Problem 1 Use the convolution integral to find the zero-state response for x(t)-u(t), and h(t)- eu(t)
Problem 4. Use the convolution integral to find the response y(t) of the LTI system with impulse response h(t) to input x(t) a) x(I)-2expl_2t)u(t) , h(1)-expl-t)u(t)
Problem 3. Find by convolution for each pair of waveforms the response to the input r(t) of the LTI system with impulse response h(t). Express your result graphically or analytically as you choose. r(t)u(t) x(t) = eta(-t) a(t) h(t) = e-ta(t) h(t)-eu) h(t) -1 h t) x(t) = sin(nt) (u(t)-u(t-2)) h t) 1, t<0; 1-sin(2Tt), t2 0 x(t) = Problem 3. Find by convolution for each pair of waveforms the response to the input r(t) of the LTI system with...
A system has an input, x(t) and an impulse response, h(t). Using the convolution integral, find and plot the system output, y(t), for the combination given below. x(t) is P3.2(e) and h(t) is P3.2(f). 1/2 cycle of 2 cos at -2. (e)
Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t – 7)dt is greatly simplified when either the input f(t) or impulse response h(t) is the sum of weighted impulse functions. This fact will be used later in the semester when we study the operation of communication systems using Fourier analysis methods. a) Use the convolution integral to prove that f(t) *8(t – T) = f(t – T) and 8(t – T) *h(t) = h(t...
Solving simple system differential equation to understand Zero-State response, Initial Condition response, Total response, and Steady State response: Unit Impulse response and Convolution Integral (Zero-State response): 9) Two LTI systems in parallel h1(t)- e "u(t) and h2(t)- h1(t-2) a. Find the expression of the combined unit impulse response h(t) b. Find the zero state response y2s(t) in the expression of piecewise function to the input signal x(t)-[u(t)-u(t-10)] Sketch y2s(t) Show that the combined system h(t) is causal as well as...
2(a). Compute and plot the convolution of ytryh)x where h(t) t)-u(t-4), x(t)u(t)-u(t-1) and zero else b). Compute and plot the convolution y(n) h(n)*x (n) where h(n)-1, for 0Sns4, x(n) 1, n 0, 1 and zero else.
Q3) 2.22. For the following pairs of waveforms, use the convolution integral to find the response y(t) of the LTI system with impulse response h(t) to the input x(t). Sketch your results. x(t) = elut) (Do this both when a + B and when a = B.) h(t) = e-Blut)
4. A linear time invariant system has the following impulse response: h(t) =2e-at u(t) Use convolution to find the response y(t) to the following input: x(t) = u(t)-u(t-4) Sketch y(t) for the case when a = 1
1. Evaluate and sketch the convolution integral (the output y(t)) for a system with input x(t) and impulse response h(t), where x(t) = u(1-2) and h(t)= "u(t) u(t) is the unit step function. Please show clearly all the necessary steps of convolution. Determine the values of the output y(t) at 1 = 0,1 = 3,1 = 00. (3 pts)
Problem 5 5. Find the state transition matrix, the zero-input response, the zero-state response, and the complete response for the following continuous-time system -2 0 3 -5 1]x(t) x(t) = dt x(t)u() x(0) = 2/3 y(t) =[0 u(t) = et for t20