Please show all steps Either the following signals:f(t) = 0 if t <0 g (t) = 0 if t<-1f(t) = 1-t if 0st<1 and g (t) = 1 if - 1sts1f(t) = 0 if t 21 g (t) = 0 if t> 1(i) Give the graphical representations of the signals (f) and (g).(ii) Give a physical meaning of the convolution product of two signals.We set h (x) = f (t) *g (t) where *'represents the convolution product.(iii) Determine the signal (h).(iv) Give the graphic representation of signal (h).tes)WE

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Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.21MCQ

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Graph the following functions for the given x[n]= {…,0,2,-2,0,1,3,-2,-3,1,-1,0,…} signal. a) y[n]=x[n](u[n+3]-u[n-2])-2∂[n]+3∂[n-3]x[n b) y[n]=2x[-n]+(x[n])²+x[-n+2]
1. a) Show that if y(t)=h(t)*x(t), then Y(s)=H(x)X(s). 2. b) Use the result given in (a) to find f(t) if F(s)=as(s+a)2.
If G(s) = 1 / (s + 2), find the response c(t) if the input r(t) = u(t), a unit step, assuming zero initial condition.
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: If F(s) = s 4+ 5s3+20s 2 + 40s + 50 , Investigate the stability of this system
Signal and system The mathematical model of a system is y" (t) + ay'(t) + by(t) = a (t) + ca (t) where a=1, b=2 and c=1. 1) Find zeros and poles of the system. 2) Show them onto the S-Plane (the complex plane) 3) Discuss the BIBO stability of the system.
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The response of a system, h(t) is given as in Figure 1 below where the amplitudeof this signal is 7. Then,this system is excited by an input of x(t) = (u(t) × (u(-t)+u(t))) /1. 1)Illustrate the input signal, x(t). 2)Calculate the convolution output of the system y(t) = x(t) ∗ h(t). Nextdetermine y(t) when t is 1 sec 2)Prove the solution in Q2 is comparable when solving in frequency domain(Laplace). Next, sketch the signal for convolution output.
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Either the following signals: f(t)=0 if t<0 f(t)=1−t/2 if 0≤t<2 f(t)=0 if t≥2 And g(t)=0 if t<−2 g(t)=1 if −2≤t≤2 g(t)=0 if t>2 (i) Give the graphical representations of the signals (f) and (g). (ii) Give a physical meaning of the convolution product of two signals. We set h(x) = f (t) *g (t) where '*' represents the convolution product. (iii) Determine the signal (h). (iv) Give the graphical representation of the signal (h).
3. Consider the following second-order differential causal system: y ̈(t)+6y ̇(t)+8y(t) = 2x(t), x(t) = e−3t u(t), y(0) = 2, y ̇(0) = −6, (here, u(t) = step function) where x(t) and y(t) are the input and output of the system, respectively. Find the natural response yn(t), forced response yf (t), and total solution y(t) of the system.

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