Explanation Given data: Refer to Figure 15.36 in the textbook. Formula used: Write the general expression to find the convolution integral. y ( t ) = h ( t ) ∗ x ( t ) = ∫ 0 t x ( λ ) h ( t − λ ) d λ (1) Calculation: The equation (1) can be rewritten as, z ( t ) = ∫ 0 t y ( λ ) x ( t − λ ) d λ (2) For t < 0 : Figure 1 shows the convolution of x ( t ) and y ( t ) for t < 0 . In Figure 1, for t < 0 there is no overlap of the two functions so that z ( 0 ) = 0 . For 0 < t < 2 : Suppose the given Figure of x ( t ) is fold and shift it by t as shown in Figure 2. Figure 2 shows the convolution of x ( t ) and y ( t ) for 0 < t < 2 . From Figure 2, x ( t − λ ) and y ( λ ) overlap from 0 to t . Therefore, x ( t − λ ) = 2 and y ( λ ) = 4 . Substitute 2 for x ( t − λ ) and 4 for y ( λ ) in equation (2) to find z ( t ) for 0 < t < 2 . z ( t ) = ∫ 0 t ( 2 ) ( 4 ) d λ = 8 ( λ ) 0 t = 8 ( t − 0 ) = 8 t For 2 < t < 6 : Figure 3 shows the convolution of x ( t ) and y ( t ) for 2 < t < 6 . The overlap shown in Figure 3. Therefore, z ( t ) = ∫ 0 2 ( 2 ) ( 4 ) d λ + ∫ 0 t ( 2 ) ( − 4 ) d λ = 8 ( λ ) 0 2 − 8 ( λ ) 0 t = 8 ( 2 − 0 ) − 8 ( t − 0 ) = 16 − 8 t For 6 < t < 8 : Figure 4 shows the convolution of x ( t ) and y ( t ) for 6 < t < 8 . The overlap shown in Figure 4

6th Edition

ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Transfer function

A transfer function (also known as system function or network function) of a system, subsystem, or component is a mathematical function that modifies the output of a system in each possible input. They are widely used in electronics and control systems.

Convolution Integral

Among all the electrical engineering students, this topic of convolution integral is very confusing. It is a mathematical operation of two functions f and g that produce another third type of function (f * g) , and this expresses how the shape of one is …

Question

Chapter 15, Problem 41P

To determine

Graphically convolve x(t) and y(t) shown in Figure 15.36. Find z(t)=x(t)∗y(t).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 15, Problem 40P

Chapter 15, Problem 42P

Students have asked these similar questions

A robot gripper is shown on Fig.1a. The block diagram of the control system is shown in Fig.1b. This system is conditionally stable because it is stable only for a range of the gain K. Using the Routh-Hurwitz criterion method to determine the range of gain for which the system is stable. Find the steady-state error due to unit step input. Sketch the root locus of the system and analyze its stability. Find the value of K so that the phase margin is minimum, and record the values of the phase margin, gain margin, Mr, and BW. Then draw the Bode plot of the system and discuss its stability using the Nyquist stability method. What is the value of this maximum overshoot for both large and small values of K due to unit step input? Draw the response of the open-loop and closed-loop of the system according to the unit step system for k=15, 25, 50. Discuss how to improve the system response if needed.

Please show the steps

Don't use ai to answer I will report you answer

Chapter 15 Solutions

Fundamentals of Electric Circuits

Ch. 15.2 - Prob. 1PP Ch. 15.2 - Prob. 2PP Ch. 15.3 - Prob. 3PP Ch. 15.3 - Prob. 4PP Ch. 15.3 - Prob. 5PP Ch. 15.3 - Prob. 6PP Ch. 15.3 - Obtain the initial and the final values of...Ch. 15.4 - Prob. 8PP Ch. 15.4 - Find f(t) if F(s)=48(s+2)(s+1)(s+3)(s+4)Ch. 15.4 - Obtain g(t) if G(s)=s3+2s+6s(s+1)2(s+3)

