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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...

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.

Aliasing

Aliasing

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.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...

Basic Discrete Time Signals

Basic Discrete Time Signals

The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...

Upsampling

Upsampling

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...

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...

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Related Experiment Video

Updated: Sep 25, 2025

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

Published on: June 27, 2013

Transient abnormal signal acquisition system based on approximate entropy and sample entropy.

Jun Jiang¹, Shulin Tian¹, Yu Tian¹

¹School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, China.

The Review of Scientific Instruments

|April 30, 2022

Summary

This study introduces a new system for detecting transient abnormal signals in time domain measurements using approximate entropy (ApEn) and sample entropy (SampEn). Sample entropy demonstrated superior sensitivity and broader applicability for detecting these signal anomalies.

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Area of Science:

Signal Processing
Measurement Science
Complexity Science

Background:

Increasing signal complexity in time domain measurements leads to loss of periodic stationarity and emergence of transient non-stationarity.
Transient abnormal signals, including burrs, harmonics, noises, and modulating waves, frequently disrupt periodic signals.
Existing methods may lack sensitivity in detecting these complex transient anomalies.

Purpose of the Study:

To design a transient abnormal signal acquisition system for time domain measurements.
To apply entropy estimation techniques, specifically approximate entropy (ApEn) and sample entropy (SampEn), for real-time signal complexity analysis.
To differentiate signal complexities for effective abnormal signal detection.

Main Methods:

Development of a transient abnormal signal acquisition system.
Real-time computation of approximate entropy (ApEn) and sample entropy (SampEn) during data acquisition.
Utilizing entropy values to distinguish signal complexities and identify transient anomalies.

Main Results:

The designed system successfully detects transient abnormal signals by analyzing signal complexity.
Experimental results indicate that sample entropy (SampEn) exhibits higher sensitivity compared to approximate entropy (ApEn).
Sample entropy (SampEn) shows a wider range of applicability in detecting various transient abnormal signals.

Conclusions:

The proposed entropy-based approach provides a novel method for transient abnormal signal detection in time domain measurements.
Sample entropy (SampEn) is a more effective metric than approximate entropy (ApEn) for this specific application.
This research offers a new capability for designing time-domain measuring instruments with integrated abnormal signal detection.