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What has the author Okan K Ersoy written?
Okan K. Ersoy has written: 'Fourier-related transforms, fast algorithms, and applications' -- subject(s): Fourier transformations
What has the author J Zorn written?
J. Zorn has written: 'Methods of evaluating Fourier transforms with applications to control engineering'
What are the differences between Laplace and Fourier transforms?
Laplace and Fourier transforms are mathematical tools used to analyze functions in different ways. The main difference is that Laplace transforms are used for functions that are defined for all real numbers, while Fourier transforms are used for functions that are periodic. Additionally, Laplace transforms focus on the behavior of a function as it approaches infinity, while Fourier transforms analyze the frequency components of a function.
What are the key differences between Laplace and Fourier transforms and how do they each contribute to signal processing and analysis?
Laplace transforms are used for analyzing continuous-time signals and systems, while Fourier transforms are used for analyzing frequency content of signals. Laplace transforms are more general and can handle a wider range of functions, while Fourier transforms are specifically for periodic signals. Both transforms are essential in signal processing for understanding and manipulating signals in different domains.
What has the author Athanasios Papoulis written?
Athanasios Papoulis has written: 'The Fourier integral and its applications' -- subject(s): Fourier series 'Circuits and Systems' -- subject(s): Electric circuits, Electric networks 'Solutions manual to accompany Probability, random variables and stochastic processes' 'Systems and transforms with applications in optics' -- subject(s): Optics, System analysis, Transformations (Mathematics)
What has the author Fritz Oberhettinger written?
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
What has the author Folke Bolinder written?
Folke Bolinder has written: 'Fourier transforms in the theory of inhomogeneous transmission lines' -- subject(s): Electric lines, Fourier series
What has the author Charles Tong written?
Charles Tong has written: 'Ordered fast Fourier transforms on a massively parallel hypercube multiprocessor' -- subject- s -: Fourier transformations, Multiprocessors
What has the author J F James written?
J. F. James has written: 'A student's guide to Fourier transforms' -- subject(s): Fourier transformations, Mathematical physics, Engineering mathematics
What has the author Roger Clifton Jennison written?
Roger Clifton Jennison has written: 'Fourier transforms and convolutions for the experimentalist'
Can you give an example of how Fast Fourier Transforms are used in financial models?
There is a beautiful paper by Ales Cerny entitled "Introduction to Fast Fourier Transform in finance", which gives many interesting examples.
How does the graph of Fourier Series differ to the graph of Fourier Transform?
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.
