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.
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Abbreviations
- x(t):
-
Time domain signal
- x ν (t):
-
Time block of signal
- x m (t):
-
Time segment of time block
- h e (t):
-
External time window
- T :
-
Time center of the external window
- h i (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
- c 2 :
-
Chirp rate (i.e., frequency speed) of the higher order chirp-Fourier transform
- c 3 :
-
Frequency acceleration of the higher order chirp-Fourier transform
- c 4,...,c N :
-
Higher order parameters of the higher order chirp-Fouriertransform
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Gelman, L., Petrunin, I. The new multidimensional time/multi-frequency transform for higher order spectral analysis. Multidim Syst Sign Process 18, 317–325 (2007). https://doi.org/10.1007/s11045-006-0005-9
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DOI: https://doi.org/10.1007/s11045-006-0005-9