In this paper we shall examine the quadratic Fourier transform which is introduced by the generalized quadratic function for one order parameter in the ordinary Fourier transform. This will be done by analyzing corresponding six subcases of the quadratic Fourier transform within a reproducing kernel Hilbert spaces framework.

This article introduces a systematic study for computational aspects of classical wavelet TRANSFORMS over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet TRANSFORMS over finite fields. It is shown that each vector defined over a finite field can be represented as a finite coherent sum of classical wavelet coefficients.