  Since the evolution of digital computers, the storage of data has always been
in terms of discrete bits that can store values of either 1 or 0. Hence, all
computer programs (such as MATLAB), convert any input continuous signal into a
discrete dataset. Applying this to oscillating signals, such as audio, opens a
domain for processing as well as editing. The Fourier transform, which is an
integral over infinite limits, for the use of signal processing is discrete.
The essential feature of the Fourier transform is to decompose any signal into
a combination of multiple sinusoidal waves that are easy to deal with. The
discrete Fourier transform (DFT) can be represented as a matrix, with each data
point acting as an orthogonal point, allowing one to perform complicated
transformations on individual frequencies. Due to this formulation, all the
concepts of linear algebra and linear transforms prove to be extremely useful
here. In this paper, we first explain the theoretical basis of audio processing
using linear algebra, and then focus on a simulation coded in MATLAB, to
process and edit various audio samples. The code is open ended and easily
expandable by just defining newer matrices which can transform over the
original audio signal. Finally, this paper attempts to highlight and briefly
explain the results that emerge from the simulation
