INTRODUCTION
Fourier transform was first devised by Jean-Baptiste Joseph Fourier 8th
century French mathematician.
A Fourier transform is a way of decomposing a signal into pure sine
waves, each with its own amplitude and frequency that add to make it up.
Some of the applications of Fourier transform are as follows:
- Signal Processing: Filtering, Compression
- Communication Systems : Modulation and Demodulation, Spectrum
Analysis:
- Audio Processing : Audio Compression, Equalization
- Image Processing : Image Analysis, Image Compression
- Medical Imaging : MRI and CT Imaging
- Physics : Quantum Mechanics, Spectroscopy
- Control Systems : System Analysis, Filter Design
- Vibration Analysis : Structural Health Monitoring, Modal
Analysis
- Electrical Engineering : Power System Analysis, Filter Design
- Seismology : Earthquake Analysis
Fourier Transform can be done on signals as infinite continuous waves
and when you take their Fourier transform, you get an infinite
continuous frequency spectrum.
But real-world signals are not continuous. They are finite and made up
of individual samples or data points obtained from the sensors.
Considering an example of seismometer, even if a seismometer signal
looks smooth and continuous, it doesn’t record ground motion with
infinite precision. There is some fundamental graininess to the data so
what we obtain is discreet finite data. So, we can’t use the idealized
Fourier transform. Instead, you must perform a Discreet Fourier
Transform.