Fourier Transformation Of Fourier Transform

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Fourier Transform

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Fourier Transform
Introduction
Fourier Transform is a fundamentally important mathematical function that is derived by decomposing any given function and representing it using a series of sinusoidal functions. The function particularly works by breaking a signal or function into its alternate representation given by sines and cosines (Lysaker et al. 1579). Generally, the mathematical operation converts signals of time domain into signals of frequency domain. In real life situations, waves tend to be complex signals that can together but have different features in terms of behavior and magnitude. The function is given by:

Where, the independent variable x=time in seconds and ξ =frequency
The mathematical model derived its name from its developer, Joseph Fourier, in the early 19th century. The history of Fourier Transform dates back to 1822 when Joseph Fourier demonstrated that some complex functions could effectively be written as an infinite sum of sinusoidal waves. The researcher particularly used the principle of Fourier Transform in solving various differential equations regarding heat dissipation. Currently, Fourier Transform has a diverse array of applications ranging from music, to digital medical image processing such as magnetic resonance imaging (MRI). This paper focuses on the use of Fourier Transform in modern medical magnetic resonance
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