CT Convolution

The questions below are due on Thursday March 20, 2025; 02:00:00 PM.

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1 Write an expression for \small (x*h)(t). You may use u() for the unit step function \small u(\:\text{-}\,) and delta() for the the delta function \small\delta(\:\text{-}\,).

\small (x*h)(t) =~

2 Consider the two following signals, \small f and \small g.

Which of the following (if any) is a plot of \small (f*g)(t) from \small -4 to \small +4\,?

Which graph matches?

3 Consider a polynomial term \small p(t) that is clamped to zero before \small t=0, so that

p(t) = \alpha t^k\times u(t)

where \small k is a non-negative integer.

Write an expression for the convolution of \small p(t) with the unit step function \small u(t). You may use alpha for \small\alpha, u() for the unit step function \small u(\:\text{-}\,), and delta() for the the delta function \small\delta(\:\text{-}\,).

\small (p*u)(t) =~