A wavelet function can be viewed as a high pass filter, which aproximates a data set (a signal or time series). The result of the wavelet function is the difference between value calculated by the wavelet function and the actual data. The scaling function calculates a smoothed version of the data, which becomes the input for the next iteration of the wavelet function. In the context of filtering, an ideal wavelet/scaling function pair would exactly split the spectrum. For example, if the sampled frequency range is 0 to 1024 Hz, the result of the wavelet function would be signals from 512 to 1025 Hz. The result of the scaling function would be signals from 0 to 511.

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