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DFT and FFT with Python and It is applications on various signals

Fast Fourier Transform (FFT) is one of the most important algorithms in computer science, electronics and signal processing engineering. It is a fast solver for Discrete Fourier Transform (DFT). Basically, DFT or FFT transforms signals from time-amplitude domain to frequency-amplitude domain. The reverse form of the FFT is known as Inverse Fast Fourier Transform which converts, naturally, signals from frequency domain to time domain.

FFT is heavily used in communication, radar or computer systems. For example OFDM (orthogonal frequency division multiplexing) is developed based on IFFT and FFT. Since Python is most common used scientific programming language beside Matlab, I would like to present some information about FFT and using it in Python.




This blog post (https://jakevdp.github.io/blog/2013/08/28/understanding-the-fft/) includes the basics of the FFT and very clear comparison of  it to DFT. Another blog post (https://www.ritchievink.com/blog/2017/04/23/understanding-the-fourier-transform-by-example/) which includes a very good example of the FFT. This page (https://plot.ly/python/fft-filters/) has FFT filters using Python. An OFDM example which utilizes FFT and IFFT in Python is presented here (https://dspillustrations.com/pages/posts/misc/python-ofdm-example.html) .

An extra link: (http://www.music.helsinki.fi/tmt/opetus/uusmedia/esim/index-e.html) in which you can find some .wav sound examples to process using FFT. An application of short-term FFT on sounds: short term 
Sound Processing with Short Time Fourier Transform

Another working Python example of the short-term FFT which examine .wav files to find out power of the sound at specific frequency and time blocks.

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