Q2) a) Find the energy of the signals x(t) and y(t) below: TIP: use the trigonometric identity: sin²(t) = ½ (1-cos(2x)) 0 sin f b) Find the energy of the signal z(t)=x(t)+y(t). c) Sketch the signals r(t)=2 sin(t) * (u(t) - u(t-2π)); and s(t) = 2 sin(2t) * (u(t) - u(t-2π)) d) Find the energy of r(t): y(1) e) Find the energy of s(t): f) Find the energy of q(t) = r(t)+s(t) TIP: use the trigonometric identity: sin(a)* sin(b) = ½ * [cos(a-b) - cos(a+b) ] g) Compare the results of b) and f) and select the correct answer: TIP: write the formula for the energy of x(t)+y(t) and use (x(t)+y(t))² = x(t)² + 2x(t)y(t) + y(t)² () for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is always Ex+Ey. ( ) for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is always (Ex)²+ (Ey)² () for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is Ex+Ey only if the integral of the signal x(t)y(t) between -infinity and +infinity is 0. () for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is never equal to Ex+Ey.
Q2) a) Find the energy of the signals x(t) and y(t) below: TIP: use the trigonometric identity: sin²(t) = ½ (1-cos(2x)) 0 sin f b) Find the energy of the signal z(t)=x(t)+y(t). c) Sketch the signals r(t)=2 sin(t) * (u(t) - u(t-2π)); and s(t) = 2 sin(2t) * (u(t) - u(t-2π)) d) Find the energy of r(t): y(1) e) Find the energy of s(t): f) Find the energy of q(t) = r(t)+s(t) TIP: use the trigonometric identity: sin(a)* sin(b) = ½ * [cos(a-b) - cos(a+b) ] g) Compare the results of b) and f) and select the correct answer: TIP: write the formula for the energy of x(t)+y(t) and use (x(t)+y(t))² = x(t)² + 2x(t)y(t) + y(t)² () for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is always Ex+Ey. ( ) for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is always (Ex)²+ (Ey)² () for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is Ex+Ey only if the integral of the signal x(t)y(t) between -infinity and +infinity is 0. () for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is never equal to Ex+Ey.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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e, f, g
![Q2) a) Find the energy of the signals x(t) and y(t) below:
TIP: use the trigonometric identity: sin²(t) = ½ (1-cos(2x))
1
0
x(1)
sin t
d) Find the energy of r(t):
1
e) Find the energy of s(t):
y(1)
b) Find the energy of the signal z(t)=x(t)+y(t).
c) Sketch the signals r(t)=2 sin(t) * (u(t) - u(t-2π)); and s(t) = 2 sin(2t) * (u(t) - u(t-2π))
27
f) Find the energy of q(t) = r(t)+s(t)
TIP: use the trigonometric identity: sin(a)* sin(b) = ½ * [cos(a-b) - cos(a+b) ]
g) Compare the results of b) and f) and select the correct answer:
TIP: write the formula for the energy of x(t)+y(t) and use (x(t)+y(t))² = x(t)² + 2x(t)y(t) + y(t)²
() for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is always Ex+Ey.
() for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is always (Ex)²+ (Ey)²
() for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is Ex+Ey only if the integral of
the signal x(t)y(t) between -infinity and +infinity is 0.
() for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is never equal to Ex+Ey.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac565010-669d-49c5-8c58-19dca7d8b9f0%2Fc2bdc573-87d1-4031-9d00-bbe2aab97723%2Fus8z671_processed.png&w=3840&q=75)
Transcribed Image Text:Q2) a) Find the energy of the signals x(t) and y(t) below:
TIP: use the trigonometric identity: sin²(t) = ½ (1-cos(2x))
1
0
x(1)
sin t
d) Find the energy of r(t):
1
e) Find the energy of s(t):
y(1)
b) Find the energy of the signal z(t)=x(t)+y(t).
c) Sketch the signals r(t)=2 sin(t) * (u(t) - u(t-2π)); and s(t) = 2 sin(2t) * (u(t) - u(t-2π))
27
f) Find the energy of q(t) = r(t)+s(t)
TIP: use the trigonometric identity: sin(a)* sin(b) = ½ * [cos(a-b) - cos(a+b) ]
g) Compare the results of b) and f) and select the correct answer:
TIP: write the formula for the energy of x(t)+y(t) and use (x(t)+y(t))² = x(t)² + 2x(t)y(t) + y(t)²
() for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is always Ex+Ey.
() for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is always (Ex)²+ (Ey)²
() for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is Ex+Ey only if the integral of
the signal x(t)y(t) between -infinity and +infinity is 0.
() for any 2 signals with energies Ex>0 and Ey>0, the energy of x(t)+y(t) is never equal to Ex+Ey.
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