Ejercicios de fasores

1. 60 Chapter 2 Mathematical Description of Continuous-Time Signals
% the function squared, divide the
% period and display the result
disp([‘(b) Px = ‘,num2str(Px)]) ;
The output of this program is
(a) Ex = 21.5177
(b) Px = 75.015
Analytical computations:
¥
5 .
5
5
.
5
x( ) − / −
.
e−t / =
5 16 21 888 = − × éë
= = t = t
−¥
4 16 / t
(a) Ex t dt e dt e d
.
.
2 10 2
2 5
5
2 5
5
5 5
2 5
ùû
.
.
(The small difference in results is probably due to the error inherent in trapezoidal-rule
integration. It could be reduced by using time points spaced more closely together.
5
5
1
10
(b) Px = − t dt = t dt = t = =
−
( 3
) ( )5 Check.
1
5
9
1
5
3
375
5
2 75
5
2
0
3
0
2.10 SUMMARY OF IMPORTANT POINTS
1. The term continuous and the term continuous-time mean different things.
2. A continuous-time impulse, although very useful in signal and system analysis,
is not a function in the ordinary sense.
3. Many practical signals can be described by combinations of shifted and/or
scaled standard functions, and the order in which scaling and shifting are done is
signifi cant.
4. Signal energy is, in general, not the same thing as the actual physical energy
delivered by a signal.
5. A signal with fi nite signal energy is called an energy signal and a signal with
infi nite signal energy and fi nite average power is called a power signal.
EXERCISES WITH ANSWERS
(On each exercise, the answers listed are in random order.)
Signal Functions
1. If g(t) = 7e−2t−3 write out and simplify
(a) g(3) (b) g(2 − t) (c) g((t /10) + 4)
(d) g( jt) (e) g( jt) + g(− jt)
2
(f ) g(( jt − 3) / 2) + g((− jt − 3) /
2)
2
Answers: 7 cos(t), 7e−7+2t , 7e− j2t−3, 7e−(t /5)−11, 7e−3 cos(2t), 7e−9

2. 2. If g(x) = x2 − 4x + 4 write out and simplify
(a) g(z) (b) g(u + v) (c) g(e jt )
(d) g(g(t)) (e) g(2)
Answers: ( e jt − 2)2, z2 − 4z + 4, 0, u2+ v2 + 2 u v − 4 u − 4v + 4,
t4 − 8t3 + 20t2 −16t + 4
3. What would be the value of g in each of the following MATLAB
instructions?
t = 3 ; g = sin(t) ;
x = 1:5 ; g = cos(pi*x) ;
f = -1:0.5:1 ; w = 2*pi*f ; g = 1./(1+j*w’) ;
Answers: 0.1411, [−1,1,−1,1,−1],
+
+
j
j
0 0247 0 155
0 0920 0 289
. .
. .
1
−
−
j
j0.155
0 0920 0 289
0 0247
. .
.
é
êêêêêêê
ë
ù
úúúúúúú
û
4. Let two functions be defi ned by
x ( )
, sin
, sin
1
1 20 0
1 20 0
t
t
t
=
( ) ³
− ( ) <
ìíî
p
p
and x ( )
, sin( )
, sin( )
2
2 0
2 0
t
t t
t t
=
³
− <
ìíî
p
p
.
Graph the product of these two functions versus time over the time range, −2 < t < 2.
Answer:
t
x(t)
2
-2 2
-2
Scaling and Shifting
5. For each function g(t) graph g(−t), − g(t), g(t −1), and g(2t).
(a) (b)
t
g(t)
2
4
t
g(t)
1
-1
3
-3
Exercises with Answers 61

