This document discusses the history and applications of Fourier analysis. It notes that Fourier analysis was invented by Jean Baptiste Joseph Fourier, a French mathematician and physicist born in the late 18th century. The document then lists some of the main applications of Fourier analysis, such as signal processing, image processing, heat distribution mapping, wave simplification, and light simplification. It provides examples of how Fourier analysis can be used to transform signals from the time domain to the frequency domain using Fourier series equations. Charts are shown demonstrating this transformation for simple sine waves. The document cautions that Fourier analysis works best for stationary waves and that more advanced techniques are needed for non-stationary waves like music or speech.

1. History and Real Life
Applications of
Fourier Analaysis
By
Syed Ahmed Zaki
ID:131-15-2169
Sec:A
Dept. of CSE

2. History
 Fourier series is invented by French mathematician Jean
Baptiste Joseph Fourier. He was also a physicst and
historian too.
 He was born in Auxerre, France
 He was a son of a tailor,
 He orphaned at the age nine.
Joseph Fourier
 He then joined army and educated at the scientific section
of the army corps.
 Day by day he then admitted himself in many other
renowned institute of France and other countries.(e.g. Ecole
Polytechnique,Institute of Egypt )

3. Applications
 Signal Processing
 Image processing
 Heat distribution mapping
 Wave simplification
 Light Simplication(Interference , Deffraction etc.)
 Radiation measurements etc.

4. Examples
The general equation for fourier transformation is
Where, x(t) = Time domain signal
and e^(-i2πft) = mother or basic function
By this equation we can transform from time
domain to frequency domain

5. Let,
Where A=amplitude
f=frequency
Suppose for 50 Hz of frequency we get x(t) value of
time domain and place it to the Fourier series
equation written above and by integration we get
the frequecy transformation like below.

6. Example in graph:
Pic: 50 Hz frequency to Time domain and Frequency domain
by fourier series.
(Amplitude vs Time) and (Amplitude vs Frequency)

7. Example in graph(Complex):
For more complex form of 100,250,400 Hz frequecy
it will be also easy with fourier series

8. Caution
Both of this example and fourier series are for stationary
wave(Standing wave), which remains in a constant
position Example: Jump rope wave, Mechanical Wave ,
Light wave etc.
Standing wave
If we want to use non-stationary wave(like music wave,
human speech etc.)simplification then we have to use
2D transformation logic and tools.
Travelling Wave

10. Thank you all