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Fourier Transform is a mathematical model which helps to transform the signals between two different domains, such as transforming signal from frequency domain to time domain or vice versa. Fourier transform has many applications in Engineering and Physics, such as signal processing, RADAR, and so on. Fourier's theorem states that any (reasonably well-behaved) function can be written in terms of trigonometric or exponential functions. We'll eventually prove this theorem in Section 3.8.3, but for now we'll accept it without proof, so that we don't get caught up in all the details right at the start. Fourier Integral a formula for the decomposition of a nonperiodic function into harmonic components whose frequencies range over a continuous set of values. If a function f ( x) satisfies the Dirichlet condition on every finite interval and if the integral converges, then Fourier and Laplace Transforms - August 2003 Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. The Fourier transform is crucial to any discussion of time series analysis, and this chapter discusses the definition of the transform and begins introducing some of the ways it is useful. We will use a Mathematica-esque notation. This includes using the symbol I for the square root of minus one.