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Design of best wavelet packet bases for spectrum estimation

Wavelet packet transform has recently emerged as a novel spectrum estimation technique with attractions such as good time-frequency resolution, low variance of estimate and low complexity. Key to the successful operation of the system is the choice of the wavelet used. Commonly known wavelets are not frequency selective in nature and hence result in estimates with poor frequency resolution. To alleviate this problem, we design and develop a family of wavelets that are maximally frequency selective in nature. To this end, the design constraints are first enlisted. Then the problem, originally non-convex, is reformulated into a convex optimization problem and solved using Semi Definite Programming (SDP) tools. Through simulation studies the benefits of the newly designed wavelets are demonstrated.