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Plancherel's theorem states that the integral of the squared modulus of a function is equal to the integral of the squared modulus of its spectrum. It corresponds to ...

A test for the convergence of Fourier series. Let phi_x(t)=f(x+t)+f(x-t)-2f(x), then if int_0^pi(|phi_x(t)|dt)/t is finite, the Fourier series converges to f(x) at x.

A surface on which the Gaussian curvature K is everywhere positive. When K is everywhere negative, a surface is called anticlastic. A point at which the Gaussian curvature is ...

The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name ...

A non-Euclidean space with constant negative Gaussian curvature.

A principal ideal domain is an integral domain in which every proper ideal can be generated by a single element. The term "principal ideal domain" is often abbreviated P.I.D. ...

When the Gaussian curvature K is everywhere negative, a surface is called anticlastic and is saddle-shaped. A surface on which K is everywhere positive is called synclastic. ...

The Bump-Ng theorem (and also the title of the paper in which it was proved) states that the zeros of the Mellin transform of Hermite functions have real part equal to 1/2.

The engineering terminology for one use of Fourier transforms. By breaking up a wave pulse into its frequency spectrum f_nu=F(nu)e^(2piinut), (1) the entire signal can be ...

Leakage, more explicitly called spectral leakage, is a smearing of power across a frequency spectrum that occurs when the signal being measured is not periodic in the sample ...