Abstract
This chapter introduces linear systems. It begins with a review of the properties of the Fourier transform and provides examples of 2D Fourier transform pairs. Following this, it introduces the discrete Fourier transforms. The usefulness of this transform lies in the fact that when substituted into the wave equation, one can reduce a 3D partial differential equation (PDE) to a 1D ordinary differential equation (ODE). The chapter also presents the properties and examples of 2D Fourier transform in a tabular form. Based on this understanding, the chapter describes the Fast Fourier transform algorithms that are used for simulations using MATLAB. In addition, the chapter demonstrates the use of Discrete Fourier Transform as a way of numerically approximating the continuous Fourier transform of a function. It also discusses properties of linear systems and illustrates the concept of convolution and correlation. It concludes with a discussion on linear systems and convolution and illustrates a correlation between them.
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