The Poisson Summation Formula is an identity relating the periodic summation of a function to the values of that function's continuous Fourier transform, so that the Fourier series coefficients of the periodized function are exactly given by discrete samples of the transform, and conversely. Discovered by Simeon Denis Poisson, it is a fundamental tool of Fourier analysis that links a function's behavior in physical space to its behavior in frequency space, with applications ranging from number theory to signal processing.
Facts
StatementThe Poisson summation formula relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Proved By
Source Poisson summation formula (Wikipedia)
Sources
1. Poisson summation formula (Wikipedia)
Lead paragraphQuote, Lead paragraph
In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.