Fourier Transforms: Principles and Applications

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The Fourier transform is an important area of mathematics. It is an extension of the Fourier series, in which all periodic functions are expressed as the sum of sine and cosine wave functions. The Fourier transform is relevant when the time period of a represented function approaches infinity. This mathematical tool decomposes a signal, which is a function of time, into its constituent frequencies. The basic properties of the Fourier transform are linearity, invertibility and periodicity, etc. Fourier transforms have applications in solving differential equations, in quantum mechanics and signal processing. Besides these, it is of great significance in spectroscopy, especially nuclear magnetic resonance, magnetic resonance imaging and mass spectroscopy. This book provides comprehensive insights into the principles and applications of Fourier transforms. Different approaches, evaluations, methodologies and advanced studies on Fourier transforms have been included in this book. Coherent flow of topics, student-friendly language and extensive use of examples make this book an invaluable source of knowledge.