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WIP: better Meyer FIR approximation #311

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grlee77
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@grlee77 grlee77 commented Apr 25, 2017

Do not merge this PR. It is just a demo of generating more accurate FIR approximations for the Meyer wavelet (see #261). We can choose one of these to replace the current approximation.

The 102 coefficient approximation here is in agreement up to 4 or 5 digits with the filter coefficients used by Matlab. The 66 coefficient approximation is as in the reference provided by @holgern. And is close in accuracy to the 102 coefficient case. Note that the sample points are shifted by 0.5 between these two cases.

figure_3

figure_2

Both of these have much better accuracy than the current approximation:

Error (pywt dmey) = 0.0036067702113178066
Error (dmey102) = 4.351866673799496e-06
Error (dmey66_async) = 9.899204593989887e-06

If the asynchronous sampling case is extended out to 102 samples, accuracy is further improved.

Error (dmey102_async) = 9.934928444371677e-07

The 66 sample case is probably the best computation time / accuracy tradeoff.

@rgommers
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as just discussed: likely makes sense, but let's not look at this till after 1.0

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