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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
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The human ear cannot distinguish between two sources of sound if they happen to reach within a specific time interval, typically 0.1 seconds apart. More than this, and they are perceived as separate sources.
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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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Microseismic Time Delay Estimation Method Based on Continuous Wavelet.

Cunpeng Du1, Shengwen Yu1, Haitao Yin2

  • 1College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266510, China.

Sensors (Basel, Switzerland)
|April 23, 2022
PubMed
Summary
This summary is machine-generated.

A new method improves microseismic event location accuracy by using continuous wavelet transform for denoising and time-delay estimation. This fast, efficient technique enhances precision, especially in noisy conditions.

Keywords:
continuous wavelet transformcross-correlationmicroseismic signalsimilarity coefficient methodtime delay estimation

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Area of Science:

  • Geophysics
  • Signal Processing

Background:

  • Microseismic event location accuracy is often compromised by observation noise and traditional estimation methods.
  • Inaccurate time-delay estimation significantly impacts the precision of microseismic event localization.

Purpose of the Study:

  • To propose a fast and efficient microseismic time-delay estimation method.
  • To enhance the accuracy of microseismic event location, particularly in low signal-to-noise ratio environments.

Main Methods:

  • Denoising original signals using continuous wavelet transform (CWT).
  • Applying CWT for time-frequency transform and band-pass filtering to reduce noise interference.
  • Calculating similarity between time-frequency signals using time and frequency domain integration based on phase spectrum correlation.

Main Results:

  • The proposed method demonstrates superior precision and accuracy compared to traditional cross-correlation and generalized cross-correlation phase transformation methods.
  • The technique is particularly effective in improving time-delay estimation for microseismic signals with low signal-to-noise ratios.

Conclusions:

  • A novel time-delay estimation method for non-stationary random signals has been presented.
  • This approach offers a significant improvement in microseismic data analysis and event localization.