Piecewise-Constant Pseudo Sinusoid Function

pps functions are a new set of frequency preserving discrete valued orthogonal functions. These functions are generated by extending the core functions developed in this paper. The core functions are generated by a new procedure that ensures that pps functions cross the x-axis at the same points as the sinusoids. The performance of pps functions is studied with respect to spectral resolution and spectra of various input signals. If spectra are used to determine similarity of orthogonal functions, the performance indicates that the locations of zero-crossings play an important role in determining the similarity of orthogonal functions.