Linear time-invariant systems in the wavelet domain

This paper investigates how linear processing of one dimensional (1-D) signals might be undertaken in the wavelet transform domain. Some linear mathematics is derived which encapsulates the overall process. It is found that this requires some fundamental development in shiftable Wavelet Bases. Although shiftable Wavelet bases are not used in the present study, it is possible to corroborate the theory with some simple FIR examples, based on the dyadic Wavelet Transform. It is found that with perfectly shifted wavelet transforms, the error will be on the order of that of the numerical precision of the simulation environment used, i.e. Matlab with Wavelab