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Next: Maximally Flat Impulse Response Up: Recursive Implementation of General Previous: Recursive Implementation of General

Interpolation and Irregularly Spaced Data

We can generalize this recursive realization to the case where the times at which data arrives are not equally spaced points. In this case we put
eqnarray138
with impulse response
equation148
as before. Note that if the times tex2html_wrap_inline1140 are successive integers, that is tex2html_wrap_inline1142, then this filter coincides with (15). We note that
equation156
permits us to compute derivatives of tex2html_wrap_inline1144, where tex2html_wrap_inline1146 is the matrix logarithm. The DC gain for irregularly spaced data depends on the sequence of times tex2html_wrap_inline1140, so that a gain-normalized filter requires a method of keeping track of these times. One convenient approach is to approximate the normalized filter by adjoining extra states
eqnarray167


Fri Jun 27 03:10:38 EDT 1997

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