Question: Please show all the process using formulas belwo Convolution . Definition: h(t) * x(t) = [_ h(t -T)x(T)dr = [_ h(r)x(t -T)dr . II (t)

Please show all the process using formulas belwo

Please show all the process using formulas belwoPlease show all the process using formulas belwoPlease show all the process using formulas belwoPlease show all the process using formulas belwo
Convolution . Definition: h(t) * x(t) = [_ h(t -T)x(T)dr = [_ h(r)x(t -T)dr . II (t) * 12(t) = 12(t) * 1(t) . ri(t) * (x2(t) * x3(t)) = (x1(t) * 12(t)) * ra(t)) associativety property of convolu- tion . II (t) * (12(t) + ra(t)) = =1(t) * 12(t) + m,(t) * 13(t) distributivity property of convolutionDiscrete Time . yln] = x[n] * h[n] >xx x[k]h[n - k] . Distributive Property x[n] * (h, [n] + hz[n]) = x[n] * h, [n] + x[n] * h2[n] . H(w) = [ h(t)e jutdt = [H(w)lejLH(w) frequency response of H . (Fourier transform of h(t) . y(t) = h(t) * x(t) = [_h(t -T)x()dr = [_ h(r)x(t -T)dr = h(t) * x(t) . H [ejt] = H(w)ejut . Y (w) = X (W) H(w)Fourier Transform and it's Inverse . x(t) = FIX(jw) = -x X (jw)ejut dw . X (jw) = F[x(t)] = [X x(t)e-jutdtCompute the convolution of each of the following pairs of signals a(t) and h(t) by calculating X (jw) and H(jw), using the convolution prop- erty, and inverse transforming. (a) x(t) = te-Hu(t), h(t) = e-du(t) (b) x(t) = te-tu(t), h(t) = te-du(t) (c) x(t) = e-tu(t), h(t) = eu(-t)

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