Overview: Redundant Haar wavelet
We use Redundant Haar wavelet transformation that represents an initial price series by the sum of the band pass filters named wavelets, and the residual low-frequency filter:
Price =  + Residual,
Where N – - number of examined scales. It is necessary to say that the number of the used data values (i.e. the lookback period),on which wavelets compute is equal  , therefore the greatest possible scale  . 512 previous price values are more than enough for any practical problems. Waveleti i are similar to oscillators with consistently growing lookback periods while Residual term is similar to moving average. It is possible to read about Redundant Haar wavelets at http://www.multiresolution.comin more details.
The white noise filtration is made as follows. A signal or noise is defined on every scale. If noise is identified then the appropriate wavelet has zero value. If the signal is identified then the appropriate wavelet remains without change. Then we make inverse wavelet transformation and we receive the filtered signal.
Trend is determined as a significant movement on the considered scale, i.e. the signal / noise ratio for trend identification should be more than the given threshold of sensitivity. As noise is Gaussian by supposition, it is possible to apply statistical " Sigma rule " by setting a threshold in a range of 2 to 3.
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