Sharper Bounds for Haar Wavelet Coefficients Corresponding to Continuous Real Valued Function Defined on Unit Interval

Haar wavelet is the only wavelet family with an explicit expression among all Daubechies wavelet families. This beneficial capability is exploited here to compute some bounds for Haar wavelet (detail) coefficients corresponding to real-valued continuous function on [0,1]. Obtained sharper bounds for the said coefficients at higher resolutions are helpful to study the degree of closeness to zero. We hypothesize that when there are any abrupt changes in the size of detail coefficients, the undererlying function has discontinuity and this discontinuity could be located in a small interval. Location of this kind of interval using Haar wavelet provides the smallest interval among all the Daubechies wavelet families for the given resolution.