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Since the evolution of digital computers, the storage of data has always beenin terms of discrete bits that can store values of either 1 or 0. Hence, allcomputer programs (such as MATLAB), convert any input continuous signal into adiscrete dataset. Applying this to oscillating signals, such as audio, opens adomain for processing as well as editing. The Fourier transform, which is anintegral over infinite limits, for the use of signal processing is discrete.The essential feature of the Fourier transform is to decompose any signal intoa combination of multiple sinusoidal waves that are easy to deal with. Thediscrete Fourier transform (DFT) can be represented as a matrix, with each datapoint acting as an orthogonal point, allowing one to perform complicatedtransformations on individual frequencies. Due to this formulation, all theconcepts of linear algebra and linear transforms prove to be extremely usefulhere. In this paper, we first explain the theoretical basis of audio processingusing linear algebra, and then focus on a simulation coded in MATLAB, toprocess and edit various audio samples. The code is open ended and easilyexpandable by just defining newer matrices which can transform over theoriginal audio signal. Finally, this paper attempts to highlight and brieflyexplain the results that emerge from the simulation

Simulating the DFT Algorithm for Audio Processing