A Fourier series may be defined as an expansion of a function in a series of sines and cosines such as.

1. HELLO!
GOOD MORNING
GOOD PEOPLES

2. FOURIER
SERIES

3. What is Fourier Series?
A Fourier series may be defined as an expansion of a
function in a series of sines and cosines such as.
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿

4. WHO IS HE?
Any periodic function can be
rewritten as a weighted sum of
Sines and Cosines of different
frequencies.
JOSEPH FOURIER(1768-1830)

5. Why are Fourier series important?
Fourier methods are definitely a widely applied tool of analysis. They are
used in ALL areas of signal processing.
Such as:
Audio, images, radar, sonar, x-ray crystallography, etc.
They are used in many computational algorithms that require convolutions
that have nothing to do with signals.
They are used in numerical solutions of ordinary and partial differential
equations which can be used to model almost anything.

6. Types of FOURIER SERIES
Trigonometric Fourier Series (TFS)
Exponential Fourier Series (EFS)

7. Half Range Cosine Series
An even function can be expanded using half its range from
0 to L or
L to 0 or
L to 2L

8. THANK YOU