Efficient analysis of the stability of sigma-delta modulators using wavelets

A new method is presented to efficiently estimate the stability boundary for sigma-delta modulators. Wavelet decomposition is used to cut up the input and output signals of the quantizer into different frequency portions. For the portion around the limit cycle an amplification factor and phase shift are calculated. This represents the transfer of the quantizer at that point. The so-formed linear system can then be analyzed using the phase margin. Only a small number of data points need to be evaluated making this method forty times faster than the traditional approach of long transient simulations, with only a very small error