Chapter 8: Case Studies for CT Systems
Problem 8.1:
(a)
The AM signal is given by
s (t ) = A[1 + 3k sin(2f1t ) + 2k cos(2f 2t )] cos(2f ct ) .
To ensure that the envelope of s(t) 0 for all t
(1 + 3k sin(2f1t ) + 2k cos(2f 2t ) 0 .
Taking the worst case sc
Chapter 6: Laplace Transform
Problem 6.1
X ( s) =
(a)
x(t )e st dt = e 5t u (t )e st dt +
0
e 4t u (t )e st dt = e ( s +5)t dt +
e
( 4 s )t
dt .
0
II
I
Integral I reduces to
I = e
( s + 5) t
0
e ( s +5)t
1
1
dt =
=
[0 1] =
( s + 5) 0 ( s + 5)
s+5
provide
Chapter 1: Introduction to Signals
Problem 1.1:
i) z[m,n,k] is a three dimensional (3D) DT signal. The independent variables are given by m, n, and k,
while z is the dependent variable. Digital video is an example of a 3D DT signal of the form z[m,n,k]. T
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ENGINEERING BIOMECHANICS: STATICS1
Beatriz Guevarez, Joshua Ros, Nayka Rivera, Sharon Vzquez and Melvia Villega
46
Particle Physics and Cosmology
CHAPTER OUTLINE
46.1 The Fundamental Forces in Nature 46.2 Positrons and Other Antiparticles 46.3 Mesons and the Beginning of Particle Physics 46.4 Classication of Particles 46.5 Conservation Laws 46.6 Strange Particles a
Chapter 3: Time Domain Analysis of LTIC Systems
Problem 3.1
Linearity: For x3(t) = x1(t) + x2(t) applied as the input, the output y3(t) is given by
d n y3
dt n
+ an 1
d n 1 y3
+
dt n 1
+ a1
dy3
d m 1 (x1 (t ) + x2 (t )
d m (x1 (t ) + x2 (t )
+ a0 y3 (t )
Chapter 4: Signal Representation using Fourier Series
Problem 4.1
(a)
Using Definition 4.4, the CT function x1(t) can be represented as x1(t) = c11(t) + c22(t) + c33(t)
with the coefficients cn, for n = 1,2, and 3, given by
T
c1 =
1
2T
x1 (t )1 (t )dt =