## Abstract

We develop a class of compactly supported window functions V _{m} so that each polynomial p(x) of degree m-1 as well as p(x) modulated with an integerfrequency has a locally finite representation in terms of the local cosine basis ¥ = {¥ _{j} ^{k} (x) = V _{m} (x - j/2 - 1/4) cos((2k + 1)π(x - j))}. Explicit formulations for V _{m} and its Fourier transform are derived. It is shown that these window functions are non-negative, have minimal support of length m, and maximal smoothness of order 2m - 2. Furthermore, we determine the exactRiesz bounds of ¥. Smoothness and stability for these bases are superior as compared to other local cosine bases with similar properties in the literature. Consequently, the bases ¥ are particularly useful for applications in signal and image processing.

Original language | English |
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Pages (from-to) | 475-496 |

Number of pages | 22 |

Journal | Journal of Fourier Analysis and Applications |

Volume | 10 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2004 |

Externally published | Yes |

## Keywords

- Riesz bases
- Wilson bases
- Zak transform