The design of overall finite impulse response (FIR) filter for sigma-delta analog-to-digital converters is formulated as a quadratic program with the total output noise as the objective function, subject to the passband and stopband constraints. The formulation is so flexible that it can suit different requirements for suppressing the quantization noise as well as rejecting the out-of-band spurious signal. Both one-stage single rate and multistage multirate filter structures are considered. For the purpose of suppressing the quantization noise, the multistage multirate FIR filter with comb filters as prefilters has much lower complexity with little performance degradation relative to the one-stage optimal filter.
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