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Sampling Continuous Time Signal

Sampling Continuous Time Signal

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.
In the...

Bandpass Sampling

Bandpass Sampling

In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2....

Sampling Methods: Overview

Sampling Methods: Overview

A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling.
In analytical chemistry, the choice of...

Reconstruction of Signal using Interpolation

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...

Sampling Theorem

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.

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

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Related Experiment Video

Updated: Aug 13, 2025

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

Full waveform inversion based on the ensemble Kalman filter method using uniform sampling without replacement.

Jian Wang¹, Dinghui Yang¹, Hao Jing¹

¹Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.

Science Bulletin

|January 20, 2023

Summary

This summary is machine-generated.

Full waveform inversion (FWI) now offers higher resolution Earth imaging. A new semi-random FWI method integrates ensemble Kalman filter and uniform sampling, overcoming traditional limitations of non-uniqueness and initial model dependency.

Keywords:

Data assimilation Ensemble Kalman filter Full waveform inversion Uniform sampling without replacement

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Last Updated: Aug 13, 2025

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Area of Science:

Geophysics
Seismology
Earth Science

Background:

Full waveform inversion (FWI) is crucial for understanding Earth's interior structure.
FWI utilizes both traveltime and amplitude data for high-resolution Earth imaging.
Conventional FWI methods face challenges with non-uniqueness and high computational costs.

Purpose of the Study:

To develop a novel Full waveform inversion (FWI) method.
To address the limitations of conventional FWI, specifically non-uniqueness and initial model dependency.
To enhance the resolution and convergence domain of FWI.

Main Methods:

Integration of the ensemble Kalman filter with uniform sampling without replacement.
Implementation within a semi-random framework.
Application to seismic data for Earth structure modeling.

Main Results:

Achieved high-resolution imaging results.
Demonstrated a wider convergence domain compared to conventional methods.
Successfully overcame the strong dependence on the initial model.

Conclusions:

The proposed semi-random FWI method offers significant improvements over traditional approaches.
This new method enhances the reliability and applicability of FWI for geophysical exploration.
The integration of ensemble Kalman filter and uniform sampling provides a robust framework for high-resolution Earth structure analysis.