Spectral estimation of wideband noise in delta-sigma modulators

Spectral leakage is a well-known phenomenon induced by the windowing process and usually revealed in the frequency domain. Scientific literature has deeply investigated the spectral leakage of narrow-band components. However, the problem of windowing a wide-band colored noise has not yet been fully characterized. In this paper, the effect of the windowing process on the estimate of the in-band Delta Sigma-shaped quantization-noise power spectral density is investigated. The reported analysis holds for any modulator order and for any kind of real and symmetric window and proves the necessity of the windowing process in order to reduce the in-band noise power estimation bias. Moreover, an a priori criterion for designing the optimal window that reduces the shaped-noise spectral leakage and for choosing the minimum number of acquired samples to be employed is derived.