Q3) 2.22. For the following pairs of waveforms, use the convolution integral to find the response...
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...
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...
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)
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
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
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...
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)
Calculate the convolution integral of the following signals. Find the energy and power of the input and output signals. x(t) y(t) x(t) = cos(it)[u(t + 1) – uſt – 3)] h(t) = u(t + 2) – uſt – 1) del mes h(t) de ser LTI System
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...