An almost leakage free method for assessing Σ-Δ modulator spectra

This paper addresses the problem of spectral analysis of Σ-Δ modulator output spectra. Often, data containing a periodic signal are evaluated using fast-Fourier-transform (FFT) based spectral analysis. If the data set is not sampled coherently, long- and short-range leakage can hamper or prevent the frequency domain analysis, particularly if frequencies near the excitation sine frequency are of interest. Techniques such as windowing or coherent sampling help, but unfortunately may add their own effects to the spectra under scrutiny. Where coherent sampling is not easily possible, another approach to reliable spectrum analysis is a hybrid computation of the spectrum using the output bit stream from a Σ-Δ modulator. This will yield spectral information and an assessment of modulator performance. The method is demonstrated on MATLAB simulated Σ-Δ modulator bit-stream data from a single-loop, first order modulator as well as a single-loop, third order modulator, both excited by a multitone sinusoidal excitation