Multidimensional Systems and Signal Processing

, Volume 18, Issue 4, pp 317–325 | Cite as

The new multidimensional time/multi-frequency transform for higher order spectral analysis

Communication Brief


A new multidimensional time/multi-frequency higher order spectral(HOS) transform is proposed for transient signals with nonlinear polynomial variation of instantaneous frequency: the short time higher order chirp spectra (HOCS) based on the higher order chirp-Fourier transform and time-domain windowing technique. The proposed transform is compared with the classical multi-frequency HOS based on the Fourier transform. It is shown that the proposed transform is more effective for processing of transient processes in comparison with the classical transform.


Multidimensional transform Multi-frequency Spectral analysis High order spectra Chirp-Fourier transform 



Time domain signal


Time block of signal


Time segment of time block


External time window


Time center of the external window


Internal time window

\({H(f_{1}, f_{2},\ldots, f_{n-1},c_{2},c_{3},\dots,c_{N}, T)}\)



Order of the HOCS

\({X_{m}(f_{n\sum}, c_{2},c_{3},...,c_{N})}\)

Higher order chirp-Fourier transform


Order of the higher order chirp-Fourier transform


Chirp rate (i.e., frequency speed) of the higher order chirp-Fourier transform


Frequency acceleration of the higher order chirp-Fourier transform


Higher order parameters of the higher order chirp-Fouriertransform


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.School of EngineeringCranfield UniversityCranfieldUK

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