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Next: Properties of the Maximally Up: Recursive Windowing of Time Previous: Interpolation and Irregularly Spaced

Maximally Flat Impulse Response

A very nice filter for windowing can be given by choosing an exponential decay tex2html_wrap_inline1150, and setting
equation184
and tex2html_wrap_inline1152. Then we will determine b so that
eqnarray190
Now our choice of A by specifying tex2html_wrap_inline1158 looks more natural, and, noting that for k<d we have
equation204
and from the binomial theorem we have the solution
equation218

We should also explain that since tex2html_wrap_inline1146 has been chosen to be triangular, so is A, and the eigenvalues of tex2html_wrap_inline1146, (in this case the repeated eigenvalue tex2html_wrap_inline1150) is the logarithm of the repeated eigenvalue of A, namely tex2html_wrap_inline1172. Since we want A to be a stable matrix, we have tex2html_wrap_inline1176.




Fri Jun 27 03:10:38 EDT 1997

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