Chapter 17, Problem 15P

(a)

To determine

Derive the operational transforms of $F\left\{f\left(t-a\right)\right\}=e^{-j\omega a}F\left(\omega \right)$.

(b)

To determine

Derive the operational transforms of $F\left\{e^{j{\omega }_{0}t}f\left(t\right)\right\}=F\left(\omega -{\omega }_0\right)$.

(c)

To determine

Derive the operational transforms of $F\left\{f\left(t\right)\cos {\omega }_{0}t\right\}=\frac{1}{2}F\left(\omega -{\omega }_0\right)+\frac{1}{2}F\left(\omega +{\omega }_0\right)$.