Orthogonality of exponential transients

Article Abstract:

Simple orthogonal representations are shown to exist for signals of a decaying rather than solely a sinusoidal nature; a weighing function is described to express the orthogonality. Alternate, nonuniform sampling techniques are shown to be appropriate for representing and processing these signals. A simple discrete representation that is very similar to the discrete Fourier transform can be derived from use of this nonuniform sampling scheme. Traditional frequency spectrum-based approaches to signal analysis can thus be replaced by techniques that are more suitable to the specific decaying signal type.

Scientific Research, Sampling, Signal Attenuation, Spectrometry, Frequency

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Comments on "Orthogonality of Exponential Transients"

Article Abstract:

A previous letter discussed representation of a decaying time function by a weighted sum of exponentials of a specific form in which non-negative decay rates are given. The problem can be solved with greater generality and more straightforwardly through use of classical vector-space techniques. It is assumed that decay rates are given. Some results about inner product spaces are summarized and applied to a specific function space containing the exponential transients.

Mathematical models, Problem solving, Theorem Proving, Transient State

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A Simple Method to Improve the Transients in Adaptive Systems

Article Abstract:

Adaptation transients in adaptive systems are improved using a method based on classical optimization techniques. A modified adaptation mechanism slides the optimization-correction horizon forward in time in an a priori mode. In a posteriori mode, the parameters are recomputed over this horizon to generate an adaptive plant input. Block diagrams show the adaptation mechanism and internal data structure. Also illustrated is an experimental example.

Control systems, Adaptive control, Optimization, Systems

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