Revision as of 20:07, 22 April 2018

Table of CT Fourier Series Coefficients and Properties

Function	Fourier Series	Coefficients

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Property Name	Property	Proof
Linearity	$\mathfrak{F}{(c_1g(t) + c_2h(t)} = c_1G(f) + c_2H(f) \| <math>\mathfrak{F}(ax_{1}[n] + bx_{2}[n]) = \sum_{n=-\infty}^{\infty}[ax_{1}[n] + bx_{2}[n]]e^{-j\omega n}$ $\sum_{n=-\infty}^{\infty}ax_{1}[n]e^{-j\omega n} + \sum_{n=-\infty}^{\infty}bx_{2}[n]e^{-j\omega n}$ $=a\chi_{1}(\omega) + b\chi_{2}(\omega)$ ________________________________

@@ Line 32: / Line 32: @@
 |-
 | Linearity
-| x(t), y(t) are periodic with period T
+| <math>\mathfrak{F}{(c_1g(t) + c_2h(t)} = c_1G(f) + c_2H(f)
 |  <math>\mathfrak{F}(ax_{1}[n] + bx_{2}[n]) = \sum_{n=-\infty}^{\infty}[ax_{1}[n] + bx_{2}[n]]e^{-j\omega n}</math><br />
 <math>\sum_{n=-\infty}^{\infty}ax_{1}[n]e^{-j\omega n} + \sum_{n=-\infty}^{\infty}bx_{2}[n]e^{-j\omega n}</math><br />