0
What else can I help you with?
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 is the importance of Fourier transforms?
Fourier transforms are crucial in various fields of science and engineering as they enable the analysis of signals in the frequency domain, facilitating the understanding of their frequency components. This mathematical tool transforms complex time-domain signals into simpler sinusoidal functions, making it easier to filter, compress, and reconstruct signals. Applications range from audio and image processing to solving differential equations in physics, demonstrating its fundamental role in modern technology. Overall, Fourier transforms enhance our ability to analyze and manipulate data across a wide array of disciplines.
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 is Ratio of Fourier transform?
The ratio of Fourier transforms typically refers to the comparison of two Fourier-transformed functions, often expressed as a fraction where the numerator and denominator are the Fourier transforms of different signals or functions. This ratio can be useful in various applications, such as analyzing the frequency response of systems or comparing the spectral characteristics of signals. It can also provide insights into the phase and amplitude relationships between the two functions in the frequency domain. The specific interpretation may depend on the context in which the ratio is used.
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
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.
