The Prism: Recursive FIR Signal Processing for Instrumentation Applications

Abstract

This paper provides the mathematical background for the precise, repeat integral signal monitor (Prism), a signal processing network node used in a variety of sensing and instrumentation applications. The key operation is a double Fourier-style integration, which can be implemented recursively using sliding windows and precisely using Romberg integration. The Prism generates one or two outputs; if two are generated, they are orthogonal, analogous to an analytic signal, from which sinusoid properties, such as frequency, phase, and amplitude, can readily be derived. The Prism outputs are finite impulse response (FIR), but the calculation is recursive, resulting in a low computational cost which is independent of filter length. This paper compares the Prism’s computational efficiency with both a least squares FIR filter design and an equivalent Prism filter implemented as a conventional convolution. The advantages of the Prism include design simplicity, low computational cost, and a linear phase response, making it a useful network node for a wide range of instrumentation and signal processing tasks.