12,901 research outputs found
'Computing modified Bessel functions with large modulation index for sound synthesis applications
Ordinary Bessel functions are a common function used when examining the spectral properties of frequency modulated signals, particularly in sound synthesis applications. Recently, it was shown that modified Bessel functions can also be used for sound synthesis. However, to limit the impact of aliasing distortion when using these functions, it is essential to set an upper limit on the frequency-dependent modulation index used when computing these functions. However, it can be impossible to do this beyond a certain threshold when using standard mathematical software tools such as Matlab, or the scientific toolbox of the Python language, because of numerical overflow issues. This short paper presents an approach to overcome this limitation using the MaxStar algorithm. Results are also presented to demonstrate the usefulness of this solution
Computation of the Marcum Q-function
Methods and an algorithm for computing the generalized Marcum function
() and the complementary function () are described.
These functions appear in problems of different technical and scientific areas
such as, for example, radar detection and communications, statistics and
probability theory, where they are called the non-central chi-square or the non
central gamma cumulative distribution functions.
The algorithm for computing the Marcum functions combines different methods
of evaluation in different regions: series expansions, integral
representations, asymptotic expansions, and use of three-term homogeneous
recurrence relations. A relative accuracy close to can be obtained
in the parameter region ,
, while for larger parameters the accuracy decreases (close to
for and close to for ).Comment: Accepted for publication in ACM Trans. Math. Soft
A Fast Algorithm for Sampling from the Posterior of a von Mises distribution
Motivated by molecular biology, there has been an upsurge of research
activities in directional statistics in general and its Bayesian aspect in
particular. The central distribution for the circular case is von Mises
distribution which has two parameters (mean and concentration) akin to the
univariate normal distribution. However, there has been a challenge to sample
efficiently from the posterior distribution of the concentration parameter. We
describe a novel, highly efficient algorithm to sample from the posterior
distribution and fill this long-standing gap
On Non-Oscillating Integrals for Computing Inhomogeneous Airy Functions
Integral representations are considered of solutions of the inhomogeneous
Airy differential equation . The solutions of these equations
are also known as Scorer functions. Certain functional relations for these
functions are used to confine the discussion to one function and to a certain
sector in the complex plane. By using steepest descent methods from
asymptotics, the standard integral representations of the Scorer functions are
modified in order to obtain non-oscillating integrals for complex values of
. In this way stable representations for numerical evaluations of the
functions are obtained. The methods are illustrated with numerical results.Comment: 12 pages, 5 figure
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