In this section, the wavelet transform of a continuous time signal, x(t), is considered where discrete values of the dilation and translation parameters, a and b, are used.

A natural way to sample the parameters a and b is to use a logarithmic discretization of the a scale and link this, in turn, to the size of steps taken between b locations. To link b to a, we move in discrete steps to each location b which is proportional to the a scale. This kind of discretization of the wavelet has the form:

mt a t nb a

a, ( ) = −

 

0 (3.2)

where: The integer m controls the wavelet dilation The integer n controls the wavelet translation a0 is a specified fixed dilation step parameter set at a value greater than 1 b0 is the location parameter which must be greater than zero

The control parameters m and n are contained in the set of all integers, both positive and negative. It can be seen from Equation 3.2, that the size of the translation steps, Db b am= 0 0 , is directly proportional to the wavelet scale, am0 .