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2. Using direct convolution (i.e., the integral), determine the convolution between r(t) and h(t), where h(t)...
4. Use the convolution integral to find f, where f = g*h, and g(t) = et ult) h(t) = e-2t u(t) Note that both of these are causal to simplify the integration.
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)
Question 5 Using the graphical method (i.e., the method used during the lectures), compute x* h(t), where x(t) = e-and h is as shown in the figure. (You must compute x* h, not hx.) For each separate case in your solution, you must state the convolution result and the corresponding range of t as well as show the fully-labelled graph from which this result is derived. Each convolution result may be stated in the form of an integral, but the...
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...
Prove the following: Using Convolution, determine y(t) when x(t) = 4u(t) and h(t) = e-2t u(t) for t > 0 answer: y(t) = 2[1-e-2t]
solve with steps and please write as clear as possible. Determine, analytically, the convolution y(t)-r(t) * h(t), where a(t)0, otherwise, and h(t) 1, 1<t < 3 o, otherwise.
a) In the lecture, we derived the transform of r(t) = e-atu(t), where u(t) is the unit step function. Using the linearity and scaling properties, derive the Fourier transform of e-a41 = 2(t) + 3(-1). b) Using part (a) and the duality property, determine the Fourier transform of 1/(1++). c) II y(0) 1 + (36) find the Fourier transform of y(). 1
1. Prove that h(t) * (t) = (t) *h(t) 2. A system has an impulse function h(t) = sinº (3t)u(t). Find the unit step (NOTE: an integral table is posted on D2L.) 3. Consider a system with input (t) and output y(t). Let r(t) y(t) = 1 + x(t-1) Is this system linear? Is it causal? Is it BIBO stable? Justify your answer
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot y'() c) Plot y(2t-3) d) calculate the energy of y(t) note: r(t) = t for t 0 and 0 for t < 0 Problem 2: Let x(t)s u(t)-u(t-2) and y(t) = t[u(t)-u(t-1)] a) b) plot x(t) and y(t) evaluate graphically and plot z(t) = x(t) * y(t) Problem 3: An LTI system has the impulse response h(t) = 5e-tu(t)-16e-2tu(t) + 13e-3t u(t) The input...
Please show using MATLAB Answer 7. Obtain the convolution of the pairs of signals in Figure 7 h(t) a(t) 0 2 h(t) r(t) 0 0 Figure 7: Signal pairs Therefore, y(t) = 0 otherwise 7. Obtain the convolution of the pairs of signals in Figure 7 h(t) a(t) 0 2 h(t) r(t) 0 0 Figure 7: Signal pairs Therefore, y(t) = 0 otherwise