What is it about?
Generalized Fourier transforms are introduced. This work gives basic properties of such transforms in the space of square-integrable functions on an interval.
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Why is it important?
The generalized transforms extend the power of the original FT while retaining its efficiency. There are numerous practical applications to Signal Processing and also theoretical ones, e.g. an application to the noise-cancelling phenomenon called Broadband Redundancy.
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This page is a summary of: The Dirichlet ring and unconditional bases in L 2[0, 2π], Functional Analysis and Its Applications, July 2013, Springer Science + Business Media,
DOI: 10.1007/s10688-013-0028-6.
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