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Related Concept Videos

Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

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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.
In the...
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Basic Discrete Time Signals01:16

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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.
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Basic Continuous Time Signals01:22

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Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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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.
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An even signal, whether in continuous-time or discrete-time, is defined by its symmetry with its time-reversed version. Mathematically, this is represented as
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Related Experiment Video

Updated: Oct 9, 2025

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
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Zero-Delay Joint Source Channel Coding for a Bivariate Gaussian Source over the Broadcast Channel with One-Bit ADC

Weijie Zhao1,2, Xuechen Chen1

  • 1School of Computer Science and Engineering, Central South University, Changsha 410083, China.

Entropy (Basel, Switzerland)
|December 24, 2021
PubMed
Summary

This study explores transmitting bivariate Gaussian sources over a Gaussian broadcast channel using one-bit analog-to-digital converters (ADCs). New nonparametric mappings significantly reduce distortion, approaching theoretical bounds for low signal-to-noise ratios.

Keywords:
average distortionbivariate Gaussian sourcesbroadcast channeljoint source channel codingone-bit ADCzero-delay transmission

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Area of Science:

  • Information Theory
  • Digital Communications
  • Signal Processing

Background:

  • Broadcast channels are crucial for efficient data distribution.
  • One-bit analog-to-digital converters (ADCs) offer reduced power and cost but limit resolution.
  • Gaussian broadcast channels with bivariate sources present complex transmission challenges.

Purpose of the Study:

  • To investigate zero-delay transmission strategies for bivariate Gaussian sources over Gaussian broadcast channels with one-bit ADCs.
  • To derive an outer bound on the conditional distortion region.
  • To develop novel nonparametric and parametric mappings for minimizing average distortion.

Main Methods:

  • Derivation of an outer bound on the conditional distortion region.
  • Development of two nonparametric mapping design methods: joint encoder-decoder optimization and numerical optimization using necessary conditions.
  • Design of a gradient descent algorithm for optimal encoder development.
  • Proposal of parametric mappings inspired by optimized nonparametric structures.

Main Results:

  • Proposed nonparametric mappings outperform existing parametric mappings and uncoded schemes.
  • Parametric mappings show improvement over uncoded schemes and previous methods for infinite resolution ADCs.
  • Nonparametric mappings achieve average distortions close to the derived bound in low signal-to-noise ratio regions for one-bit ADCs.

Conclusions:

  • Nonparametric mappings are highly effective for bivariate Gaussian source transmission over one-bit ADC broadcast channels.
  • The proposed methods provide near-optimal performance in low SNR regimes.
  • Further analysis is needed to understand the performance differences between nonparametric mapping approaches.