**FOURIER SERIES:
**

In mathematics, a Fourier series is a way to represent a wave-like function as the sum of simple sine waves. More formally, it decomposes any periodic function or periodic signal into the sum of a set of simple oscillating functions, namely sine and cosine with the harmonics of periods. So, Fourier series are used in the analysis of periodic functions.

Fourier Series:

where,

Here i used python programming tool instead of manual calculation to represent the Fourier

Series with some examples

.

**PYTHON CODE:**

import numpy as np

import matplotlib.pyplot as plt

resolution = 0.0001

x = np.arange(-np.pi,np.pi,resolution)

square = np.array(x) ……

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**OUTPUT WAVEFORM:**

1) Naming consistency between A_n and a_n, B_n and b_n

2) Add comments to the python code

3) Waveforms needs to make more sense. Instead of calling it first harmonic can you say sin(1*x)*f(x).

4) Help decode the output of the python code

DC, first, third

Plot of

DC+a_1*sin(x)+a_3*sin(3x)