Time-frequency analysis of (<i>k</i>, <i>a</i>)-generalized wavelet transform and applications

The (k, a)-generalized wavelet transform is a novel addition to the class of transforms, which has gained respectable status in realm time-frequency signal analysis within short period time. Since study both theoretically interesting and practically useful, this article, we investigated several subjects for transform. First, analyze concentration on sets finite measure. In particular, prove Donoho–Stark Benedicks-type uncertainty principles. We versions Heisenberg-type principles transformation. Furthermore, involving reproducing kernel spectral theories, investigate time frequency scalogram same Finally, provide Shapiro’s mean dispersion type theorems at end.