Discrete-time continuous-dilation wavelet transforms

We present a new form of wavelet transform called "discrete-time continuous-dilation wavelet transform" (DCWT). It is computed by correlating a given discrete-time signal with continuous dilations of a discrete-time mother wavelet. The results developed are based on the definition of a discrete-time scaling (dilation) operator through a mapping between the discrete and continuous frequencies. The forward and inverse discrete-time continuous-dilation wavelet transforms are formulated. The admissibility condition is derived, and examples of discrete-time wavelet construction are provided. The potential advantage of this new wavelet transform is that it is naturally suited for discrete-time signals and provides analysis and synthesis of such signals over a continuous range of scaling factors.