Origin of Rice's formula

The origin of S.O. Rice's formula for the average rate of level crossings of a rather general random process is traced to his 1936 private notes entitled Singing Transmission Lines. The notes formulate an engineering problem in terms of the probability distribution of the absolute maximum of an envelope process in a closed interval. Rice showed that if the envelope of the reflected wave on a loaded transmission line were to equal or exceed the maximum value in the closed interval, then `singing' or oscillation could be expected to occur and the analog transmission system would become unstable and useless for the transmission of information. The formula and its generalizations are now basic for the analysis of level crossings and first and second passage times of random processes     

Laser clipping distortion in analog and digital channels

The exact carrier-to-nonlinear distortion (C/NLD) ratio, resulting from laser clipping, is computed for the low, center, and high channels of the analog and digital bands of a hybrid fiber/coax system. The computed results indicate that high capacity digital channels can be added to present analog systems without affecting the high performance analog channels     

Eliminating inductive noise of external chip interconnections

On-chip balanced drivers can essentially eliminate inductive noise, without any power dissipation penalty, and independently of the number of chip drivers switching simultaneously or the switching speed. In addition, balanced interconnections on PWBs and MCMs substantially reduce crosstalk, increase noise immunity, and eliminate ground noise     

Bandwidth from a large excursion of Gaussian noise

Some statistics properties of large excursions of Gaussian processes are presented, along with exact asymptotic formulas for calculating the root-mean-square (RMS) bandwidths of the underlying wideband or narrowband Gaussian processes in terms of the excursion level, height, and duration. The measured trajectory of a large excursion is used to illustrate the method. A somewhat similar phenomenon occurs for the envelope of a narrowband Gaussian process