10/10,13,16,17 - Fourier Transform Properties

Properties of the Fourier Transform

Linearity

$F[ax(t)+bx(t)]$	$=\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}[ax(t)+bx(t)]e^{-j2\pi ft}dt$
	$=a\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}x(t)e^{-j2\pi ft}dt+b\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}x(t)e^{-j2\pi ft}dt$
	$=aF[x(t)]+bF[x(t)]$

Time Invariance

$f(n+1)$	$=(n+1{)}^2$
	$=n^2+2n+1$