Estimation of the In-Band Delta–Sigma Noise Power Based on Windowed Data

Spectral figures of merit of Delta-Sigma (DeltaSigma) converters are usually evaluated in the frequency domain by estimating the power of the narrow- and wide-band components from the power spectral density (PSD) of the modulator output. Because of the finite number of processed samples, both components are affected by a spectral leakage. Scientific literature has widely investigated the leakage of the fundamental and its higher harmonics, which can be prevented if the sampling and the input frequencies are synchronized accurately. Conversely, effect of the finite number of samples on the PSD of DeltaSigma-shaped wideband noise has not been treated in the technical literature yet. To date, windows commonly used for reducing leakage of the fundamental (i.e., the Hanning, Blackman-Harris, or flattop sequences) are also used for windowing the DeltaSigma-shaped quantization noise. By noticing that published PSDs of low-order DeltaSigma modulators are usually obtained by employing the Hanning window Norsworthy (Oversampling Delta-Sigma Data Converters: Theory, Design, and Simulation. Piscataway, NJ: IEEE Press, 1997), Markus and Temes (IEEE Trans. Circuits Syst. I, vol. 51, no. 1, p. 63, 2004), in this paper, the deviation in the estimate of the noise power induced by the use of the general class of the cosine windows-to which the Hanning one belongs-is investigated. This is employed for deriving an a priori criterion for the selection of the best cosine window that reduces the spectral leakage of the shaped wideband noise and for the choice of the minimum number of acquired samples needed to bound the relative error in the estimated in-band noise power below a given value