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Spectral Representation of Two-Sided Signals from and Applications to Signal Processing

Published: 01 June 2024 Publication History

Abstract

We study spectral representation as well as predictability and recoverability problems for nonvanishing discrete-time signals from, i.e., for bounded discrete-time signals, including signals that do not vanish at . We extend the notions of transfer functions, the spectrum gaps, bandlimitness, and filters to these general type signals. We present some frequency conditions for predictability and data recoverability and propose some prediction and data recovery methods.

References

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Dokuchaev N.Predictors for Discrete Time Processes with Energy Decay on Higher FrequenciesIEEE Trans. Signal Process.201260116027-6030https://doi.org/10.1109/TSP.2012.2212436
[2]
Dokuchaev N.Near-ideal Causal Smoothing Filters for the Real SequencesSignal Process.20161181285-293https://doi.org/10.1016/j.sigpro.2015.07.002
[3]
Dokuchaev, N.G., Spectral Representation of Nonvanishing Discrete-Time Signals and the Prediction Problem, to appear in Probl. Peredachi Inf., 2024, vol. 60, no. 3.
[4]
Kahane, J.-P., Séries de Fourier absolument convergentes, Berlin: Springer, 1970. https://doi.org/10.1007/978-3-662-59158-1
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Katznelson, Y., An Introduction to Harmonic Analysis, Cambridge, UK: Cambridge Univ. Press, 2004, 3rd ed. https://doi.org/10.1017/CBO9781139165372
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Rudin, W., Functional Analysis, New York: McGraw-Hill, 1973.

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Information & Contributors

Information

Published In

cover image Problems of Information Transmission
Problems of Information Transmission  Volume 60, Issue 2
Jun 2024
70 pages

Publisher

Plenum Press

United States

Publication History

Accepted: 10 September 2024
Revision received: 16 August 2024
Received: 18 June 2024
Published: 01 June 2024

Author Tags

  1. nonvanishing signals
  2. spectral representation
  3. transfer functions
  4. data recovery
  5. predictors

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