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Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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Beyond Nyquist sampling: a cost-based approach.

Ayça Ozçelikkale1, Haldun M Ozaktas

  • 1Department of Electrical Engineering, Bilkent University, Ankara, Turkey. ayca@ee.bilkent.edu.tr

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|April 19, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a new framework for optimally representing optical fields with limited bits. It explores the trade-off between sampling density and amplitude accuracy for efficient data representation.

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Area of Science:

  • Optics and Photonics
  • Information Theory
  • Signal Processing

Background:

  • Representing optical fields efficiently is crucial for various applications.
  • Traditional methods often separate sampling and quantization, potentially missing optimal solutions.
  • Limited bits necessitate careful consideration of both spatial resolution and amplitude accuracy.

Purpose of the Study:

  • To develop a sampling-based framework for optimal optical field representation within a finite bit budget.
  • To investigate the interplay between sampling strategies and quantization accuracy.
  • To establish performance bounds and trade-off curves between representation error and bit cost.

Main Methods:

  • A novel sampling framework is proposed.
  • Optimization of sample number and spacing is performed for a given bit budget.
  • Performance bounds are derived, illustrating error-cost trade-offs.
  • Comparison with conventional separate sampling and quantization approaches.

Main Results:

  • The framework determines optimal sampling parameters (number and spacing) for minimizing representation error.
  • Performance bounds reveal trade-offs between optical field representation error and bit budget.
  • Analysis highlights the importance of jointly considering sampling and quantization.
  • Sampling rates deviating from the Nyquist rate can be more efficient in certain scenarios.

Conclusions:

  • The proposed framework enables efficient optical field representation under bit constraints.
  • Joint optimization of sampling and quantization outperforms separate treatment in specific cases.
  • Understanding the interplay between spatial resolution and amplitude accuracy is key to efficient optical field encoding.
  • This work offers a more nuanced approach to digital optical field representation.