Continuous-Time Convolution
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Each of the following parts defines a new signal y_i(t) in terms of signals f_i(t) and g_i(t). The signals f_i(t) and g_i(t) are defined in terms of exponential functions and the unit step function u(t):
u(t) = \cases{1&if $t\ge0$\cr0&otherwise\cr}
Determine a closed-form solution for each y_i(t).
Your solutions should not include integrals, convolutions, or infinite sums,
but may include separate expressions for different regions of t.
Part a. Determine a closed-form expression for y_1(t)=(f_1*g_1)(t) where f_1(t)=g_1(t)=u(t).
Part b. Determine a closed-form expression for y_2(t)=(f_2*g_2)(t) where f_2(t)=u(t) and g_2(t)=e^{-t}u(t).
Part c. Determine a closed-form expression for y_3(t)=(f_3*g_3)(t) where f_3(t)=e^{-t}u(t) and g_3(t)=e^{-2t}u(t).
Part d. Determine a closed-form expression for y_4(t)=(f_4*g_4)(t) where f_4(t)=g_4(t)=e^{-t}u(t).
Please upload a single pdf file that contains your answers to all parts of this problem: No file selected
