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Related Concept Videos

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A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...
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Transformations in mathematics alter the position or orientation of a function’s graph while preserving its fundamental shape. One important type of transformation is the horizontal shift, which involves modifying the input variable within a function’s equation. This operation affects where outputs occur along the horizontal axis but does not alter the function’s overall structure.A horizontal shift is achieved by replacing the input variable x with either x + c or x - c,...
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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.
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The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
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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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Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...
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Transformation-cost time-series method for analyzing irregularly sampled data.

Ibrahim Ozken1,2, Deniz Eroglu2,3, Thomas Stemler4

  • 1Department of Physics, Ege University, 35100 Izmir, Turkey.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 15, 2015
PubMed
Summary
This summary is machine-generated.

The TrAnsformation-Cost Time-Series (TACTS) method analyzes irregularly sampled time-series data without interpolation. This novel approach transforms segments to create a regularly sampled cost time series for standard analysis.

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Area of Science:

  • Time-series analysis
  • Data science
  • Geoscience

Background:

  • Irregularly sampled datasets pose challenges for traditional time-series analysis.
  • Interpolation methods can distort data and bias subsequence analysis.

Purpose of the Study:

  • Introduce the TrAnsformation-Cost Time-Series (TACTS) method for analyzing irregularly sampled data.
  • Provide a robust alternative to interpolation that preserves data quality.

Main Methods:

  • TACTS transforms time-series segments based on the cost of converting one segment to the next.
  • A limited set of operations with associated costs are used for transformation.
  • The resulting transformation-cost time series is regularly sampled and amenable to standard analysis.

Main Results:

  • The TACTS method demonstrates stability against noise and various irregular sampling patterns.
  • Numerical examples using the logistic map and Rössler oscillator validate the method.
  • Guidance is provided for selecting appropriate costs for different time series.

Conclusions:

  • The TACTS method offers a reliable approach for analyzing irregularly sampled time-series data.
  • The method's utility is confirmed through paleoclimate data analysis from Borneo speleothems.