Spectral Bounds Research Articles

Spectral Bounds and Oscillations of a Differential–Difference System of Neutral Type

This paper is concerned with the oscillatory behavior of a differential–difference system of neutral type. Spectral bounds are used in order to obtain sufficient conditions such that all their solutions are oscillatory.

Spectral Density Bounds on an FM Wave

Upper and lower bounds on the spectral density of a sinusoidal carrier frequency modulated by a band-limited Gaussian noise signal are derived and we show that these bounds are very close to each other if the ratio of the rms frequency deviation to the maximum modulating frequency is even moderately high. We then show that the results obtained from the quasi-static approximation, often used in such cases, are too small for large <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</tex> and that this low-frequency approximation cannot be used in cases where the behavior on the tails is of importance.

Spectral Density Bounds of a PM Wave

In this paper we derive upper and lower bounds of the spectrum of a sinusoidal carrier phase modulated by gaussian noise having a rectangular power spectrum. It has been found in practice that such a random process adequately simulates for some purposes, a frequency division multiplex signal, a composite speech signal, and so on. We show that these upper and lower bounds of the spectrum are very close to each other if the root mean square phase deviation of the carrier is even moderately high. Also, a simple method called the saddle-point method can be used at all frequencies f to estimate the spectrum with less than ten percent error. We also show that the results obtained from the quasistatic approximation, often used in such cases, are too small for large f, and that this low-frequency approximation cannot be used in cases where the behavior on the tails is of importance.