Noise-Error Determination of Combinational Circuits by Walsh Functions

The stochastic behavior of digital combinational circuits is analyzed by the use of Walsh functions. An n-input Boolean function is represented as a Walsh series and the error caused by noise is measured in terms of a distance which is the fraction of the time that the system output due to noise-corrupted signal differs from that due to signal alone. It is shown that the error can be expressed as the sum of two parts: one part depends only on noise statistics, and the other on both signal and noise. Some interesting properties of both parts are discussed and typical examples are given.