In mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the wavelets vary continuously. The continuous wavelet transform of a function at a scale (a>0) and translational value is expressed by the following integral is the dual function of and is admissible constant, where hat means Fourier transform operator. Sometimes, , then the admissible constant becomes This inverse transform suggests that a wavelet should be defined as