In modeling the effects of round-off and truncation in digital filter implementations, q...

In modeling the effects of round-off and truncation in digital filter implementations, quantized variables are represented as

whereQ[·] denotes either rounding or truncation to (B+1) bits and e[n] is the quantization error. We assume that the quantization noise sequence is a stationary white-noise sequence such that

and that the amplitudes of the noise sequence values are uniformly distributed over the quantization step = 2^−B. The 1st-order probability densities for rounding and truncation are shown in Figures P6.54(a) and (b), respectively.

(a) Determine the mean m_e and the variance for the noise owing to rounding.

(b) Determine the mean m_e and the variance for the noise owing to truncation.