HW 05

Find the following Fourier Transforms

• $F[e^{j{\omega }_{0}t}]$
• $F[\cos {\omega }_{0}t]$
• $F[\sum _{-\mathrm{\infty }}^{\mathrm{\infty }}{\alpha }_n{e}^{j2\pi nt/T}]$
• $F[\sin {\omega }_{0}t]$

Solutions

$F[e^{j{\omega }_{0}t}]$	$=\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}{e}^{j{\omega }_{0}t}{e}^{-j\omega t}dt$
	$=\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}{e}^{j({\omega }_0-\omega )t}dt$
	$=\delta ({\omega }_0-\omega )$