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# Fourier series

In communication system Fourier series is tool which is use to decompose continuous periodic into its sinusoidal component. or we can say it decompose any periodic function or periodic signal into the sum of sin and cosine waves. by our video given above you can get clear idea how it decompose periodic function into sum of sin and cosine wave.

## Types of Fourier Series

- trigonometric or quadrature Fourier Series
- polar Fourier Series
- Exponential Fourier Series

## Dirichlet condition

- f(t) should be deterministic in -T/2 ≤ f(t) + T/2
- Finite number of discontinuities
- Finite number of minima and maxima
- f(t) must be absolute integral over period T

## important points

### Case 1. when f(t) is even signal

- for even signal only cosine functions are present (a0,an ≠ 0) (bn = 0)
- for odd signal only sin functions are present (a0,an = 0) (bn ≠ 0)

### Case 2. when f(t) is half wave symmetry

### f(t) = -f(t ± T/2)

- for half wave symmetry only odd harmonics present
- in Fourier series on sin term with odd harmonics present

### Case 3. when f(t) is full wave symmetry

### f(t ± T/2) = f(t)

- for full wave symmetry only even harmonics are present

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To buy signal and system book by G.K. publication** click here**

To buy signal and system schaums outline** click here**

All books mentioned above is very good books for signal and system, we would recommend schoums outline for gate preparation, it is wonderful book to clear basic concepts.

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