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}]
Prove the following: Using Convolution, determine y(t) when x(t) = 4u(t) and h(t) = e-2t u(t)...
Prob. 5 (a) Let x(t) = u(t) and h(t) = e-looor u(t) + e-lotu(t). -00 <t< oo using graphical convolution(s). Determine y(t) = h(t) * x(t) for Prob. 5 (cont.) (b) Let zln] = uln] and h[n]-G)nuln] + (-))' hnnDetermine vinl -h) rin) for -00n< oo using graphical convolution(s) Prob. 5 (a) Let x(t) = u(t) and h(t) = e-looor u(t) + e-lotu(t). -00
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)
8) Convolution Integral (7 points). Given the following signals x(t) and h(t), compute and plot the convolution y(t) = x(t) *h(t). x(t) = u(t+2) - u(t – 4) h(t) = 5u(t)e-2t
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);
use Fourier Transforms to convolve f(t) = e-2t u(t-2) and h (t) = e-4t u(t-3). Check your answer by performing the time-domain convolution. use Fourier Transforms to convolve f(t) = e-2t u(t-2) and h (t) = e-4t u(t-3). Check your answer by performing the time-domain convolution.
By using convolution theorem, not laplace. !!!!!!! Determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t): (i) x(t)=u(t), h(t)=u(t): (iii) x(1) 11(1) _ 211(-1) + 11( -2), h(1) 11( 1) _ 11(-1);
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.
4. Convolution EX4. The input X(t) and impulse response h(t) for a system are given. Using convolution evaluating the system output y(t). X(t)=1 O<t1 h(t)=sin pi*t 0<<2 =0 else where =0 elsewhere Xit) ↑ hlt) E mer
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)
determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t): (1) x(t) = u(t), h(t) = u(t) (2) x(t) = exp(2t)u(-t), h(t) = exp(-3t)u(t)