Ch. 15.4 - Find g(t) given that G(s)=20(s+1)(s2+4s+13)Ch. 15.5 - Graphically convolve the two functions in Fig....Ch. 15.5 - Given g(t) and f(t) in Fig. 15.20, graphically...Ch. 15.5 - Use convolution to find vo(t) in the circuit of...Ch. 15.6 - Prob. 15PP Ch. 15.6 - Prob. 16PP Ch. 15 - Prob. 1RQ Ch. 15 - Prob. 2RQ Ch. 15 - Prob. 3RQ Ch. 15 - Prob. 4RQ Ch. 15 - Prob. 5RQ Ch. 15 - If F(s) = 1/(s + 2), then f(t) is (a) e2t u(t) (b)...Ch. 15 - Prob. 7RQ Ch. 15 - Prob. 8RQ Ch. 15 - Prob. 9RQ Ch. 15 - Prob. 10RQ Ch. 15 - Prob. 1P Ch. 15 - Prob. 2P Ch. 15 - Prob. 3P Ch. 15 - Prob. 4P Ch. 15 - Prob. 5P Ch. 15 - Prob. 6P Ch. 15 - Prob. 7P Ch. 15 - Prob. 8P Ch. 15 - Prob. 9P Ch. 15 - Prob. 10P Ch. 15 - Find F(s) if: (a) ft=6etcosh2t (b) ft=3te2tsinh4t...Ch. 15 - If g(t) = 4e 2t cos 4t, find G(s).Ch. 15 - Prob. 13P Ch. 15 - Prob. 14P Ch. 15 - Prob. 15P Ch. 15 - Prob. 16P Ch. 15 - Prob. 17P Ch. 15 - Prob. 18P Ch. 15 - Prob. 19P Ch. 15 - Prob. 20P Ch. 15 - Prob. 21P Ch. 15 - Prob. 22P Ch. 15 - Prob. 23P Ch. 15 - Design a problem to help other students better...Ch. 15 - Let F(s)=18(s+1)(s+2)(s+3) (a) Use the initial and...Ch. 15 - Determine the initial and final values of f(t), if...Ch. 15 - Prob. 27P Ch. 15 - Prob. 28P Ch. 15 - Prob. 29P Ch. 15 - Prob. 30P Ch. 15 - Find f(t) for each F(s): (a) 10ss+1s+2s+3 (b)...Ch. 15 - Prob. 32P Ch. 15 - Prob. 33P Ch. 15 - Prob. 34P Ch. 15 - Obtain f(t) for the following transforms: (a)...Ch. 15 - Prob. 36P Ch. 15 - Prob. 37P Ch. 15 - Prob. 38P Ch. 15 - Determine f(t) if: (a)...Ch. 15 - Show that...Ch. 15 - Prob. 41P Ch. 15 - Design a problem to help other students better...Ch. 15 - Prob. 43P Ch. 15 - Prob. 44P Ch. 15 - Given h(t) = 4e2tu(t) and x(t) = (t) 2e 2tu(t),...Ch. 15 - Given the following functions...Ch. 15 - A system has the transfer function...Ch. 15 - Find f(t) using convolution given that: (a)...Ch. 15 - Prob. 49P Ch. 15 - Prob. 50P Ch. 15 - Given that v(0) = 5 and dv(0)/dt = 10, solve...Ch. 15 - Prob. 52P Ch. 15 - Prob. 53P Ch. 15 - Design a problem to help other students better...Ch. 15 - Prob. 55P Ch. 15 - Solve for v(t) in the integrodifferential equation...Ch. 15 - Prob. 57P Ch. 15 - Given that dvdt+2v+50tv()d=4u(t) with v(0) = 1,...Ch. 15 - Solve the integrodifferential equation...Ch. 15 - Prob. 60P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,