The transforms and applications handbook

By A. Poularikas. 2000

838 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/5d09c28c0c8a125540711b513c6a2b1525da9546

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

An unconditionally stable scheme for the finite-difference time-domain method (2003, background): “Since Laguerre polynomials are defined from to , they are suitable for a causal system [7], [8].”
In-Situ Optimized PWAS Phased Arrays for Lamb Wave Structural Health Monitoring (2007, background): “The Hilbert transform of a signal x(t) is defined as [Poularikas 2006] H(x(t))=− 1 π ∫ +∞”
Solution of time domain electric field Integral equation using the Laguerre polynomials (2004, background): “In [15], we can show that the first derivative of with respect to time is”
Pricing variance and volatility swaps in a stochastic volatility model with regime switching: discrete observations case (2013, neutral): “…ð1; 0, tk 1,Dt,V0Þ ¼ f ð iþ 1; 0, tk 1,Dt,V0Þ f ð1; 0, tk 1,Dt,V0Þ : ð32Þ The final step is to note the relationship f ð ; 0, tk 1,Dt,V0Þ ¼ F½ pð ytk 1 Þ and the property of the Fourier transform, with the Fourier transform being defined as F½ ðxÞ ¼ R1 1 e i x ðxÞdx (see, e.g., Poularikas (2000)).”
Pricing VIX options with stochastic volatility and random jumps (2011, positive): “To achieve this purpose, we first show that the following equality holds by utilizing the Laplace transform (Lewis 2000; Poularikas 2000; Sepp 2007): ∞ ∫”
A CLOSED‐FORM EXACT SOLUTION FOR PRICING VARIANCE SWAPS WITH STOCHASTIC VOLATILITY (2010, methodology): “Based on the generalized Fourier transform, we can do the transformation F [e jαt] = 2πδα(ω),(A.4) where j = √−1 and δα(ω) is the generalized delta function satisfying∫ ∞ −∞ δα(t) (t) dt = (α),(A.5) with α being any complex number.”
On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles (2006, background): “We remark that En is the square of the (n2 − 1)order Hankel transform of D 1 2 n (see also [27,28]).”
A new approach to detect broken rotor bars in induction machines by current spectrum analysis (2007, methodology): “methods [ 13 ]. One of these methods is the use of the Fourier Transform.”