Least Squares Design for Time-Shifting Filter
This sheet derives a design for a non-symmetric FIR filter for time shifting a signal,
given equally-spaced samples of the signal value. The method constructs the
filter characteristic by locally fitting a polynomial model to the data stream using
least-squares techniques, then evaluating the model at an an arbitrary location.
The length of the desired filter and the order of the polynomial model can be
specified.
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The design only needs to shift the data stream by +- 1/2 location.
For larger shifts,
the filter characteristic can be shifted an appropriate number
of integer locations.
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Construct the model fit.
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Evaluate the polynomial model as the specified frational time shift.
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An example:
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Apply the shift filter to
the following
data sequence.
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The value at the
selected shift location:
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The page above was generated by Mathcad 12 (Mathcad (t) is a registered trade name of Mathsoft Engineering and Education, Inc.)
Microstar Laboratories, Inc.
