ABSTRACT
This chapter provides a comprehensive coverage of the theory of wavelet transforms and their kin, including the stockwell transform, two-dimensional (or polar) wavelet transform, ridgelet transform, curvelet transform, ripplet transform, shearlet transform and bendlet transform. The fundamental ideas and results involved in the formulation of the respective integral transforms are discussed in detail, with special attention given to the applications from a signal processing perspective. All the major concepts are illustrated with suitable examples followed by illustrative depictions. The Haar measure is used in many parts of analysis, number theory, group theory, representation theory, statistics, probability theory and ergodic theory. The chapter aims to gain an intuition regarding the unitary representations of locally compact groups on separable and complex Hilbert spaces. It recalls the notions of adjoint and unitary operators on Hilbert spaces.
