Truncation noise analysis of noise shaping DSP systems with application to CIC decimators

In ordinary digital filters, reducing the wordlength of a signal in truncation always increases the quantization error variance at system output. We show that this law is not always valid if quantization noise shaping, e.g., error feedback, is used. This fact should be taken into account in the design of wordlength optimization algorithms. Furthermore, we show that cascaded integrator-comb (CIC) decimators provide inherent noise shaping. This is a consequence of pole-zero cancellation at passband, which has become possible through the use of modulo arithmetic. Thus, the wordlengths in the comb stages can be kept small, which can also reduce the complexity of the successive filter stage(s) usually following a CIC decimator.