3. 62 Chapter 2 Mathematical Description of Continuous-Time Signals
Answers:
t
g(-t)
-2
4
,
t
g(-t)
1
-1
3
-3 ,
t
-g(t)
2
-4 ,
t
-g(t)
1
-1
3
-3 ,
t
g(t-1)
1 3
4
,
t
g(t-1)
1 2
3
-3 ,
t
g(2t)
1
4
,
t
g(2t)
3
-3
1
2
1
2
-
6. Find the values of the following signals at the indicated times.
(a) x(t) = 2 rect(t /4), x(−1)
(b) x(t) = 5rect(t /2) sgn(2t), x(0.5)
(c) x(t) = 9 rect(t /10) sgn(3(t − 2)), x(1)
Answers: −9, 2, 5
7. For each pair of functions in Figure E.7 provide the values of the constants A,
t0 and w in the shifting and/or scaling to g2 (t) = Ag1((t − t0 )/w).
2
1
0
-1
-2
-4 -2 0 2 4
t
g1(t)
(a)
2
1
0
-1
-2
-4 -2 0 2 4
t
g2(t)
(a)
2
1
0
-1
-2
-4 -2 0 2 4
t
g1(t)
(b)
2
1
0
-1
-2
-4 -2 0 2 4
t
g2(t)
(b)
2
1
0
-1
-2
-4 -2 0 2 4
t
g1(t)
(c)
2
1
0
-1
-2
-4 -2 0 2 4
t
g2(t)
(c)
Figure E.7
Answers: A = 2, t0 = 1,w = 1; A = −1/2, t0 = −1,w = 2; A = −2, t0 = 0 ,w = 1/2

4. 8. For each pair of functions in Figure E.8 provide the values of the constants A,
t0 and a in the functional shifting and/or scaling to g2 (t) = Ag1(w(t − t0 )).
(a)
8
4
0
-4
-8
-10 -5 0 5 10
t
g1(t)
8
4
0
-4
-8
-10 -5 0 5 10
t
g2(t)
(b)
g1(t)
g2(t)
8
4
0
-4
-8
-10 -5 0 5 10
t
8
4
0
-4
-8
-10 -5 0 5 10
t
(c)
g1(t)
g2(t)
8
4
0
-4
-8
-10 -5 0 5 10
t
8
4
0
-4
-8
-10 -5 0 5 10
t
(d)
g1(t)
g2(t)
8
4
0
-4
-8
-10 -5 0 5 10
t
8
4
0
-4
-8
-10 -5 0 5 10
t
(e)
g1(t)
g2(t)
8
4
0
-4
-8
-10 -5 0 5 10
t
8
4
0
-4
-8
-10 -5 0 5 10
t
Figure E.8
Exercises with Answers 63

5. 64 Chapter 2 Mathematical Description of Continuous-Time Signals
Answers: A = 3, t0 = 2, w = 2
A = −3, t0 = −6, w = 1/3 or A = −3, t0 = 3, w = −1/3,
A = −2, t0 = −2, w = 1/3,
A = 3, t0 = −2, w = 1/2,
A = 2, t0 = 2, w = −2
9. Figure E.9 shows a graphed function g1(t), which is zero for all time outside the
range graphed. Let some other functions be defi ned by
g2 (t) = 3g1(2 − t), g3(t) = −2 g1(t /4), g4 ( ) g1
− æè
3
2
t
t =
öø
Find these values.
(a) g2 (1) (b) g3(−1) (c) [g4 (t) g3(t)]t=2
−
1
(d) g4 ( )
3
t dt
−
Figure E.9
t
g1(t)
-4 -3 -2 -1
4
3
2
1
-1
-2
-3
-4
1 2 3 4
Answers: −7/2, −3/2, −2, −3
10. A function G( f ) is defi ned by
G( f ) = e− j2 f rect( f 2) p / .
Graph the magnitude and phase of G( f −10) + G( f +10) over the range,
−20 < f < 20.
f
|G( f )|
1
-20 20
f
G( f )
p
-20 20
-p

6. Answer:
− æè
f
f + æè
2p 10 2p f + öø
10
2
10 10 − − + −
− + + = j f e j
G( f ) G( f ) e ( ) rect (
öø
10 10
2
) rect
11. Write an expression consisting of a summation of unit-step functions to represent
a signal that consists of rectangular pulses of width 6 ms and height 3, which
occur at a uniform rate of 100 pulses per second with the leading edge of the fi rst
pulse occurring at time t = 0.
¥å
= − − − −
Answer: x(t) 3 [u(t 0 . 01 n) u(t 0 . 01 n 0 . 006
)]
n
=
0
Derivatives and Integrals
12. Graph the derivative of x(t) = (1− e−t ) u(t).
Answer:
t
x(t)
1
-1 4
-1
dx/dt
1
-1 4 t
-1
13. Find the numerical value of each integral.
8
3 2 4
1
(a) [d(t + ) − d( t)]dt
−
/
5 2
(b) d2
1 2
(3t) dt
/
Answers: −1/2, 1
14. Graph the integral from negative infi nity to time t of the functions in Figure E.14,
which are zero for all time t < 0.
g(t)
t
1
1 2 3
1
2
g(t)
t
1
1 2 3
Figure E.14
Answers:
g(t) dt
t
1
1 2 3
12
,
g(t) dt
t
1
1 2 3
Exercises with Answers 65

