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to , i.e., we have

where

is the th Fourier coefficient of . This implies that in order to study convergence of Fourier series it is enough to study properties of the Dirichlet kernel.

The Dirichlet kernel was named for Peter Gustav Lejeune Dirichlet.

Applications

In signal processing, the Dirichlet kernel is often called the periodic sinc function:

:

where is an odd integer. In this

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