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Upsampling01:22

Upsampling

272
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...
272
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

297
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...
297
Sampling Theorem01:15

Sampling Theorem

416
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.
416
Aliasing01:18

Aliasing

169
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...
169
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

267
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...
267
Bandpass Sampling01:17

Bandpass Sampling

221
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....
221

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Updated: Jul 30, 2025

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Lock-in amplification based on sigma-delta oversampling.

J Leis1

  • 1School Engineering, University of Southern Queensland, Toowoomba, Qld 4350, Australia.

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|May 12, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a new algorithm for synchronous detection, integrating analog-to-digital conversion and signal mixing. This simplifies lock-in amplifier complexity without sacrificing accuracy, enabling easier low-resolution, high-rate sampling.

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Area of Science:

  • Measurement Science
  • Signal Processing

Background:

  • Synchronous detection is crucial for measuring weak signals amidst noise.
  • Current methods often use separate high-resolution analog-to-digital converters (ADCs) with sigma-delta modulation.

Purpose of the Study:

  • To develop a unified processing algorithm for oversampled ADCs and signal mixing.
  • To reduce computational complexity and hardware requirements in lock-in amplifiers.

Main Methods:

  • Derivation of a novel processing algorithm.
  • Integration of oversampled analog-to-digital conversion with digital signal mixing.
  • Digital implementation of reference signal mixing and phase-quadrature components.

Main Results:

  • Substantial reduction in computational complexity for lock-in amplifiers.
  • No loss of measurement accuracy compared to standard methods.
  • Relaxation of high-resolution ADC requirements, favoring low-resolution, high-rate sampling.

Conclusions:

  • The proposed algorithm effectively combines ADC and mixing functions.
  • The technique offers practical advantages in hardware implementation and signal measurement.
  • Experimental validation confirms the theoretical and simulated results.