Question

Describe the concept of Fourier series and its application to AC waveforms.

Answer 1

Fourier series is a mathematical tool used to represent a periodic function as a sum of sine and cosine functions with different frequencies, amplitudes, and phases. It was introduced by French mathematician Jean-Baptiste Joseph Fourier in the early 19th century and has since become a fundamental concept in various fields, particularly in signal processing, mathematics, physics, and engineering.

The basic idea behind the Fourier series is that any periodic function with a well-defined period can be expressed as an infinite sum of sinusoidal components. These components have frequencies that are integer multiples of the fundamental frequency, which is the reciprocal of the period of the function. Mathematically, the Fourier series representation of a periodic function f(t) with period T can be written as:


(

)
=

0
+
∑

=
1
∞
[


cos
⁡
(
2



0

)
+


sin
⁡
(
2



0

)
]
,
f(t)=a
0
    ​

+∑
n=1
∞
    ​

[a
n
    ​

cos(2πnf
0
    ​

t)+b
n
    ​

sin(2πnf
0
    ​

t)],

where:


0
a
0
    ​

 is the average value of the function over one period.


a
n
    ​

 and


b
n
    ​

 are coefficients that determine the amplitude and phase of the