Radon transformation of the Wigner spectrum

John C. Wood; Daniel T. Barry

doi:10.1117/12.130943

30 November 1992 Radon transformation of the Wigner spectrum

John C. Wood, Daniel T. Barry

Proceedings Volume 1770, Advanced Signal Processing Algorithms, Architectures, and Implementations III; (1992) https://doi.org/10.1117/12.130943
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

The radon transform of the Wigner spectrum has been shown to be the optimal detection scheme for linear FM signals, but the properties of this representation have not been well characterized. By the projection slice theorem, each line integral through the Wigner spectrum corresponds to the inverse Fourier transform of a radial slice through the ambiguity plane. Since line integrals through the Wigner spectrum can be calculated by dechirping, calculation of the Wigner spectrum may be viewed as a tomographic reconstruction problem. In this paper we show that all time-frequency transforms of Cohen's class may be achieved by simple changes in backprojection reconstruction filtering. The resolution-ringing trade-off that occurs in computed tomography is shown to be analogous to the resolution-cross-term trade-off that occurs in time-frequency kernel selection. `Ideal' reconstruction using a purely differentiating backprojection filter yields the Wigner distribution while low-pass differentiating filters produce cross-term suppressing distributions such as the spectrogram or the Born-Jordan distribution. The one-to-one identities between the Wigner, Radon-Wigner, and ambiguity planes suggest that the Radon-Wigner domain may be a new design space for time-frequency filtering and kernel design. The distribution of white noise in this space is presented as well as some simple examples of time-varying filtering.

Citation Download Citation

John C. Wood and Daniel T. Barry "Radon transformation of the Wigner spectrum", Proc. SPIE 1770, Advanced Signal Processing Algorithms, Architectures, and Implementations III, (30 November 1992); https://doi.org/10.1117/12.130943

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