Invariant transformation of the t-ω plane with respect to Wigner distribution

Linear and non-linear coordinate transformations of the t-ω plane may be used to shift around the areas of high energy concentration of a Wigner Distribution (WD). However, it is important that such transformations are invariant w.r.t. WD, i.e., the transformed WD's are WD realizable. This paper derives the conditions under which such transformations are invariant. Both linear and nonlinear transformations are considered and special cases of rational spectra are discussed. The results are important and form an analytical basis for such transformations.