An Intriguing Property of Scaling Function in Wavelet Theory and its Verification Using Daubechies-Lagarias Algorithm

The advent of wavelet in itself is a revolution in the field of signal processing. The simultaneous localization of signal in both its time and frequency domain was what attracted the engineers the most. However, most of them still fail to appreciate the contribution of Ingrid Daubechies, whose scaling and wavelet functions have several surprising features. Here, we try to throw light into the astonishing features of the Daubechies scaling and wavelet functions. Understanding of these features appears to be very important for mathematicians for exploring and exploiting new function spaces. The main purpose of this article is to convince ourselves (readers) the exotic properties of scaling and wavelet functions through computational experiments.