Corpus ID: 44194028

Wavelet decomposition and bandwidth of functions defined on vector spaces over finite fields

@inproceedings{Iosevich2016WaveletDA,
  title={Wavelet decomposition and bandwidth of functions defined on vector spaces over finite fields},
  author={Alex Iosevich and Allen Qiankun Liu and Azita Mayeli and Jonathan Pakianathan},
  year={2016}
}
  • Alex Iosevich, Allen Qiankun Liu, +1 author Jonathan Pakianathan
  • Published 2016
  • Mathematics
  • In this paper we study how zeros of the Fourier transform of a function $f: \mathbb{Z}_p^d \to \mathbb{C}$ are related to the structure of the function itself. In particular, we introduce a notion of bandwidth of such functions and discuss its connection with the decomposition of this function into wavelets. Connections of these concepts with the tomography principle and the Nyquist-Shannon sampling theorem are explored. We examine a variety of cases such as when the Fourier transform of the… CONTINUE READING

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    References

    Publications referenced by this paper.
    SHOWING 1-7 OF 7 REFERENCES

    Certain Topics in Telegraph Transmission Theory

    • Harry Nyquist
    • Engineering
    • Transactions of the American Institute of Electrical Engineers
    • 2002

    Sampling-50 years after Shannon

    VIEW 1 EXCERPT

    Communication in the presence of noise

    et al

    • C. Aten
    • Tiling sets and spectral sets over finite fields, submitted for publication.
    • 1090
    VIEW 1 EXCERPT