Topological category

From formulasearchengine
Jump to navigation Jump to search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

In signal processing, any periodic function    with period P can be represented by a summation of an infinite number of instances of an aperiodic function,   , that are offset by integer multiples of P.  This representation is called periodic summation:

When    is alternatively represented as a complex Fourier series, the Fourier coefficients are proportional to the values (or "samples") of the continuous Fourier transform of    at intervals of  [1][2]  That identity is a form of the Poisson summation formula. Similarly, a Fourier series whose coefficients are samples of function    is equivalent to a periodic summation of the Fourier transform of  ,  which is known as a discrete-time Fourier transform.

Quotient space as domain

If a periodic function is represented using the quotient space domain then one can write

instead. The arguments of are equivalence classes of real numbers that share the same fractional part when divided by .

Citations

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

See also

  1. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  2. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534