Optimization in the study of a sinusoidal waveform of known periodicity in the presence of noise. Application in radio astronomy, 1

Details Optimization in the study of a sinusoidal waveform of known periodicity in the presence of noise. Application in radio astronomy, 1 Optimization in the study of a sinusoidal waveform of known periodicity in the presence of noise. Application in radio astronomy, 1

Oct 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976stin...7712955v&link_type=abstract

Optimization in the study of a sinusoidal waveform of known periodicity in the presence of noise. Application in radio astronomy

Mathematics

Probability

Optimization, Radio Astronomy, Signal To Noise Ratios, Sine Waves, Data Sampling, Fourier Series, Least Squares Method, Probability Distribution Functions

Scientific paper

In connection with the problems involved in the optimum utilization of information, the following deals with the measurement, in the presence of noise, of the amplitude and phase of a sinusoid who period is known. The aim is twofold: first, to achieve as good a precision as the signal to noise ratio and the observing time permit, and secondly, to attain such a precision with the minimum number of points measured with the minimum accuracy. The following approaches are treated: least mean square curve fitting, optimization of the physical filter, convolution by a sinusoid having the same period as the signal, summation, Fourier series analysis. These methods, singly or suitably combined, lead to the same results, and the probability distribution functions of the amplitude and phase thus obtained are established. The effects of sampling and quantization on the final signal to noise ratio are then studied as a function of the characteristics of the filter preceding the recorder; several results are established or reproduced, and then applied to the case where filtering is performed by integration over a finite interval of time.

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