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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)
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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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.
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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