Advanced Signal Processing

1. (Hilbert Space) Eigenfunctions of Auditory Perception

Dynamical modeling of human hearing anatomy date back to at least as early as the 1950 work Peterson and Bogert (and arguably to at least as early as the 1924 work of Wegel and Lane). Filter and filter-bank modeling derived from this work date back to at least as early as the 1974 work of Patterson (and arguably to at least as early as the 1946 vacuum-tube work of Tucker) and have been dominated by the gammatone basis-function representation (see for example History and Future of Auditory Filter Models (2010)). As truly impressive as this historic and heroic “bottom-up” work is, however, the effects of the human nervous system and other aspects of hearing perception and cognition are not captured by these models and systems.

In past, recent, and continuing work of the NRI founder, an “auditory eigenfunction” approach has been devised for sophisticated basis-function modelling of the fundamental functional structure of human auditory perception: the frequency range and the time duration correlation window of human hearing. Human perceptual “auditory eigenfunctions” result as solutions to an eigenfunction equation representing a model of human hearing, wherein the model comprises a frequency-domain bandpass operation approximating the frequency range of human hearing and a time-limiting operation in the time-domain approximating the time duration correlation window of human hearing. The resulting (non-wavelet) eigenfunctions (similar to but fundamentally differing from the Slepian Prolate Spheroidal Wave Function signal theory arising from frequency-domain lowpass operations) represent a perception-oriented basis functions for mathematically representing audio information in a Hilbert-space representation of an audio signal space model of human auditory perception. The eigenfunctions, signals, and methods have many important potential applications including:

  • Audio signal encoding/decoding based on Hilbert space (finite energy) eigenfunctions,
  • Creating and implementation of entirely new auditory languages (or modification to existing auditory languages) which are in various ways performance optimized for human auditory perception (for example with or without the constraints of human vocal-tract rendering),
  • New types of speech synthesis, potentially particularly useful in speech synthesis involving rapid phoneme production,
  • Multi-channel data sonification (see NRI’s work in Data Visualization and Sonification)
  • Various types of audio-based user interfaces.

NRI’s perception-based auditory eigenfunction methods can be implemented in specialized digital integrated circuit (IC) chips, as IP cores, and as software and libraries for general-purpose DSPs and mixed-signal processor chips.

2. Synthesis of Scalar and Vector Hysteresis

NRI’s early work in fixed, parameterized, and controllable scalar hysteresis synthesis dates to before 1999 (see section 7.2.7 and Figure 61 of US Patent 7,309,828 below). This work, originally directed at musical signal processing, can be used for other applications, including feedback control systems and hysteresis compensation. This work is quite interesting and useful in its own regard, but later NRI work in hysteresis synthesis extended this earlier work to the extremely interesting (and possibly new) area of vector-input and vector-output hysteresis. In basic implementations, NRI vector hysteresis synthesis includes receiving and processing of a plurality of input signals with at least one parameterized multivariable nonlinearity (serving as a parameterized hysteron) to produce at least one output signal. The plurality of input signals is also processed by at least one controller function (including at least some sort memory capability) that produces at least one control signal responsive to at least one of the input signals. The resulting control signal(s) can be used to control the parameterized hysteron to invoke a hysteretic response to at least one of the input signals. Additional provisions can be added to control various aspects of the synthesized hysteresis effects. Application areas for NRI’s innovative scalar and vector hysteresis synthesis include signal processing, electromagnetic system compensation, gear-system compensation, feedback controllers, feedforward compensation, music synthesis, and computer simulations as may be used in physics, engineering, economics, chemistry and other areas where hysteretic effects occur. There are likely analytic applications at a symbolic equation level as well.

