1. Under what conditions will be synchronized averaging fail to reduce noise?

2. A certain signal analysis technique requires the following operations in order: (a) differentiation, (b) squaring, and (c) lowpass filtering with a filter H(w). Considering a generic signal z(t) as the input, write the time-domain and frequency-domain expressions for the output of each stage. Will changing the order of the operations change the final result? Why (not)?