Scaling Function
The wavelet function and the scaling function define a wavelet. The scaling function is primarily responsible for improving the coverage of the wavelet spectrum. This could be difficult since time is inversely proportional to frequency. In other words, if we want to double the spectrum coverage of the wavelet in the time domain, we would have to sacrifice half of the bandwidth in the frequency domain. Instead of covering all the spectrum with an infinite number of levels, we use a finite combination of the scaling function to cover the spectrum. As a result, the number of wavelets required to cover the entire spectrum has been greatly reduced.
Read more about this topic: Continuous Wavelet Transform
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