Even more interesting are NRI’s cross-feedback-controlled hysteron-synthesized hysteresis networks. The method includes receiving and processing multiple input signals with at least two parameterized multivariable nonlinearities, each parameterized multivariable nonlinearity serving as a parameterized hysteron, to produce at least one associated output signal. The output signals are processed by controller functions, each comprising memory and producing at least one control signal responsive to at least one of the output signals and for controlling an associated parameterized hysteron. Externally viewed, the resulting synthesis provides a complex compounded hysteretic response to at least one of the input signals, and can be used in the modeling and nonlinear control of systems involving networks of gears, electrical transformers, economic processes, or other networked hysteretic elements. (There are likely potentially important applications in creating new types of neural networks and cellular processors, as well as new approaches for the differential and numerical modeling of critical phenomena and metastability in condensed matter.)

NRI’s scalar and vector hysteresis synthesis methods can be implemented in analog or digital integrated circuit (IC) chips, as IP cores, and as software and libraries for general-purpose DSPs and mixed-signal processor chips.

3. Advanced Simplified Frequency Comparator Employing Symbol Dynamics

Surprisingly, the state-space of two or more asynchronous square-waves can be used to define a “symbol dynamics” framework from which varieties of conditions may be detected in parallel, including phase, ambiguity states, and frequency comparison. Detection may be implemented via state or transition analysis. An example application realizes a simplified high-performance arbitrary rate pure-logic circuit real-time frequency comparator for asynchronous square-wave signals. Minor additional circuitry can be added to additionally simultaneously detect various classes of symmetry conditions unique to enveloping events occurring for square-wave signal pairs.

This NRI work was sold in August 2011; see the “Advanced Signal Processing” section of Patent Assets Sold for detailed technical descriptions provided within the appropriate NRI patents listed there.

The structures and properties of these unusual dynamical systems remains extremely interesting and appears to have a great deal more to offer and contribute to the body of signal and system methods. NRI plans to return to further study, creation, and development of this technology and its theory in the future.

4. “Through-Zero” Pulse-Width Modulation

Closely related to the above, but from a signal modulation/co-modulation/synthesis framework rather than state-space framework is the notion of “Through-Zero” Pulse-Width Modulation. This is a continuation of earlier work published in a series co-authored with B. Hutchins (“A New Look at Pulse Width Modulation, Part 3,” Electronotes, Vol. 12 No. 118, October 1980, pp. 3-24).
This NRI work was also sold in August 2011sold in August 2011; see the “Advanced Signal Processing” section of Patent Assets Sold for detailed technical descriptions provided within the appropriate NRI patents listed there.
The structures and properties of these unusual signals also remains extremely interesting and appears to have a great deal more to offer and contribute to the body of signal and system methods. NRI plans to return to further study, creation, and development of this technology and its theory in the future.

Issued Patents

TitlePatent NumberApplication NumberPriority DatesPDFText OnlyRelated Patents
Audio Signal Encoding and Decoding Based On Human Auditory Perception Eigenfunction Model in Hilbert Space9,990,93015/469,42907/31/2009PDFText Advanced Signal Processing
Auditory Eigenfunction Systems and Methods (Corrected to be: Auditory Eigenfunction Approach to Auditory Language Design, Implementation, and Rendering Optimized for Human Auditory Perception)9,613,61714/089,60507/31/2009PDFText Advanced Signal Processing
Advanced Synthesized Hysteresis for Signal Processing, Controllers, Music, and Computer Simulations in Physics, Engineering, and Economics
8,706,44913/186,459
07/20/2010PDFText Advanced Signal Processing
Auditory Eigenfunction Systems and Methods8,620,64312/849,01307/31/2009PDFText Advanced Signal Processing
Hysteresis Waveshaping7,309,82810/702,31805/15/1999PDFText Advanced Signal Processing

Pending Patents

TitlePublication NumberApplication NumberPriority DatesPDFText OnlyRelated Patents
Cross-feedback-controlled hysteron synthesized hysteresis networks for signal processing, controllers, music, and computer simulations in physics, engineering, and economics2014/016370214/180,57907/20/2010PDFText Advanced Signal Processing

Pending Unpublished Applications

TitleApplication NumberPriority DatesRelated Patents