A GENERALIZATION OF WOODWARD'S THEOREM AND THE SPECTRUM OF A HIGH HARMONIC OF A SINUSOID PLUS NARROW-BAND GAUSSIAN NOISE
Abstract
Woodward's theorem asserts that the power spectrum of a slowly frequency-modulated signal is given by the first-order probability density of the modulation. It can be extended to cover the case where there is slow amplitude modulation as well (correlated or uncorrelated and deterministic or random) by weighting each frequency by the mean-square amplitude associated with it. The modulation can be regarded as slow if its bandwidth is small compared to the frequency excursion. If a narrow-band waveform is multiplied in frequency up to a high harmonic, its spectrum becomes broad by comparison with its modulating frequencies, and this extension of Woodward's theorem provides an easy way of determining the spectrum. It is applied to the case of a sinusoid plus narrow-band gussian noise that has been passed through a power-law device to generate a high harmonic. The power spectrum is determined and its accuracy is estimated. Consideration is given to the accuracy with which the spectral density can be measured in a given time and to its use as an indicator of the presence of a signal. In the cases susceptible to analysis, the optimum harmonic to use for this purpose appears to be the first. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 28, 1961
- Accession Number
- AD0263056
Entities
People
- Nelson M. Blachman
Organizations
- Sylvania Electric Products