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Related Concept Videos

Sampling Distribution01:12

Sampling Distribution

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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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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Bandpass Sampling01:17

Bandpass Sampling

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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.
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Upsampling01:22

Upsampling

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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...
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Aliasing01:18

Aliasing

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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.
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Sampling Theorem01:15

Sampling Theorem

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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.
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On the Rate-Distortion Function of Sampled Cyclostationary Gaussian Processes.

Emeka Abakasanga1, Nir Shlezinger2, Ron Dabora1

  • 1Department of Electrical and Computer Engineering, Ben-Gurion University, Be'er-Sheva 8410501, Israel.

Entropy (Basel, Switzerland)
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Summary

This study analyzes the rate-distortion tradeoff for sampled communication signals. Asynchronous sampling challenges traditional information theory, but a new framework reveals its impact on signal processing performance.

Keywords:
information spectrumrate-distortion functionwide-sense almost cyclostationarywide-sense cyclostationary

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Area of Science:

  • Information Theory
  • Signal Processing
  • Communications Engineering

Background:

  • Man-made communication signals are modeled as continuous-time (CT) wide-sense cyclostationary (WSCS) processes.
  • Digital processing requires sampling CT processes into discrete-time (DT) processes.
  • Sampling can be synchronous (DT process is WSCS) or asynchronous (DT process is wide-sense almost cyclostationary - WSACS).

Purpose of the Study:

  • To investigate the fundamental rate-distortion tradeoff for source codes applied to sampled CT WSCS processes.
  • To address the challenges in analyzing the rate-distortion function (RDF) for asynchronous sampling due to information instability.
  • To provide novel insights into the relationship between sampling synchronization and the RDF.

Main Methods:

  • Utilizing the information-spectrum framework to analyze the RDF for asynchronous sampling.
  • Expressing the RDF in the low distortion regime as a limit superior of RDFs from synchronously sampled processes.
  • Comparing the behavior of RDFs for asynchronous sampling against classic information-theoretic tools.

Main Results:

  • Developed a characterization for the RDF of asynchronously sampled CT WSCS processes.
  • Demonstrated that asynchronous sampling poses challenges for classic information-theoretic tools.
  • Showed that small variations in sampling rate and time offset significantly impact the RDF, unlike in stationary processes.

Conclusions:

  • The information-spectrum framework offers a viable approach for RDF analysis under asynchronous sampling.
  • Sampling synchronization is a critical factor influencing the rate-distortion performance of source-coded sampled signals.
  • Findings highlight the need to consider sampling specifics in designing efficient communication systems.