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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 ...

For a given bounded function f(x) over a partition of a given interval, the upper sum is the sum of box areas M^*Deltax_k using the supremum M of the function f(x) in each ...

Recall the definition of the autocorrelation function C(t) of a function E(t), C(t)=int_(-infty)^inftyE^_(tau)E(t+tau)dtau. (1) Also recall that the Fourier transform of E(t) ...

A discrete fast Fourier transform algorithm which can be implemented for N=2, 3, 4, 5, 7, 8, 11, 13, and 16 points.

The zero product property asserts that, for elements a and b, ab=0=>a=0 or b=0. This property is especially relevant when considering algebraic structures because, e.g., ...

Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples.

Define S_n(x) = sum_(k=1)^(infty)(sin(kx))/(k^n) (1) C_n(x) = sum_(k=1)^(infty)(cos(kx))/(k^n), (2) then the Clausen functions are defined by ...

There are two sorts of transforms known as the fractional Fourier transform. The linear fractional Fourier transform is a discrete Fourier transform in which the exponent is ...

The Hall-Janko near octagon, also known as the Cohen-Tits near octagon, is a weakly regular graph on 315 vertices with parameters (n,k,lambda,mu)=(315,(10),(1),(0,1)). It is ...

The logarithmic integral is defined as the Cauchy principal value li(x) = PVint_0^x(dt)/(lnt) (1) = ...