In this thesis, we develop an approximation to the continuous wavelet transform (CWT) which is unique in that it does not require an exact scaling relationship between the levels of the transform, but asymptotically approaches an irrational scaling ratio of 2\sp1/n\sb0 where n\sb0 is related to the number of vanishing moments of the original scaling filter. The autocorrelation sequences of the scaling and wavelet filters associated with the Daubechies family of orthonormal compactly supported wavelets are shown to converge to smooth symmetric wavelets which approximate the Deslauriers and Dubuc limiting functions. We show why this transform is superior to a conventional dyadic wavelet transform for the edge detection application, and analyze its performance in denoising applications.