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Modified Stockwell Transforms and Time-Frequency Analysis

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 189))

Abstract

We give results complementary to those in the paper [4] from the perspective of time-frequency analysis [1] to the effect that high frequencies can be amplified and low frequencies diminished. Time-frequency spectra for the chirp, the sum of the cosine functions and the Gaussian-modulated sinusoidal pulse are presented for comparisons, The property of the absolutely referenced phase information of modified Stockwell transforms is given in terms of Riesz transforms.

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References

  1. L. Cohen, Time-Frequency Analysis, Prentice-Ball, 1995.

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  2. I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992.

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  3. J. Du, M.W. Wong and H. Zhu, Continuous and discrete inversion formulas for the Stockwell transform, Integral Transforms Spec. Funct. 18 (2007), 537–543.

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Guo, Q., Molahajloo, S., Wong, M.W. (2008). Modified Stockwell Transforms and Time-Frequency Analysis. In: Rodino, L., Wong, M.W. (eds) New Developments in Pseudo-Differential Operators. Operator Theory: Advances and Applications, vol 189. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8969-7_13

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