HW 05

Find the following Fourier Transforms

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

Solutions

$F[e^{j\omega _{0}t}]$	$=\int _{-\infty }^{\infty }e^{j\omega _{0}t}e^{-j\omega t}dt$
	$=\int _{-\infty }^{\infty }e^{j(\omega _{0}-\omega )t}dt$
	$=\delta (\omega _{0}-\omega )\,\!$