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Related Concept Videos

Aliasing01:18

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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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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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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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Related Experiment Video

Updated: Aug 5, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Quantized Information in Spectral Cyberspace.

Milton A Garcés1,2

  • 1Infrasound Laboratory, University of Hawaii, Kailua-Kona, HI 96740, USA.

Entropy (Basel, Switzerland)
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Summary

This study introduces a new method for analyzing signals using Gabor atoms, enhancing spectral analysis and uncertainty quantification. The approach offers robust, sensor-agnostic processing for diverse applications like machine learning.

Keywords:
Fourier transformGabor atomsLamb waveStockwell transformTongaacoustic-gravity waveacousticscyberspectral informationinfrasoundlogonsquantum waveletrelative entropysignal processingspectral cyberspacespectral entropywavelet entropywavelet transform

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Area of Science:

  • Signal Processing
  • Information Theory
  • Time-Frequency Analysis

Background:

  • Traditional spectral analysis methods face limitations in quantifying information and uncertainty.
  • Time-frequency representations are crucial for analyzing complex signals but require robust quantification techniques.

Purpose of the Study:

  • To develop a novel method for spectral power, information, and uncertainty quantification using constant-Q Gabor atoms.
  • To establish stable multiresolution spectral entropy algorithms for enhanced signal analysis.
  • To provide sensor-agnostic transformations for signal processing, pattern recognition, and machine learning.

Main Methods:

  • Utilized constant-Q Gabor atoms for time-frequency analysis.
  • Developed stable multiresolution spectral entropy algorithms employing continuous wavelet and Stockwell transforms.
  • Applied processing and scaling methods tailored to signal signatures, desired information, and uncertainty levels.

Main Results:

  • Demonstrated the efficacy of the constant-Q Gabor atom for spectral quantification.
  • Successfully constructed stable multiresolution spectral entropy algorithms.
  • Presented case studies using Lamb wave signatures and information spectra from the 2022 Tonga eruption.

Conclusions:

  • The developed methods provide resilient transformations from physical to information metrics.
  • The approach is suitable for sensor-agnostic signal processing, pattern recognition, and machine learning.
  • The choice of processing and scaling is adaptable based on signal characteristics and analytical goals.