Abstract
We considered the issue of intuitive analysis, processing, and synthesis of unknown pulse sequences in a detailed form. We studied both classical methods of analysis with all pluses and minuses and the developed prospective method created on their basis. The developed method is adaptive, it is based on the consistent use of various methods of spectral analysis, which increases reliability, sensitivity, and resolution capability of visual analysis of echo-pulse images. Thus, we solved the problem on processing pulse signals. The proposed method makes it possible to increase resolution capability in the processing of signals and images without using a priori information on the form of elementary pulses. It is resistant to the influence of measuring noise. We presented the results of numerical simulation and actual verification on the example of a seismic image. The considered method has a significant development potential, both in theoretical and application aspects (first of all, in areas of ultrasonic medical diagnosis, seismic imaging, and non-destructive testing).
Highlights
If a noise level is small and resolution capability of a recording system is sufficient to provide a visual analysis of s(t) superposition, the estimation of its parameters L, ai, ti is usually not a significant problem
Problems arise in situations where resolution capability is not enough to perform visual analysis due to overlapping of elementary impulses [5]
The representation of expression (7) in the form of linear prediction model (8) does not, solve the task on increasing resolution capability of visual analysis of superpositions of overlapping signals because we must carry out an analysis in the time domain, and not in the spectral domain
Summary
A large number of problems in the field of ultrasonic diagnosis [1], reflective seismology [2], radiolocation [3], and spectroscopy [4] are related to the analysis of superpositions of pulse signals in the form: L. i=1 where s(t) is the superposition of a signal; L is the number of measurements discrete steps of a signal s(t); gi(t) represents some elementary impulse with ai amplitude and ti time delay; n(t) is the measurement noise. If a noise level is small and resolution capability of a recording system is sufficient to provide a visual analysis of s(t) superposition, the estimation of its parameters L, ai, ti is usually not a significant problem. Problems arise in situations where resolution capability is not enough to perform visual analysis due to overlapping of elementary impulses [5]. It is actual to develop a new method for decomposition of superpositions of signals to solve image processing problems of insufficient resolution or problems of signals with overlapping impulses
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