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In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
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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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Local maximum synchrosqueezes form scaling-basis chirplet transform.

Yating Hou1,2, Liming Wang1,2, Xiuli Luo1,2

  • 1State Key Laboratory of Dynamic Testing Technology, North University of China, Taiyuan, China.

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|November 29, 2022
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Summary
This summary is machine-generated.

A new time-frequency analysis (TFA) method, the local maximum synchrosqueezing scaling-basis chirplet transform (LMSBCT), enhances signal analysis. It improves time-frequency energy concentration and instantaneous frequency accuracy for nonstationary signals.

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Area of Science:

  • Signal Processing
  • Applied Mathematics

Background:

  • Traditional time-frequency analysis (TFA) methods struggle with nonstationary signals.
  • Existing methods lack sufficient time-frequency energy concentration and accurate instantaneous frequency tracking.

Purpose of the Study:

  • To introduce a novel TFA method, the local maximum synchrosqueezing scaling-basis chirplet transform (LMSBCT).
  • To enhance the analysis of nonstationary signals, particularly those with frequency modulation and low signal-to-noise ratios.

Main Methods:

  • The proposed LMSBCT method combines the scaling-basis chirplet transform (SBCT) with local maximum synchrosqueezing.
  • It incorporates energy rearrangement in the frequency domain for improved resolution.

Main Results:

  • LMSBCT demonstrates superior time-frequency energy concentration compared to traditional methods.
  • The method accurately tracks instantaneous frequency trajectories, even for complex signals.
  • Effective handling of strong frequency-modulated and multicomponent signals with close frequencies and low SNR was observed.

Conclusions:

  • LMSBCT offers significant improvements over existing TFA techniques.
  • The proposed method provides a robust solution for analyzing challenging nonstationary signals.
  • Numerical simulations and real experiments validate the method's effectiveness.