| The theory and some applications of piecewise constant wavelets are developed in this thesis.;Non-normalized continuous wavelet transforms of periodic functions f∈LinfinityR , which are taken with respect to piecewise constant wavelets , are periodic in time and in scale. We shall use this fact, to develop a method to detect periodic components in noisy signals s = f + N, where f is a known periodic signal and N noise. Our method is based on the redundancy in continuous wavelet transforms and their discrete counterparts, as well as on waveletgram averaging techniques.;We shall investigate our discretized version of the continuous wavelet transformation, to obtain conditions, which imply that the analyzing elements in our wavelet transformation form a frame for l2Z . The same is done to obtain frames l2Zd .;All wavelets with the property, that the non-normalized wavelet transforms of periodic functions f∈LinfinityT are periodic in scale and time, are classified. Our result is generalized to higher dimensions. |
