Scaling Function in Wavelet Analysis

1. What is scaling function in wavelets?
2. What is the scaling function?
3. What is basis function in wavelet transform?

What is scaling function in wavelets?

The scaling function filters the lowest level of the transform and ensures all the spectrum is covered. See for a detailed explanation. For a wavelet with compact support, φ(t) can be considered finite in length and is equivalent to the scaling filter g. Meyer wavelets can be defined by scaling functions.

What is the scaling function?

The graph y=k⋅f(x) (where k is a real number) is similar to the graph y=f(x), but each point's distance from the x-axis is multiplied by k. A similar thing happens when we graph y=f(k⋅x), only now the distance from the y-axis changes. These operations are called "scaling."

What is basis function in wavelet transform?

Wavelets provide a tiling of time-frequency space that gives a balance between time and frequency resolution. The Q-factor of a filter or basis function is defined as the central frequency to bandwidth ratio. Wavelet bases are chosen to provide constant Q (Unser and Aldroubi, 1996).