Basic Concepts in Systems Theory and Signal Processing

Abstract

Signals are functions of one or more independent variables. Electrophysiological signals like the ECG, EMG, EEG, and hemodynamic signals like blood pressure, blood flow, are all time-varying or time-dependent signals. Any set of processes that affects the nature of a signal may be called a system. The myocardium that generates the ECG, the heart that drives blood pressure and flow are parts of physiological systems. While any real biological system is nonlinear and time-variant, for simplicity of analysis we assume that physiological systems are linear in the range of interest and time-invariant in short intervals subjected to analysis. Convolution is a mathematical technique that defines the input-output relation of a linear system. Signals can also be described by a set of primitive functions like sinusoids – this is the basis of Fourier conversions. Transforming signals and systems by Fourier conversion into the “frequency-domain” simplifies a number of operations like convolution and differentiation to simple algebraic ones. This greatly enhances our power of analysis. This chapter outlines the basis of time-domain and frequency-domain analysis for physiological signals and systems.

…while I am describing to you how Nature works, you won’t understand why Nature works that way.

– Richard Feynman