Higher Order Crossings from a Parametric Family of Linear Filters
When a time series is filtered, the effect of the filter can be described by counting the resulting number of zero-crossings. By extension, we can apply to a time series a family of filters and obtain the corresponding family of zero-crossing counts. The resulting family of counts is referred to as...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Text |
| Language: | English |
| Published: |
1989
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| Subjects: | |
| Online Access: | http://www.dtic.mil/docs/citations/ADA213427 http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA213427 |
| Summary: | When a time series is filtered, the effect of the filter can be described by counting the resulting number of zero-crossings. By extension, we can apply to a time series a family of filters and obtain the corresponding family of zero-crossing counts. The resulting family of counts is referred to as higher order crossings or HOC. Thus, HOC are zero-crossing counts observed in a time series and in its filtered versions. The main application of HOC is in the description of the oscillation observed in oscillatory time series. Moreover, in the special case of stationary Gaussian time series there are quite a few HOC families and also HOC sequences that determine the spectrum up to a constant. This paper is organized as follows. In section 2 we define and also give examples of HOC from parametric families of linear filters. We outline there our motivation for studying HOC in connection with oscillatory time series. In section 3 we construct an adaptive HOC sequence form (0.1) that converges to a frequency in the presence of noise. As a matter of fact, the main result there, Corollary 1, has prompted our interest in pursuing HOC in connection with parametric linear operations. In section 4 we obtain more results about the HOC family from (0.1). Our main result there is the connection between the zero- crossing rate, as a function of the parameter, and the correlation generating function under the Gaussian assumption. In section 5 we analyze a vocal sound time series of a megaptera novaeangliae (humpback) whale. |
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