Tomograms, Wavelets, and Quasidistributions in the Geometric Picture

Different types of integral transforms of the analytic signal employed in information processing are studied within the framework of a new unified approach. They include tomographic probabilities, wavelet transform, Ville–Wigner function, etc. The connection of a vector (analytic signal) with projections of the transformed vector onto different axes in the signal space provides different integral transforms. The tomogram of the analytic signal is introduced by means of average Dirac (or Kronecker) delta-function of Hermitian operator. The relations of the wavelet and the Ville–Wigner quasidistribution to time–frequency, time--scale, and frequency–scale tomograms are studied.