This is a list of some well-known periodic functions. The constant function _ () = , where c is independent of x, is periodic with any period, but lacks a fundamental period. A definition is given for some of the following functions, though each function may have many equivalent definitions.
All trigonometric functions listed have period , unless otherwise stated. For the following trigonometric functions:
Un is the nth up/down number,
Bn is the nth Bernoulli number
in Jacobi elliptic functions,
The following functions have period and take as their argument. The symbol is the floor function of and is the sign function.
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Le cours étudie les concepts fondamentaux de l'analyse vectorielle et l'analyse de Fourier en vue de leur utilisation pour résoudre des problèmes pluridisciplinaires d'ingénierie scientifique.
In geometry, a hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle. The parametric equations for a hypotrochoid are: where θ is the angle formed by the horizontal and the center of the rolling circle (these are not polar equations because θ is not the polar angle). When measured in radian, θ takes values from 0 to (where LCM is least common multiple).
In geometry, an epitrochoid (ɛpᵻˈtrɒkɔɪd or ɛpᵻˈtroʊkɔɪd) is a roulette traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point is at a distance d from the center of the exterior circle. The parametric equations for an epitrochoid are The parameter θ is geometrically the polar angle of the center of the exterior circle. (However, θ is not the polar angle of the point on the epitrochoid.) Special cases include the limaçon with R = r and the epicycloid with d = r.
In geometry, an epicycloid(also called hypercycloid) is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle. It is a particular kind of roulette. An epicycloid with a minor radius (R2) of 0 is a circle. This is a degenerate form. If the smaller circle has radius r, and the larger circle has radius R = kr, then the parametric equations for the curve can be given by either: or: in a more concise and complex form where angle θ is in turns: smaller circle has radius r the larger circle has radius kr (Assuming the initial point lies on the larger circle.
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking the form of a sum ...
IOP PUBLISHING LTD2020
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Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and L2 distances between such curves. In partic ...
2016
The beating effects which may occur in the sum of two mistuned cosine (or sine) functions whose frequencies f1, f2 satisfy f2 ≈ (k/j)f1 (where k/j is a reduced integer ratio) are known as “beats of mistuned consonances”. They have already been investigated ...