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8) Convolution Integral (7 points). Given the following signals x(t) and h(t), compute and plot the...
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.
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
Compute the convolution of the following pairs of signals x(t) and hlt) by and inverse transformin z(t)u(t), h(t)-e'u(-t)
Solve using convolution integral The signals h(t) and f(t) are as shown in Figure 12(a) and (b), respectively. Compute and sketch the graph of h(t) f(t). 1 h(t)--t+1 f(t)-u(t)-u(t-1) Figure 12(a) Figure 12(b)
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)
Determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t) USING CONVOLUTION THEOREM ONLY: iv) x(t) = exp(2t)u(−t), h(t) = exp(−3t)u(t);
2. Using direct convolution (i.e., the integral), determine the convolution between r(t) and h(t), where h(t) and r(t) are defined as (note: please do NOT just plug in the formulas we derived in the class): h(t) exp(-2t) u (t) and x(t) = exp(-t)u(t), u(t) is the unit step function. h(t) exp(-t)u (t) and r(t)= exp(-t)u(t)
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
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]
Find the convolution of the following two signals: X(t) ylt). Plot the resulting signal. 1. 0 x (t) y (t)