ABSTRACT
This chapter permits error analysis of sampling algorithms used for the synchronous detection of periodical signals. It assumes that the signal is periodic so its Fourier transform is discrete. The chapter develops some methods to find algorithms with the desired properties but this was done primarily to evaluate them. It establishes the foundations for the analysis of phase-detection algorithms. The chapter describes some discrete sampling low-pass filtering functions. It develops to study the synchronous detection in a more general manner, from a Fourier domain point of view, as developed by Freischlad and Koliopoulos and Parker and later reviewed by Larkin and Oreb. It examines how the sampling weights change, thus modifying the algorithm structure. Many different names had been given to it in the past, such as synchronous detection algorithm, but here we will call it the diagonal least-squares algorithm.
