Obtaining normalized matrix for the Haar Wavelet Transform

1. How Haar transform is related to wavelet transform?
2. What is a Haar matrix?
3. How feature is generated using Haar transform?
4. Is haar wavelet orthogonal?

How Haar transform is related to wavelet transform?

The Haar transform is the simplest of the wavelet transforms. This transform cross-multiplies a function against the Haar wavelet with various shifts and stretches, like the Fourier transform cross-multiplies a function against a sine wave with two phases and many stretches.

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.

How feature is generated using Haar transform?

The first basis function creates a running sum of the input data, the second creates a difference between the first two and the second two data samples, the third creates a difference between the first two data points, and similarly the basis function in the bottom row does the same for the last two data points.

Is haar wavelet orthogonal?

The Haar system is an orthonormal basis for L2 (R).