Sketch the pulse shape - write the integral expression for

Question

Cosine pulse:-

Consider the cosine pulse that is zero except in the interval -T/2 ₀t with f₀ = 1/2T.

(a) Sketch the pulse shape.

(b) Write the integral expression for the Fourier transform of x(t).

(c) Can you infer that you only need to integrate the product of two cosines?

(d) Find the Fourier transform. Hint: You may find it useful to use the identities