Signals as Time Series

Signals in the traditional sense of electrical engineering are most often time series, measured at equidistant intervals. However, the methods developed for processing time series can be applied to any other signal as well, as long as the independent variable is measured at equidistant points. For example, the visible and ultraviolet (UV/VIS) spectrum of some substance can be processed by methods which have originally been designed for time series, if the spectrum has been acquired at equal wavelength intervals.

This opens a wide range of methods to process signals which are originally not time signals, i.e. smoothing, integration, differentiation, all kinds of filters, etc.

Time series can be treated mathematically as a series of numbers. If the measured series is considered to be composed of a functional relationship plus a non-deterministic, random part, the time series can be denoted as:

 
with y_t being the values of the series at time t,
f(t) being the functional relationship, and
u_t being the random contribution ("noise") at time t.