Audio Processing in Python Part I: Sampling, Nyquist, and the Fast Fourier Transform

Fourier Series has been widespread in applications of engineering ranging from heat transfer, vibration analysis, fluid mechanics, noise control, and much more. After evolutions in computation and algorithm development, the use of the Fast Fourier Transform (FFT) has also become ubiquitous in applications in acoustic analysis and even turbulence research. In this tutorial, I describe the basic process for emulating a sampled signal and then processing that signal using the FFT algorithm in Python. This will allow the user to get started with analysis of acoustic-like signals and understand the fundamentals of the Fast Fourier Transform.