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

Abstract

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.

Keywords

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

Notations

x(t)

Time domain signal

xν(t)

Time block of signal

xm(t)

Time segment of time block

he(t)

External time window

T

Time center of the external window

hi(t)

Internal time window

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

HOCS

n

Order of the HOCS

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

Higher order chirp-Fourier transform

N

Order of the higher order chirp-Fourier transform

c2

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

c3

Frequency acceleration of the higher order chirp-Fourier transform

c4,...,cN

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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