Document Type
Thesis
Date of Award
5-31-1985
Degree Name
Master of Science in Electrical Engineering - (M.S.)
Department
Electrical Engineering
First Advisor
Joseph Frank
Second Advisor
Stanley S. Reisman
Third Advisor
Robert R. Meola
Abstract
The power spectral density (PSD) function is a characterization of an (ideal) signal or set of signals. It is usually associated with a stationary random process, but it need not be. In fact, to study its properties it is desirable to divorce the power PSD from any extraneous structure that may conceal its properties. Specifically, it is desirable to study Sτ(f) = | Xτ(f)|2/2T and determine how it approximates the power spectrum of a power signal S (f) = τ[R(τ)].
It is shown that it cannot be concluded (contrary to what some of the literature has reported) that S-r(f) converges to S(f). It is shown that the integral of Sτ(f) over any finite interval does converge to the integral of 5(f) over the same interval. It is demonstrated that by suitable modification of Rτ(τ) the convergence to S(f) of the now modified Sτ(f) can be assured.
A deterministic power signal is constructed with a continuous PSD function, and Sτ(f) and Rτ(τ) are calculated to demonstrate their behaviour.
The non-zero variance of Sτ(f) and the reason for it's mean equaling the ensemble power spectrum are explained on the basis of the behaviour of Sτ(f) for a deterministic signal.
A PAM CS process is analyzed with respect to Rτ(τ) and Sτ(f). It is shown that the process has the same autocorrelation for almost all sample functions. It is also demonstrated that the same procedure that causes Sτ(f) to converge to S(f) for a deterministic signal causes the variance of Sτ(f) for the PAM process to approach zero with increasing sample size.
Recommended Citation
Coleman, James Edward, "An examination of the power spectral density function" (1985). Theses. 3635.
https://digitalcommons.njit.edu/theses/3635
