ABSTRACT
The early time series work of Wiener was developed in the context of electrical engineering when the nature of the series was of a continuous analog signal. In the present digital age, variables which are naturally continuous, such as the Oxygen levels of the infant monitoring system, are not recorded continuously, but are discretized by sampling at high frequency and then recorded digitally. The recorded music industry has long since made this transition from analog vinyl records to the digitized compact disc format. Before analyzing high frequency sampled discretized signals, it is usual to smooth them to reduce observation noise and then to sub-sample them at a reduced rate, chosen so that little information is lost. This is done by confirming that there is negligible power in the spectrum beyond the Nyquist frequency associated with the sampling rate of the final recorded signal. In the context of sound recording, this enables the continuous signal to be accurately reconstructed as an electrical voltage to be fed into an amplifier and speaker system.