7. 66 Chapter 2 Mathematical Description of Continuous-Time Signals
Even and Odd Signals
15. An even function g(t) is described over the time range 0 < t < 10 by
g( )
,
2 0 3
15 3 ,
3 7
2 ,
7 10
t
t t
t t
t
=
< <
− < <
− < <
ì
í ï
î ï
.
(a) What is the value of g(t) at time t = −5?
(b) What is the value of the fi rst derivative of g(t) at time t = −6?
Answers: 3, 0
16. Find the even and odd parts of these functions.
(a) g(t) = 2t2 − 3t + 6 (b) g(t) = 20 cos(40pt − p/4)
(c) g(t)
t t
t
=
− +
+
2 3 6
1
2
(d) g(t) = t(2 − t2 )(1+ 4t2 )
(e) g(t) = t(2 − t)(1+ 4t)
Answers: t(2 − 4t2 ), (20/ 2) cos(40pt), 0, −
+
−
t
t
2 9
1
t
2
2 , 7t2,
(20/ 2) sin(40pt), 2t2 + 6 t(2 − t2 )(1+ 4t2 ),
6 5
1
2
2
+
−
t
t
, −3t
17. Graph the even and odd parts of the functions in Figure E.17.
(a) (b)
t
g(t)
1
1
t
g(t)
1 2
1
-1
Figure E.17
Answers:
t
ge(t)
1
1
t
go(t)
1
1
,
t
ge(t)
1 2
1
-1
t
go(t)
1 2
1
-1

8. 18. Graph the indicated product or quotient g(t) of the functions in Figure E.18.
(a)
t
1
-1
1
-1
t
1
-1 1
g(t)
Multiplication
(b)
1
-1
1
-1
1
-1
-1
1
t
t
g(t)
Multiplication
(c)
1
1
-1
1
t
t
g(t)
Multiplication
(d)
1
1
1
1
t
t
g(t)
Multiplication
(e)
1
... ...
-1 1
-1
1
-1 1
t
t
g(t)
Multiplication
(f)
1
1
-1
1
-1
1
t
t
g(t)
Multiplication
(g)
1
1
-1
1
t
t
g(t)
Division
(h)
1
-1 -1 1
1
!
t
t
g(t)
Division
Figure E.18
Exercises with Answers 67

9. 68 Chapter 2 Mathematical Description of Continuous-Time Signals
Answers:
g(t)
1
-1 1
t
,
g(t)
t
1
-1 1
-1 ,
g(t)
1
... ...
-1 1 t
-1
g(t)
t
1
-1 1
,
g(t)
t
-1 ,
g(t)
t
1
1
-1
g(t)
t 1
-1
1
-1 ,
g(t)
t
-1 1
-1
19. Use the properties of integrals of even and odd functions to evaluate these
integrals in the quickest way.
1
1 /
20
t dt (b) [4 cos(10 ) 8sin(5 )]
(a) (2 )
1
+
−
1 20
pt + pt dt
−
/
1 /
20
(c) 4 10
1 20
t cos( pt) dt
−
/
1 10
/
(d) t sin(10 t) dt
1 10
p
−
/
1
1
(e) e− t dt
−
1
1
(f ) te− t dt
−
Answers: 0,
8
10p
,
1
50p
, 0, 1.264, 4
Periodic Signals
20. Find the fundamental period and fundamental frequency of each of these
functions.
(a) g(t) = 10 cos(50pt) (b) g(t) = 10 cos(50pt + p/4)
(c) g(t) = cos(50pt) + sin(15pt)
(d) g(t) = cos(2pt ) + sin(3pt) + cos(5pt − 3p/4)
Answers: 2 s, 1/25 s, 2.5 Hz, 1/25 s, 1/2 Hz, 0.4 s, 25 Hz, 25 Hz

