I am using a wavelet transform and am testing the following approach to thresholding:

All coeffients (whatever their value) after the first N are set to 0

So if my timeseries window is 128 elements, I will zero all after the first 8 (N).

This seems to smooth nicely but is NOT proper Hard Thresholding.

Any thoughts on this?

  • $\begingroup$ It is impossible to answer you question, because valid thresholding is not a well-defined concept. In any case, what you are doing is essentially filtering in the transform domain. A filter that goes to zero after N samples is not smooth. The equivalent time domain signal will ring forever, which means you must expect some aliasing. $\endgroup$ Oct 16 '15 at 20:44
  • $\begingroup$ @EmanuelLandeholm By VALID I mean does it make any sense to use it! My filter IS smooth. I am using it for timeseries analysis and it appears to work quite well. I am not sure what "aliasing" is. $\endgroup$
    – ManInMoon
    Oct 21 '15 at 12:48
  • $\begingroup$ A smooth function has continuous derivatives up to some desired order. Truncation in the frequency (wavelet) domain gives you a function without continuous derivatives of the 0:th order. Like I said, the time domain version of such a filter will ring forever (Gibb's phenomenon) and any computation using such a filter requires tapering, which is a nonlinear process that will introduce aliasing. $\endgroup$ Nov 1 '15 at 18:37

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