Chapter 11: Discrete-Time Fourier Series and Transform
Problem 11.1:
(i) x[k ] = k , for 0 k 5 and x[k + 6] = x[k ] . 0 =
Dn =
1
K0
5
x[k ]e jn0k =
k =0
2 2
=
=.
K0 6
3
1 5 jn0 k
ke
6 k =0
1 jn0
e
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 s
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
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
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
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
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ENGINEERING BIOMECHANICS: STATICS1
Beatriz Guevarez, Jos
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 Pa