10. 21. One period of a periodic signal x(t) with fundamental period T0 is graphed in
Figure E.21. What is the value of x(t) at time t = 220ms?
5ms 10ms15ms
t
x(t)
4
3
2
1
-1
-2
-3
-4
T0
20ms
Figure E.21
Answer: 2
22. In Figure E.22 fi nd the fundamental period and fundamental frequency of g(t).
... ...
1
... ...
1
... ...
1
(a) (b)
... ...
1
... ...
1
(c)
t
t
t
g(t)
g(t)
t
t
g(t)
Figure E.22
Answers: 1 Hz, 2 Hz, 1/2 s, 1 s, 1/3 s, 3 Hz
Signal Energy and Power
23. Find the signal energy of these signals.
(a) x(t) = 2 rect(t) (b) x(t) = A(u(t) − u(t −10))
(c) x(t) = u(t) − u(10 − t) (d) x(t) = rect(t) cos(2pt)
(e) x(t) = rect(t) cos(4pt ) (f) x(t) = rect(t) sin(2pt)
Answers: 1/2, ¥, 10A2, 1/2, 4, 1/2
24. A signal is described by x(t) = Arect(t) + Brect(t − 0.5). What is its signal
energy?
Answer: A2 + B2 + AB
Exercises with Answers 69

11. 70 Chapter 2 Mathematical Description of Continuous-Time Signals
25. Find the average signal power of the periodic signal x(t) in Figure E.25.
3
2
1
-4 -3 -2 -1 1 2 3 4
-1
-2
-3
t
x(t)
Figure E.25
Answer: 8/9
26. Find the average signal power of these signals.
(a) x(t) = A (b) x(t) = u(t)
(c) x(t) = Acos(2 f0t + ) p u
Answers: A2, A2 /2, 1/2
EXERCISES WITHOUT ANSWERS
Signal Functions
27. Given the function defi nitions on the left, fi nd the function values on the right.
(a) g(t) = 100 sin(200pt + p/4) g(0.001)
(b) g(t) = 13 − 4t + 6t2 g(2)
(c) g(t) = −5e−2te− j2pt g(1/4)
28. Let the continuous-time unit impulse function be represented by the limit
d(x) = lim( ) rect(x ), >
a®
a a a
0
1/ / 0.
The function (1/a) rect(x /a) has an area of one regardless of the value of a.
(a) What is the area of the function d(4 x ) lim(1 a ) rect(4 x a
)
0
a
=
®
/ / ?
(b) What is the area of the function d(− 6 x ) = lim( 1 a ) rect(− 6
x a
)
®
0
a
/ / ?
(c) What is the area of the function d(bx) lim( a) rect(bx a)
a
=
®0
1/ / for b positive and
for b negative?
29. Using a change of variable and the defi nition of the unit impulse, prove that
d(a(t − t0 )) = (1/ a )d(t − t0 ).
30. Using the results of Exercise 29, show that
1
¥å
= −
(a) d d 1
(ax) ( )
a
x n a
n
=−¥
/
(b) The average value of d1(ax) is one, independent of the value of a.
(c) Even though d(at) = (1/ a )d(t), d d 1(ax) ¹ (1/ a ) 1(x)

12. Scaling and Shifting
31. Graph these singularity and related functions.
(a) g(t) = 2 u(4 − t) (b) g(t) = u(2t)
(c) g(t) = 5sgn(t − 4) (d) g(t) = 1+ sgn(4 − t)
(e) g(t ) = 5ramp(t +1) (f ) g(t) = −3ramp(2t)
(g) g(t) = 2d(t + 3) (h) g(t) = 6d(3t + 9)
(i) g(t) = −4d(2(t −1)) ( j) g(t) = 2 1(t −1 2) d /
(k) g(t) = 8 1(4t ) d (l) g(t) = −6 2 (t +1) d
(m) g(t) = 2 rect(t /3) (n) g(t) = 4 rect((t +1)/2)
(o) g(t) = −3rect(t − 2) ( p) g(t) = 0.1rect((t − 3)/4)
32. Graph these functions.
(a) g(t) = u(t) − u(t −1) (b) g(t) = rect(t −1/2)
(c) g(t) = −4 ramp(t) u(t − 2) (d) g(t) = sgn(t) sin(2pt)
(e) g(t) = 5e−t /4 u(t) (f ) g(t) = rect(t) cos(2pt)
Exercises without Answers 71
(g) g(t) = −6 rect(t) cos(3pt) (h) g(t) = u(t +1/2) ramp(1/2 − t)
(i) g(t) = rect(t +1/2) − rect(t −1/2)
t
= + − + −
−¥
d l 1 2d l d l 1 l
( j) g(t) [ ( ) ( ) ( )]d
(k) g(t) = 2 ramp(t) rect((t −1)/2)
(l) g(t) = 3rect(t /4) − 6 rect(t /2)
33. Graph these functions.
(a) g(t) = 3d(3t) + 6d(4(t − 2)) (b) g(t) = 2 1(−t 5) d /
t
= − −
−¥
d l d l l 2 2 1
(c) g(t) = d (t) rect(t ) 1 /11 (d) g(t) [ ( ) ( )]d
34. A function g(t) has the following description. It is zero for t < −5. It has a slope
of –2 in the range −5 < t < −2. It has the shape of a sine wave of unit amplitude
and with a frequency of 1/4 Hz plus a constant in the range −2 < t < 2. For t > 2
it decays exponentially toward zero with a time constant of 2 seconds. It is
continuous everywhere.
(a) Write an exact mathematical description of this function.
(b) Graph g(t) in the range −10 < t < 10.
(c) Graph g(2t) in the range −10 < t < 10 .
(d) Graph 2 g(3 − t) in the range −10 < t < 10.
(e) Graph −2 g((t +1)/2) in the range −10 < t < 10.

