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

中文翻译：

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模拟DFT算法进行音频处理

随着数字计算机的发展，数据的存储一直以离散位表示，可以存储1或0的值。因此，所有计算机程序（例如MATLAB）都将任何输入的连续信号转换为离散的数据集。将其应用于诸如音频之类的振荡信号，将打开一个域以进行处理和编辑。用于信号处理的傅立叶变换是无穷大的整数，它是离散的。傅里叶变换的基本特征是将任何信号分解为易于处理的多个正弦波的组合。离散傅里叶变换（DFT）可以表示为矩阵，每个数据点充当正交点，从而允许人们对各个频率执行复杂的变换。由于这种表述，线性代数和线性变换的所有概念在这里都非常有用。在本文中，我们首先解释了使用线性代数进行音频处理的理论基础，然后重点介绍了在MATLAB中编码的模拟，以处理和编辑各种音频样本。该代码是开放式的，并且只需定义可以在原始音频信号上转换的较新矩阵即可轻松扩展。最后，本文试图突出并简要说明模拟得出的结果 该代码是开放式的，并且只需定义可以在原始音频信号上转换的较新矩阵即可轻松扩展。最后，本文试图突出并简要说明模拟得出的结果 该代码是开放式的，并且只需定义可以在原始音频信号上转换的较新矩阵即可轻松扩展。最后，本文试图突出并简要说明模拟得出的结果