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2008•IEEE Transactions on Signal ProcessingRequires access

On the TT-Transform and Its Diagonal Elements

Carine Simon, Martín Schimmel, Juan José Dañobeitia

Open publisher page 59 citations

Abstract

The TT-transform stands for time-time transform and has been derived as an inverse Fourier transform of the time-frequencyS-transform. Up to date, only the diagonal of the TT-transform has been used for signal characterization. We show here an alternative and simplified derivation of the TT-transform which enables a better understanding of this transform. In particular, we demonstrate that the diagonal elements of the TT-transform represent a simple frequency filtered version of the original signal and, thus, that little additional information is gained through the TT-transform.

About this research paper

What this paper is about

The TT-transform stands for time-time transform and has been derived as an inverse Fourier transform of the time-frequencyS-transform. Up to date, only the diagonal of the TT-transform has been used for signal characterization. We show here an alternative and simplified derivation of the TT-transform which enables a better understanding of this transform. In particular, we demonstrate that the diagonal elements of the TT-transform represent a simple frequency filtered version of the original signal and, thus, that little additional information is gained through the TT-transform.

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Available abstract

The TT-transform stands for time-time transform and has been derived as an inverse Fourier transform of the time-frequencyS-transform. Up to date, only the diagonal of the TT-transform has been used for signal characterization. We show here an alternative and simplified derivation of the TT-transform which enables a better understanding of this transform. In particular, we demonstrate that the diagonal elements of the TT-transform represent a simple frequency filtered version of the original signal and, thus, that little additional information is gained through the TT-transform.

Key concepts: Hartley transform, Fractional Fourier transform, Constant Q transform, Diagonal, S transform, Discrete Fourier transform (general), Discrete Hartley transform, Fourier transform

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