As indicated by the derivative property, if we multiply a Fourier transform by (j) N it corresponds

As indicated by the derivative property, if we multiply a Fourier transform by (jΩ)^N it corresponds to computing an Nth derivative of its time signal. Consider the dual of this property. That is, if we compute the derivative of X(Ω) what would happen to the signal in the time domain?

(a) Let x(t) = δ(t − 1) + δ(t + 1) find its Fourier transform (using properties) X(Ω).

(b) Compute dX(Ω)/dΩ and determine its inverse Fourier transform.