There is a beautiful paper by Ales Cerny entitled "Introduction to Fast Fourier Transform in finance", which gives many interesting examples.
You can graph both with Energy on the y-axis and frequency on the x. Such a frequency domain graph of a fourier series will be discrete with a finite number of values corresponding to the coefficients a0, a1, a2, ...., b1, b2,... Also, the fourier series will have a limited domain corresponding to the longest period of your original function. A fourier transforms turns a sum into an integral and as such is a continuous function (with uncountably many values) over the entire domain (-inf,inf). Because the frequency domain is unrestricted, fourier transforms can be used to model nonperiodic functions as well while fourier series only work on periodic ones. Series: discrete, limited domain Transform: continuous, infinite domain.
Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.
Joseph Fourier is a French mathematician and physicist. Fourier is generally credited with the discovery of the greenhouse effect.
Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.
Fritz Oberhettinger has written: 'Tables of Laplace transforms' -- subject(s): Laplace transformation 'Tabellen zur Fourier Transformation' -- subject(s): Mathematics, Tables, Fourier transformations 'Tabellen zur Fourier Transformation' -- subject(s): Mathematics, Tables, Fourier transformations 'Tables of Bessel transforms' -- subject(s): Integral transforms, Bessel functions 'Anwendung der elliptischen Funktionen in Physik und Technik' -- subject(s): Elliptic functions
Okan K. Ersoy has written: 'Fourier-related transforms, fast algorithms, and applications' -- subject(s): Fourier transformations
Folke Bolinder has written: 'Fourier transforms in the theory of inhomogeneous transmission lines' -- subject(s): Electric lines, Fourier series
Charles Tong has written: 'Ordered fast Fourier transforms on a massively parallel hypercube multiprocessor' -- subject- s -: Fourier transformations, Multiprocessors
J. F. James has written: 'A student's guide to Fourier transforms' -- subject(s): Fourier transformations, Mathematical physics, Engineering mathematics
Roger Clifton Jennison has written: 'Fourier transforms and convolutions for the experimentalist'
There is a beautiful paper by Ales Cerny entitled "Introduction to Fast Fourier Transform in finance", which gives many interesting examples.
J. Zorn has written: 'Methods of evaluating Fourier transforms with applications to control engineering'
Some uses are: Signals Analysis, DSP, cryptography, steganography, and image editing.
You can graph both with Energy on the y-axis and frequency on the x. Such a frequency domain graph of a fourier series will be discrete with a finite number of values corresponding to the coefficients a0, a1, a2, ...., b1, b2,... Also, the fourier series will have a limited domain corresponding to the longest period of your original function. A fourier transforms turns a sum into an integral and as such is a continuous function (with uncountably many values) over the entire domain (-inf,inf). Because the frequency domain is unrestricted, fourier transforms can be used to model nonperiodic functions as well while fourier series only work on periodic ones. Series: discrete, limited domain Transform: continuous, infinite domain.
Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.
Daniel Huybrechts has written: 'Fourier-Mukai Transforms in Algebraic Geometry (Oxford Mathematical Monographs)' 'The geometry of moduli spaces of sheaves' -- subject(s): Sheaf theory, Moduli theory, Algebraic Surfaces 'The geometry of moduli spaces of sheaves' -- subject(s): Algebraic Surfaces, Moduli theory, Sheaf theory, Surfaces, Algebraic 'Fourier-Mukai transforms in algebraic geometry' -- subject(s): Algebraic Geometry, Fourier transformations, Geometry, Algebraic