Write the convolution of with ut in integral form see

Question

Question: 1. (a) Write the convolution of $(/) with U(t) in integral form. See whether you can identify this as the integral of $(1).

(b) What is the transform of s(t)"U(t)? Solve this using the convolution theorem.

2. Any arbitrary function can be expressed as the sum of an even and odd function; that is,

s(t) = s_e(t) + s₀(t)

s_e(t) = s(t) + s(-t)
                2

s₀(t) = s(t) - s(-t)
                2

(a) Show that s,(t) is an even function and that so(t) is an odd function.

(b) Show that S(t) = s.(t) + So(l).

(c) Find S,(t) and $0(t) for $(t) = U(t), a unit step function.

(d) Find s,(t) and So(t) for S(t) = cos20πt