Revision as of 16:10, 14 November 2018

CTFT of periodic signals and some properties with proofs

Function	CTFT	Proof
$sin(\omega_0t)$	$\frac{\pi}{j}(\delta(\omega - \omega_0) - \delta(\omega+\omega_0)$
$cos(\omega_0t)$	$\frac{1}{2}e^{j\omega_0 t} + \frac{1}{2}e^{-j\omega_0 t}$
$e^{j\omega_0t}u(t)$	$2\pi\delta(\omega - \omega_0)$

@@ Line 1: / Line 1: @@
 [[Category:bonus point project]]
-= CT Fourier Series for periodic signals and some properties with proofs=
+= CTFT of periodic signals and some properties with proofs=
 ===== - Fourier series of periodic signals =====
@@ Line 9: / Line 9: @@
 |-
 ! Function
-! Fourier Series
+! CTFT
 ! Proof
 |-
 |<math>sin(\omega_0t) </math>
-|<math>\frac{1}{2j}e^{j\omega_0 t} - \frac{1}{2j}e^{-j\omega_0 t} </math>
+|<math>\frac{\pi}{j}(\delta(\omega - \omega_0) - \delta(\omega+\omega_0)</math>
 |<math> </math>
 |-