Maximally stationary window design for overlap-add based random vibration synthesis

Abstract

The accurate synthesis of realistic waveforms conforming to certain specifications is a fundamental step in random vibration testing. Since real-time implementation of digital signal processing systems for random vibration and noise synthesis necessarily operates frame by frame, the overlap-add (OLA) method, by which frames are windowed and overlapped, is widely used in practice to avoid artifacts at frame boundaries. When a wide-sense stationary random signal is desired, however, the OLA method presents a shortcoming, because the inherent periodicity of the frame-by-frame process unavoidably produces a cyclostationary signal, i.e., its statistics present an undesired periodic behavior. We analyze the impact of the window coefficients in the cyclostationarity properties of the synthetic process, and then present algorithms for window design with the goal of maximizing a measure of its stationarity, considering both second- and fourth-order statistical properties. The proposed designs are shown to significantly improve the stationarity properties when compared to commonly used windows.