Revision as of 14:59, 14 November 2018

CT Fourier Series for periodic signals and some properties with proofs

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Function	Fourier Series	Proof
$sin(\omega_0t)$	$\frac{1}{2j}e^{j\omega_0 t} - \frac{1}{2j}e^{-j\omega_0 t}$
$cos(\omega_0t)$	$\frac{1}{2}e^{j\omega_0 t} + \frac{1}{2}e^{-j\omega_0 t}$
$e^{\alpha t}u(t)$	$\frac{1}{\alpha + j\omega}$

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 ===== - Fourier series of periodic signals =====
 {| border="1" class="wikitable"
@@ Line 9: / Line 10: @@
 ! Function
 ! Fourier Series
+! 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>cos(\omega_0t) </math>
+|<math>\frac{1}{2}e^{j\omega_0 t} + \frac{1}{2}e^{-j\omega_0 t} </math>
+|
+|-
+|<math>e^{\alpha t}u(t) </math>
+|<math>\frac{1}{\alpha + j\omega} </math>
-===== - Properties of CTFT =====
+|
-{| border="1" class="wikitable"
-|-
-! Name
-! Property
-! Proof
 |-
+}