Contraction mappings in mixed spectrum estimation. (English) Zbl 0768.62082
New directions in time series analysis. Part I, Proc. Workshop, Minneapolis/MN (USA) 1990, IMA Volumes in Mathematics and Its Applications 45, 169-191 (1992).
Summary: [For the entire collection see Zbl 0761.00003.]
Families and sequences of zero-crossing counts generated by parametric time invariant filters are called higher order crossings or HOC. Because of the close relationship between zero-crossing counts and first order autocorrelations, families of first order autocorrelations are also referred to as HOC. By means of HOC from repeated differencing and repeated summation, it is possible to obtain a complete solution of the problem of hidden periodicities in the purely discrete spectrum case. However, when noise is present, a modification is needed.
It is shown how to locate discrete frequencies in the presence of colored noise, using HOC sequences obtained by recursive filtering. By this method, the cosine of each discrete frequency is obtained as a fixed point of a certain contraction mapping. A special feature of this method is that the contraction rate can be enhanced considerably by the iterative reduction in the filter bandwidth.
Families and sequences of zero-crossing counts generated by parametric time invariant filters are called higher order crossings or HOC. Because of the close relationship between zero-crossing counts and first order autocorrelations, families of first order autocorrelations are also referred to as HOC. By means of HOC from repeated differencing and repeated summation, it is possible to obtain a complete solution of the problem of hidden periodicities in the purely discrete spectrum case. However, when noise is present, a modification is needed.
It is shown how to locate discrete frequencies in the presence of colored noise, using HOC sequences obtained by recursive filtering. By this method, the cosine of each discrete frequency is obtained as a fixed point of a certain contraction mapping. A special feature of this method is that the contraction rate can be enhanced considerably by the iterative reduction in the filter bandwidth.
MSC:
| 62M15 | Inference from stochastic processes and spectral analysis |
| 62M20 | Inference from stochastic processes and prediction |
| 62M09 | Non-Markovian processes: estimation |
