Revision as of 15:23, 14 November 2018

CTFT of periodic signals and some properties with proofs

Function	CTFT	Proof
$sin(\omega_0t)$	$\frac{\pi}{j}(\delta(\omega - \omega_0) - \delta(\omega+\omega_0))$
$cos(\omega_0t)$	$\pi(\delta(\omega - \omega_0) + \delta(\omega+\omega_0))$
$e^{j\omega_0t}$	$2\pi\delta(\omega - \omega_0)$
$\sum_{k=-\infty}^{\infty}u(t+5k) - u(t-1+5k)$

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 ===== - Properties of the Continuous-time Fourier Transform =====
 {| border="1" class="wikitable"
 |-
-! Function
+! name
-! CTFT
+! Property
-! Proof
+|-
-|-}
+| Linearity
+|
+|-
+| Time Shifting
+|
+|-
+| Frequency Shifting
+|
+|-
+| Conjugation
+|
+|-
+| Scaling
+|
+|-
+| Multiplication
+|
+|-
+| Convolution
+|
+|-
+| Differentiation
+|
+|-
+| Parseval's Relation
+|
+|-