13. 72 Chapter 2 Mathematical Description of Continuous-Time Signals
35. Using MATLAB, for each function below graph the original function and the
shifted and/or scaled function.
(a) g( )
,
,
,
,
t
t
t t
t t
t
=
− < −
− < <
− < <
− >
ì
í
ïï
ïï
î
2 1
2 1 1
3 2
1 3
6 3
−3g(4 − t) vs. t
(b) g(t) = Re(e j t + e j . t ) p 1 1p g(t /4) vs. t
(c) G( f )
5
2 2 3 G(10( f −10)) + G(10( f +10)) vs. f
f j
=
− +
36. A signal occurring in a television set is illustrated in Figure E.36. Write a
mathematical description of it.
Signal in Television
x(t)
Figure E.36 Signal occurring in a television set
t (μs)
-10 60
-10
5
37. The signal illustrated in Figure E.37 is part of a binary-phase-shift-keyed (BPSK)
binary data transmission. Write a mathematical description of it.
t (ms)
4
x(t)
1
-1
BPSK Signal
Figure E.37 BPSK signal
38. The signal illustrated in Figure E.38 is the response of an RC lowpass fi lter to a
sudden change in its input signal. Write a mathematical description of it.
t (ns)
20
x(t)
-4
-6
RC Filter Signal
-1.3333
4
Figure E.38 Transient response of an RC fi lter

14. 39. Describe the signal in Figure E.39 as a ramp function minus a summation of step
functions.
...
4
x(t)
15
t
Figure E.39
40. Mathematically describe the signal in Figure E.40.
9
... ...
9
x(t)
t
Semicircle
Figure E.40
41. Let two signals be defi ned by
x ( )
, cos( )
, cos( )
1
1 2 0
0 2 0
t
t
t
=
³
<
ìíî
p
p
and x2 (t) = sin(2pt /10).
Graph these products over the time range −5 < t < 5.
(a) x1(2t) x2 (−t) (b) x1(t /5) x2 (20t )
(c) x1(t /5) x2 (20(t +1)) (d) x1((t − 2)/5) x2 (20t)
42. Given the graphical defi nition of a function in Figure E.42, graph the indicated
shifted and/or scaled versions.
(a)
1
2
1
-2 2 3 4 5 6
-2
t
g(t)
®
®− −
t 2
t
t t
g( ) 3g( )
g(t) = 0 , t < −2 or t > 6
(b)
2
1
-2 1 2 4 6
-2
t
g(t)
3 5
® +
® − −
t t
4
t t
g( ) 2 g(( 1)/2)
g(t) is periodic with fundamental period, 4
Figure E.42
Exercises without Answers 73

