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A statistical framework to minimise and predict the range values of quantisation errors in fixed-point FIR filters architectures

<01>When FIR filter architectures are implemented in hardware, filters datapath signals and coefficients are often quantised to fit within the underlying limited precision of the system due to registers size limit, and in order to reduce excessive hardware requirements. The paper studies the effects of rounding and truncation performed in finite fixed-point arithmetic on the computations precision, and presents a new statistical quantisation model to enhance and predict the computation precision depending on the datapath wordlengths fractional precisions. Using the proposed statistical model, a hardware designer can pre-set dynamically the datapath wordlengths fractional precisions to achieve a desired computation precision.