Discrete Wave-Analysis of Continuous Stochastic Processes.
Abstract
The behaviour of a continuous time stochastic process in the neighbourhood of zero-crossings and local maxima is compared with the behaviours of a discrete sampled version of the same process. For regular processes, with finite crossing-rate or finite rate of local extremes, the behaviour of the sampled version approaches that of the continuous one as the sampling interval tends to zero. Especially the zero-crossing distance and the wave-length (i.e. the time from a local maximum to the next minimum) have asymptotically the same distributions in the discrete and the continuous case. Three numerical illustrations show that there is a good agreement even for rather big sampling intervals. For non-regular processes, with infinite crossing-rate, the sampling procedure can yield useful results. An example is given in which a small irregular disturbance is superposed over a regular process. The structure of the regular process is easily observable with a moderate sampling interval, but is completely hidden with a small interval. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1971
- Accession Number
- AD0729650
Entities
People
- Georg Lindgren
Organizations
- University of North Carolina at Chapel Hill