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Fourier Series Representation Of Continuous Periodic Signals

 

Fourier series allows us to represent a non-sinusoidal periodic function as an infinite sum of sinusoidal functions.


Types of Fourier Series:

(a) Trigonometric or quadrature fourier series

800.png 


(b) Polar fourier series :

805.png 


(c) Exponential Series :

810.png 

Exponential FS coefficient is Cn = 815.png

821.png 


Properties of fourier series are given below:

  1. Frequency shift: If 826.pngthen 831.png 
  2. Time shift:

836.png 

841.png 

  1. Linearity: 846.png

then 851.png 

  1. Differentiation in time: If 856.png

then 861.png 

  1. Time Scaling: 866.png then 872.png
  2. Parsevel’s power theorem : 877.png

then 882.png





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