Question

Text: Homework 5.0. Use the formula of convolution to find f(t) = u(t) * sin(t), where * is the convolution operator and u(t) is the unit step function. [10] 0.2 Comment on the convolution of u(t). Is this finite? [5] 0.3 Find the convolution of e^(-t) * {u(t) * u(t = 1)}. Hint: Assume e^(-t) as f1(t) and u(t) - u(t - 1) as f2(t). Draw the graph of f2(t). 0.4 Draw the waveform of f1(t) + f2(t). [10] 0.5 Find the convolution f(t) = f1(t) * f2(t). [10]

Name: home work 5 0 use formula of convolution t0 find ut sint here 1s convolution operator and ut is unit step function 10 02 comment on the convolution ut is this finite 51 03 find the convoluti 55785
Uploaded: 2023-01-16T09:59:45-08:00
Duration: 2 min 36 s
Channel: Sri K
Description: home work 5 0 use formula of convolution t0 find ut sint here 1s convolution operator and ut is unit step function 10 02 comment on the convolution ut is this finite 51 03 find the convoluti 55785

          Text: Homework 5.0. Use the formula of convolution to find f(t) = u(t) * sin(t), where * is the convolution operator and u(t) is the unit step function. [10]
    
    0.2 Comment on the convolution of u(t). Is this finite? [5]
    
    0.3 Find the convolution of e^(-t) * {u(t) * u(t = 1)}. Hint: Assume e^(-t) as f1(t) and u(t) - u(t - 1) as f2(t). Draw the graph of f2(t).
    
    0.4 Draw the waveform of f1(t) + f2(t). [10]
    
    0.5 Find the convolution f(t) = f1(t) * f2(t). [10]

home work 5 0 use formula of convolution t0 find ut sint here 1s convolution operator and ut is unit step function 10 02 comment on the convolution ut is this finite 51 03 find the convoluti 55785

Added by Matthew R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

01/16/2023

Step 1

The convolution of two functions f(t) and g(t) is defined as: $$(f * g)(t) = \int_{-\infty}^{\infty} f(\tau)g(t - \tau) d\tau$$ In our case, f(t) = u(t) and g(t) = sin(t). The unit step function u(t) is defined as: $$u(t) = \begin{cases} 0, & t < 0 \\ 1, & t Show more…

Show all steps

Thanks for your feedback!

Text: Homework 5.0. Use the formula of convolution to find f(t) = u(t) * sin(t), where * is the convolution operator and u(t) is the unit step function. [10] 0.2 Comment on the convolution of u(t). Is this finite? [5] 0.3 Find the convolution of e^(-t) * {u(t) * u(t = 1)}. Hint: Assume e^(-t) as f1(t) and u(t) - u(t - 1) as f2(t). Draw the graph of f2(t). 0.4 Draw the waveform of f1(t) + f2(t). [10] 0.5 Find the convolution f(t) = f1(t) * f2(t). [10]