Hyperbolic class of quadratic time-frequency representations Part I: Constant-Q warping, the hyperbolic paradigm, properties, and members

Antonia Papandreou-Suppappola, Franz Hlawatsch, G. Faye Boudreaux-Bartels

Research output: Contribution to journalArticle

74 Citations (Scopus)

Abstract

The time-frequency (TF) version of the wavelet transform and the `affine' quadratic/bilinear TF representations can be used for a TF analysis with constant-Q characteristic. This paper considers a new approach to constant-Q TF analysis. A specific TF warping transform is applied to Cohen's class of quadratic TF representations, which results in a new class of quadratic TF representations with constant-Q characteristic. The new class is related to a `hyperbolic TF geometry' and is thus called the hyperbolic class (HC). Two prominent TF representations previously considered in the literature, the Bertrand P0 distribution and the Altes-Marinovic Q-distribution, are members of the new HC. We show that any hyperbolic TF representation is related to both the wideband ambiguity function and a `hyperbolic ambiguity function.' It is also shown that the HC is the class of all quadratic TF representations which are invariant to `hyperbolic time-shifts' and TF scalings, operations which are important in the analysis of Doppler-invariant signals and self-similar random processes. The paper discusses the definition of the HC via constant-Q warping, some signal-theoretic fundamentals of the `hyperbolic TF geometry,' and the description of the HC by 2-D kernel functions. Several members of the HC are considered, and a list of desirable properties of hyperbolic TF representations is given together with the associated kernel constraints.

Original languageEnglish (US)
Pages (from-to)3425-3444
Number of pages20
JournalIEEE Transactions on Signal Processing
Volume41
Issue number12
DOIs
StatePublished - Dec 1993
Externally publishedYes

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Hyperbolic functions
Geometry
Random processes
Wavelet transforms

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Hyperbolic class of quadratic time-frequency representations Part I : Constant-Q warping, the hyperbolic paradigm, properties, and members. / Papandreou-Suppappola, Antonia; Hlawatsch, Franz; Boudreaux-Bartels, G. Faye.

In: IEEE Transactions on Signal Processing, Vol. 41, No. 12, 12.1993, p. 3425-3444.

Research output: Contribution to journalArticle

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