Fast, accurate and automatic extraction of parameters of nuclear magnetic resonance Free Induction Decay (FID) signal for chemical spectroscopy is a challenging problem. Recently, the Steiglitz-McBride Algorithm (SMA) has been shown to exhibit superior performance in terms of speed, accuracy and automation when applied to the extraction of T₂ relaxation parameters for myelin water imaging of brain. Applying it to FID data reveals that it falls short of the second objective, the accuracy. Especially, it struggles with the issue of missed spectral peaks when applied to chemical samples with relatively dense frequency spectra. To overcome this issue, a preprocessing stage of subband decomposition is proposed before the application of SMA to the FID signal. It is demonstrated that by doing so, a considerable improvement in accuracy is achieved. But this is not gained at the cost of the first objective, the speed. An Adaptive Subband Decomposition (ASD) is employed in conjunction with the Bayesian Information Criteria (BIC) to carry out an efficient decomposition according to spectral content of the signal under investigation. Furthermore, the ASD and BIC also serve to make the resulting algorithm independent of user-input which also fulfills the third objective, the automation. This makes the proposed algorithm favorable for fast, accurate and automatic extraction of FID signal parameters.