 V
50 k
2 F
vi
+
_
(b) Opamp circuit
out
Vcc = 6 V
Problem 5.2 Provide expressions in terms of step functions for the waveforms
displayed in Fig. P5.2.
1(t)
2(t)
6
6
4
4
2
2
2 1
2
1
2
3
4
t (s)
2 1
2
(a) Step
1
2
3
4
3
4
t (s)
(b) Bowl
3(t)
4(t)
6
6
4
4
2
2
2 1
2
1
2
3
4
t (s)
(c) Staircase up
2 1
2
1
2
t
Problem 5.4 Generate plots for each of the following functions over the time span
from 4 to +4 s.
(a) 1 (t) = 5r(t + 2) 5r(t)
(b) 2 (t) = 5r(t + 2) 5r(t) 10u(t)
(c) 3 (t) = 10 5r(t + 2) + 5r(t)
(d) 4 (t) = 10rect t+1 10rect t3
2
2
(e) 5 (t) = 5rect
t1
2
EECE 3464 FOURIER DT QUIZ 1
1. Prove that the set of complex exponential functions
2
k [n] = ej N kn
are:
(a) Periodic in both k and n with fundamental period equal to N,
(b) Orthogonal over the interval n = 0 to n = N 1; i.e., that
N 1
m [n]k [n] = Nm,k
EECE 3464 FOURIER DT QUIZ 1 SOLUTIONS
1. Prove that the set of complex exponential functions
2
k [n] = ej N kn
are:
(a) Periodic in both k and n with fundamental period equal to N,
SOLUTION
=1
k [n + N] = e
j 2 k(n+N )
N
=e
j 2 kn
N
e
j 2 kN
N
2
= ej N kn
EECE 3464 CT Fourier Quiz
Do only two problems
Show all work. Answers without accompanying work get zero credit.
1. Express h(t) and x(t) in Fourier integrals
h(t) =
x(t) =
+
1
2
H()ejt d
+
1
2
X()ejt d
to prove that
xh =
1
2
+
H()X()ejt d,
where denotes
EECE 3464
QUIZ 5 (Z Transform)
Closed book, closed notes.
Show all work. Answers without accompanying work get zero credit.
Questions are 50 points each.
(Q1)
Consider a causal DTLTI system with impulse response h[n]. The Ztransform of the
impulse respo
Northeastern University
hitstrim] and Coinputrr Engineering Department
EECE 3464 u LINEAR SYSTEMS
MitgunJ
Spring 2913.20
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EECE 3464
QUIZ 3 (Chapter 2, Part 2)
Closed book, closed notes.
Show all work. Answers without accompanying work get zero credit.
(2.59) Consider the RL circuit shown in the figure.
(a) Find the differential equation relating the output voltage y(t) acros
Problem 3 (25 points)
'vVehave the following pieces of information about a discretetime
function we denote H(z):
LTI system, whose system
 H (z) is a rational function.
= 0, and no other zeros.
 H(z)
has one zero at
 H(z)
has one realvalued pole, and
Northeastern University
Electrical and Computer Engineering Department
EECE 3:164  LINEAR SYSTEMS
Midterm 2
Spring 20132014
Thursday, April 3. 2014
LAME go LUTLQMS
The solutions I submit for this exam are based on my own work only. I have adhered to the
EECE 3464
QUIZ 2 (Chapter 2, Part 1)
Closed book, closed notes.
Show all work. Answers without accompanying work get zero credit.
(2.48) Show that if y(t) = x(t) * h(t), then y(t) = x(t) * h(t) = x(t) * h(t).
Here, denotes derivative with respect to t.
(2
Problem
2 (20 points)
vVe need an ideal lowpass filter with a passband gain of I, and a cutoH frequency of
Wc = 27T X 100 rad/s.
In our application, the signals to be filtered are bandlimited to 200 Hz.
Rather than building such a filter using analog c
EECE 3464 QUIZ # 1: closed book closed notes
SHOW ALL WORK. ANSWERS WITHOUT ACCOMPANYING WORK GET
ZERO CREDIT
1. Determine the even and odd components of the following signals:
x(t) = u(t)
x(t) = sin 0 t
x(t) = ej0 n
x[n] = (n)
2. Determine whether each o
EECE
3464 qUlZ # I: closed book closed notes
'
WORKGET
WITHOUTACCOMPANYING
SHOWALL WORK.ANSWERS
ZEROCREDIT
*":]
I
1. Determine the even and odd componentsof the following signals:
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uuJ+*Jzl;
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:
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= 9\rur*
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tat
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EECE 3464 Linear Systems
Spring 2012 Midterm Exam
Closed book, closed notes.
Show all work. Answers without accompanying work get zero credit.
Questions are 25 points each.
Solve 2 questions from cfw_Q1, Q2, Q3 in Part 1 and 2 questions from cfw_Q1, Q2, Q
useful formulas name Eulers formula . . . for cosine . . . for sine sinc function formula ej = cos() + j sin() cos() = sin() = e
j
selected Laplace transform pairs x(t) x(t) (t) u(t) ea t u(t) cos(o t) u(t) X(s) Z 1 1 s 1 s+a s 2 s2 + o o 2 s2 + o s+a 2 (
EECE 3464 FINAL EXAM SPRING 2012
Open book. No calculators of any kind. Solve 4 questions out of 5. Only first 4 answers will be graded.
(Q1)
[] + 3[ 1] + 2[ 2] = [] + [ 1].
Consider the causal DTLTI system described by the difference equation
(a)
(b)
(c
EECE 3464 FINAL EXAM SOLUTIONS
open book closed notes, no calculators, laptops or cell phones
1. A causal DT LTI system is described by the dierence equation
y[n] + 3y[n 1] + 2y[n 2] = x[n] + x[n 1].
(a) Compute the system transfer function H(z) = Y (z)/X
Prablcm 6.$8 Tbe voltngr s$cfw_[t,f $r &e cncuit of Fig P6.88 is SvEn
t4cfw_ri il0*5ucfw_rr V. Detfrtrnre ircfw_ri fst.i0. Ftotb*t.R1 = 1cfw_L .&t: I
I . 3 H. *ndC '. 1F,
I
rl
rl.
t'
:
t.
figxre P*.8$r Clfftut for Probhn*
*td 6'91
6.88
Soluti$: At t: 0