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Related Concept Videos

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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Downsampling01:20

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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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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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In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
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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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Subsampling scaling.

A Levina1,2, V Priesemann2,3

  • 1Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria.

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|May 5, 2017
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Summary
This summary is machine-generated.

Spatial subsampling biases system inferences. We developed a framework to correct these biases, revealing how neural networks self-organize to criticality during development.

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Area of Science:

  • Complex Systems Science
  • Neuroscience
  • Epidemiology

Background:

  • Real-world observations are often spatially subsampled, limiting system-wide inferences.
  • Spatial subsampling, due to inaccessibility or system size, introduces significant bias in aggregated property estimations.
  • This bias cannot be resolved by simply increasing sampling duration.

Purpose of the Study:

  • To develop an analytical framework for correcting biases introduced by spatial subsampling.
  • To infer accurate aggregated properties and distributions of the full system from subsampled data.
  • To apply the framework to diverse systems, including neuronal avalanches, epidemics, and network structures.

Main Methods:

  • Derivation of a subsampling scaling framework applicable to various observables.
  • Analytical inference of full system distributions from subsampled data.
  • Application to distinguish critical from subcritical systems and disentangle subsampling from finite-size effects.

Main Results:

  • The framework successfully corrects for spatial subsampling bias across different observables.
  • Demonstrated ability to infer true system distributions and identify critical states.
  • Application to neural networks revealed developmental self-organization to criticality.

Conclusions:

  • The subsampling scaling framework provides a robust method to overcome spatial bias in complex systems.
  • Mature neural networks exhibit power-law scaling, indicative of self-organization to criticality.
  • This approach offers insights into system development and critical dynamics.