Discrete-time scale-shift approach for wavelet construction and analysis

Abstract

We provide a sufficient condition to construct a wavelet family from a purely discrete-time signal. The construction is based on an exact mathematical definition of the scale-shift operator in discrete-time and strongly motivated by a strict equivalence between voice transform and wavelet coefficients of a discrete-time signal. Particular classes of signals which satisfy this condition are given and furthers analysis are also considered.

Keywords

• Discrete-time scale-shift
• Voice transform
• Wavelet transform
• White noise