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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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SNR Degradation in Undersampled Phase Measurement Systems.

David Salido-Monzú1, Francisco J Meca-Meca2, Ernesto Martín-Gorostiza3

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Summary

This study analyzes how undersampling affects signal-to-noise ratio (SNR) reduction in phase estimation systems. It quantifies the impact of undersampling frequency on SNR, considering filter stability for accurate infrared ranging applications.

Keywords:
digitizationnoise aliasingoptical rangingphase measurementundersampling

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Area of Science:

  • Electrical Engineering
  • Signal Processing
  • Sensor Technology

Background:

  • Phase estimation of sinusoidal signals is crucial for many measurement applications.
  • Undersampling digital systems can reduce hardware requirements, especially for simple, inexpensive sensors.
  • Filter phase stability limits noise bandwidth reduction, impacting undersampling effectiveness.

Purpose of the Study:

  • To analyze the relationship between undersampling frequency and signal-to-noise ratio (SNR) reduction.
  • To investigate the impact of filter stability on noise aliasing and SNR.
  • To quantify the effects of undersampling in an infrared ranging application.

Main Methods:

  • Analysis of SNR reduction due to noise aliasing under varying undersampling frequencies.
  • Evaluation of filter phase stability constraints on noise bandwidth.
  • Quantification of undersampling effects using in-phase and quadrature (I/Q) demodulation for phase difference measurement.

Main Results:

  • Established a direct relationship between undersampling frequency and SNR reduction.
  • Demonstrated that filter stability critically influences the achievable noise bandwidth and SNR.
  • Quantified the practical SNR loss in an infrared ranging scenario.

Conclusions:

  • Undersampling intensity is practically limited by noise aliasing and SNR requirements.
  • Filter phase stability is a key parameter dictating the trade-off between undersampling benefits and SNR degradation.
  • The findings provide practical insights for optimizing undersampling strategies in phase estimation systems.