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This paper presents the theory and application behind Wavelet Assisted Constrained Least Squares Spectral Analysis, which is a hybrid mixed-model algorithmic approach for spectral decomposition. It combines a wavelet-based and a fixed-window constrained inversion Fourier based approach to estimate more accurate and reassigned time-frequency coefficients. The results from WACLSSA are compared with its constituent techniques and demonstrate that the spectrum obtained is more compact in terms of time and frequency standard deviations. They also show absence of ringing and tailed spectra dominant in the parent techniques. The results on real data also display improvements in vertical and horizontal resolution of seismic data, with the ability to isolate zones of interest better than its predecessors. WACLSSA also illuminates and highlights a 32ms thick layer at 22Hz frequency. The frequency is selected on the basis of the dominant frequency around the spectra corresponding to the seismic signal at the well location.