15. 74 Chapter 2 Mathematical Description of Continuous-Time Signals
43. For each pair of functions graphed in Figure E.43 determine what shifting and/or
scaling has been done and write a correct functional expression for the shifted
and/or scaled function.
(a)
2
-2 1 2 3 4 5 6
-1
t
g(t)
2
-4 -3 -2 -1 1 2 3 4
-1
t
(b)
2
-2 1 2 3 4 5 6
t
g(t)
-2 -1 1 2 3 4 5 6
t
Figure E.43
In (b), assuming g(t) is periodic with fundamental period 2, fi nd two different
shifting and/or scaling changes that yield the same result.
44. Write a function of continuous time t for which the two successive changes
t ®−t and t ®t −1 leave the function unchanged.
45. Graph the magnitude and phase of each function versus f.
(a) G( f )
j f
j f
=
1+ /10
− æè
öø
f f
= +
e
(b) G( f ) rect rect
+ æè
öø
é
ë ê
ù
û ú
1000
100
1000
100
− jpf /500
(c) G( f )
1
f j f
=
− +
250 2 3
46. Graph versus f, in the range −4 < f < 4 the magnitudes and phases of
(a) X( f ) = 5rect(2 f )e+ j2pf (b) X( f ) = j5d( f + 2) − j5d( f − 2)
(c) X( f ) = (1/2) 1/4 ( f )e− j f d p
Generalized Derivative
47. Graph the generalized derivative of g(t) = 3sin(pt /2) rect(t).
Derivatives and Integrals
48. What is the numerical value of each of the following integrals?
¥
(b) d(t − ) cos(pt) dt
(a) d(t) cos(48pt) dt
−¥
¥
5
−¥
20
(c) d(t − 8) rect(t 16) dt
0
/

16. 49. What is the numerical value of each of the following integrals?
¥
(b) d p 1(t) sin(2 t ) dt
(a) d1(t) cos(48pt) dt
−¥
¥
−¥
20
d (t − ) rect(t) dt
(c) 4 4 2
0
50. Graph the time derivatives of these functions.
(a) g(t) = sin(2pt) sgn(t) (b) g(t) = cos(2pt)
Even and Odd Signals
51. Graph the even and odd parts of these signals.
(a) x(t) = rect(t −1) (b) x(t) = 2sin(4pt − p/4) rect(t)
52. Find the even and odd parts of each of these functions.
(a) g(t) = 10 sin(20pt) (b) g(t) = 20t3 (c) g(t) = 8 + 7t2
(d) g(t) = 1+ t (e) g(t) = 6t (f ) g(t) = 4t cos(10pt)
(g) g(t) = cos(pt)/pt (h) g(t) = 12 + sin(4pt)/4pt
(i) g(t) = (8 + 7t) cos(32pt ) ( j) g(t) = (8 + 7t2 ) sin(32pt)
53. Is there a function that is both even and odd simultaneously? Discuss.
54. Find and graph the even and odd parts of the function x(t) in Figure E.54.
t
x(t)
1
2
1
-1-1
-5 -4 -3 -2
2 3 4 5
Figure E.54
Periodic Signals
55. For each of the following signals, decide whether it is periodic and, if it is, fi nd
the period.
(a) g(t) = 28sin(400pt) (b) g(t) = 14 + 40 cos(60pt)
(c) g(t) = 5t − 2 cos(5000pt) (d) g(t) = 28sin(400pt) +12 cos(500pt)
(e) g(t) = 10 sin(5t ) − 4 cos(7t) (f ) g(t) = 4 sin(3t ) + 3sin( 3t)
56. Is a constant a periodic signal? Explain why it is or is not periodic and, if it is
periodic, what is its fundamental period?
Exercises without Answers 75

17. 76 Chapter 2 Mathematical Description of Continuous-Time Signals
Signal Energy and Power
57. Find the signal energy of each of these signals.
(a) x(t) = 2 rect(−t ) (b) x(t) = rect(8t)
(c) x(t) = 3rect(t /4) (d) x(t) = 2sin(200pt)
(e) x(t) = d(t )
(Hint: First fi nd the signal energy of a signal that approaches an impulse in some
limit, then take the limit.)
d
dt
= t (g) x(t) rect( ) d
(f ) x(t) (rect( ))
t
=
−¥
l l
(h) x(t) = e(−1− j8p)t u(t)
58. Find the average signal power of each of these signals.
(a) x(t) = 2sin(200pt ) (b) x(t) = d (t) 1
(c) x(t) = e j100pt
59. A signal x is periodic with fundamental period T0 = 6. This signal is described
over the time period 0 < t < 6 by
rect((t − 2)/3) − 4 rect((t − 4)/2).
What is the average signal power of this signal?