In-Band Power Estimation of Windowed Delta-Sigma Shaped Noise

Performances of ∆Σ modulators are evaluated by applying a coherently sampled tone and by estimating powers of the in–band tones and noise. In particular, the power of the shaped noise is usually estimated by subtracting the evaluated input tone from the output data and by integrating the power spectral density estimated by means of the periodogram. Although the coherency, the finite number of processed samples induces spectral leaking of the wide–band noise, thus affecting the noise power estimate. To cope with such an issue, usually data are weighted by the Hanning sequence. In this paper, the noise power estimation error induced by the use of such window is investigated, and a criterion for choosing the minimum number of samples N which bounds the relative leakage error within a specified maximum value is explicitly given. Moreover, it is shown that, for any N, such an error is negligible for modulator orders lower than 3. Higher order modulators require the use of a large number of samples to bound the relative error of the noise power estimate when high oversampling ratios are employed.