Abstract
Exact analytical and computational results of the transient scattered spectrum with Haar wavelet window function are derived for the model of a single quantised harmonic oscillator (HO) driven by the sequential sin(2)-pulse shape. Effects of the window function dilation and shift parameters (j, k) depend on the initial state of the HO. Specifically, increasing the shift parameter (k) in the off-resonance case has the effect of: (i) inducing periodic behaviour and side ringing in the spectrum in the cases of initial vacuum and number HO states, and, (ii) changing the hole burning spectral structure to asymmetrical 3-peak structure with ringing in the case of initial coherent HO state. The dilation parameter (j) causes the central spectral structure to stretch symmetrically over larger values of the detector's detuning parameter.