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Related Concept Videos

Linear time-invariant Systems01:23

Linear time-invariant Systems

447
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
447
Basic Continuous Time Signals01:22

Basic Continuous Time Signals

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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.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
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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...
373
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

529
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
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Beats01:09

Beats

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The study of music provides many examples of the superposition of waves and the constructive and destructive interference that occurs. Very few examples of music being performed consist of a single source playing a single frequency for an extended period of time. A single frequency of sound for an extended period might be monotonous to the point of irritation, similar to the unwanted drone of an aircraft engine or a loud fan. Music is pleasant and exciting due to mixing the changing frequencies...
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Prediction Intervals01:03

Prediction Intervals

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The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
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A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
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Variational Hierarchical N-BEATS Model for Long-Term Time-Series Forecasting.

Runze Yang, Longbing Cao, Jianxun Li

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    Summary
    This summary is machine-generated.

    This study introduces VH-NBEATS, a novel model for long-term time-series forecasting that leverages hierarchical timestamp information. It achieves state-of-the-art results by capturing complex seasonal and trending effects.

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    Area of Science:

    • Machine Learning
    • Time Series Analysis
    • Forecasting

    Background:

    • Long-term time-series forecasting (LTSF) presents significant challenges.
    • Existing LTSF methods often overlook hierarchical timestamp information, hindering the capture of weekly and yearly patterns.

    Purpose of the Study:

    • To propose VH-NBEATS, an interpretable variational hierarchical model extending N-BEATS.
    • To effectively incorporate hierarchical timestamp information into LTSF models.
    • To enhance LTSF performance by capturing hierarchical seasonal and trending effects.

    Main Methods:

    • Developed VH-NBEATS, featuring a hierarchical timestamp block and a harmonic seasonal block.
    • Integrated a variational autoencoder (VAE) to handle high time-series variability.
    • Evaluated the model on seven diverse real-world datasets.

    Main Results:

    • VH-NBEATS achieved state-of-the-art (SOTA) performance across all tested LTSF datasets.
    • Demonstrated the effectiveness of the hierarchical timestamp block in capturing complex temporal patterns.
    • Showcased the plug-and-play capability of the hierarchical timestamp block with existing LTSF methods.

    Conclusions:

    • VH-NBEATS offers a significant advancement in LTSF by effectively utilizing hierarchical timestamp data.
    • The proposed hierarchical timestamp block can be integrated with various forecasting models to improve performance.
    • The variational approach enhances robustness in handling volatile time-series data.