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2010•Instrumentation viewpointOpen access

The diagonal of the transform: Computationand meaning

Carine Simon, Juan José Dañobeitia, Antonio Manuel Lázaro

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Abstract

The TT-transform stands for time-time transform and has been derived as an inverse Fourier transform of the time-frequency S-transform. So far, it has been proposed that the diagonal of the TT-transform can be used for signal characterisation. We show here an alternative and simplified derivation of the TT-transform which enables a better understanding of this transform.

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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-frequency S-transform. So far, it has been proposed that the diagonal of the TT-transform can be used for signal characterisation. We show here an alternative and simplified derivation of the TT-transform which enables a better understanding of this 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-frequency S-transform. So far, it has been proposed that the diagonal of the TT-transform can be used for signal characterisation. We show here an alternative and simplified derivation of the TT-transform which enables a better understanding of this transform.

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

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