Methods for Processing Complex Waveforms through Filters for Use in Monte Carlo Noise Studies

Any N-pole linear lumped-constant time-invariant network can be represented by a linear homogeneous difference equation. If an arbitrary input waveform is sampled at equally spaced time intervals, so that eight or more samples are available at the highest significant frequency present, the output waveform can be computed in a simple manner from the difference equation. If K input samples are to be filtered, the saving in computer time, when compared to the usage of the convolution integral, is equal to K. The method is illustrated by the simulation of an FM receiver, operating at threshold, in the presence of Gaussian noise.