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The paper compares the features of three extensions of the notion of the Gabor’s analytic signal for 2-D signals: the analytic signals with single-quadrant spectra (AS), the quaternionic signals with quaternionic single-quadrant spectra (QS) and the monogenic signals (MS). A good platform of comparison are the polar representations of the AS and the QS and… (More)

- Stefan L. Hahn, Kajetana M. Snopek
- IEEE Transactions on Signal Processing
- 2005

The paper presents new notions of Wigner distributions and corresponding ambiguity functions defined by quaternionic Fourier transforms of correlation products of recently defined quaternionic and monogenic two-dimensional (2-D) signals. The properties of new defined Wigner distributions are compared with Wigner distributions of 2-D analytic signals with… (More)

- Stefan L. Hahn
- 2011

The paper is devoted to the theory of n-D complex and hypercomplex analytic signals with emphasis on the 3-dimensional (3-D) case. Their definitions are based on the proposed general n-D form of the Cauchy integral. The definitions are presented in signaland frequency domains. The new notion of lower rank signals is introduced. It is shown that starting… (More)

- Stefan L. Hahn, Kajetana M. Snopek
- IEEE Trans. Signal Processing
- 2002

- Stefan L. Hahn
- Signal Processing
- 2003

- Stefan L. Hahn
- IEEE Trans. Signal Processing
- 1996

- Stefan L. Hahn, Kajetana M. Snopek
- CAIP
- 2001

- Stefan L. Hahn
- IEEE Trans. Communications
- 1996

The paper is devoted to the polar representation of n-D complex and hypercomplex analytic signals with emphasis on the 3-dimensional (3-D) case. Their definition is based on the proposed general form of the Cauchy integral. The definitions of complex/hypercomplex signals are presented in signaland frequency domains. The new notion of lower rank signals is… (More)

- Stefan L. Hahn
- 2008

Abstract: The paper presents a study of properties of ensemble averages of Wigner time-frequency distributions (WDs) of random processes defined by statistically independent samples of stationary and nonstationary Gaussian noise and of radio-frequency telecommunication signals. We used samples of PSK and FSK signals transmitting random telegraph signals.… (More)

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