Haar scaling function

1. What is Haar scaling function?
2. What is scaling function in wavelets?
3. What is scale in wavelet transform?
4. What is a Haar matrix?

What is Haar scaling function?

Furthermore, the Haar scaling function is a solution of the refinement equation with two nonzero coefficients, (4.337) Due to (4.334) and (4.335), the related Haar wavelet function is required to be. (4.338) with two nonzero coefficients.

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 scale in wavelet transform?

Wavelets have two basic properties: scale and location. Scale (or dilation) defines how “stretched” or “squished” a wavelet is. This property is related to frequency as defined for waves. Location defines where the wavelet is positioned in time (or space). Example Wavelet: The first derivative of Gaussian Function.

What is a Haar matrix?

The Haar matrix is the 2x2 DCT matrix, so inversly, you can treat the NxN DCT(II) matrix as the Haar matrix for that block size. Or if the N is dyadic, N=2^n, then you might be asking for the transform matrix for n stages of the Haar transform.