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In this paper, an efficient and simple cascade structure for the implementation of the multiplierless bandpass filter proposed in (Kamakshi Sivaramakrishnan, et al., (2004)) is shown. The quantization of the proposed cascade structure necessitates a formal design technique for the interdependent bit-widths in the various stages of the cascade. The quantizer design, when formulated as a classical optimization problem of minimum distortion for a given rate (bit resource) constraint is solved using an approach commonly used in dependent quantization scenarios, as in source coding. The otherwise complex problem of optimal resource allocation is solved using some observational heuristics giving a partly greedy solution. This sets up the ground towards achievement of near optimal performance bounds in the rate-distortion sense. The quantization of the cascade filter structure is characterized by a convex hull of the optimal rate-distortion points.