sentences:  As the order "j" increases, these wavelets become more localized in Fourier space (frequency) and in higher frequency bands, and conversely become less localized in time ("t").Hence, when they are used as a basis for expanding an arbitrary function, they represent behaviors of the function on different timescales (and at different time offsets for different "k").However, it is possible to combine all of the negative orders ("j" < 0) together into a single family of "scaling" functions formula_6 where
  
  The function "φ" is orthogonal to itself for different "k" and is also orthogonal to the wavelet functions for non-negative "j"