Through use of a delay impulse function the theory of signal propagation in a lossless medium subject to delay control is detailed. A quasi-static delay modulation approximation is introduced to establish a simple analytical expression for the delay harmonic distortion. Experimental results for a two stage delay cascade provide good experimental justification for the presented theory.
KEYWORDS: Mathematical modeling, Optical filters, Modulation, Fourier transforms, Interference (communication), Linear filtering, Frequency modulation, Signal processing, Electronic filtering, Detection theory
Models for 1/f noise, based on power spectral density synthesis of the 1/f form, are demonstrated. These include, first, a finite summation of independent random processes which have equal power and signalling rates, or mean waveform rates, that form a geometric series with a ratio of two. Second, a continuum of independent random processes where the power in a given random process is inversely proportional to the signalling rate, or mean waveform rate, and these rates form a continuum. The random processes can be that of a filtered random walk, signalling random process, generalized signalling random process or a shot noise process. It is shown that the pulse function associated with these random processes is relatively unimportant. It is shown that low frequency modulation of signal components which fragment off a wide-bandwidth random process can lead to 1/f noise.