Multiresolution Analysis and Approximation of Audio Signal: the Haar wavelet
Here we show a finite discrete signal and its multiresolution analysis of level p=1,2,3,4,5,6,7,8,9.10 based on the Haar wavelet, which is also called the Daubechies 1 wavelet and the simplest wavelet function. A sigal is an element of finite dimensional vector space of real numbers,
which is decomposed as a direct sum of subspaces the form
R^{N}
=
(level p approximation)
+
(level p detail)
+
...
+
(level 2 detail)
+
(level 1 detail).
Higher level subspace consist of elements of lower frequcny,
and the approximation is the lowest frequency part.

Audio Signal

Basic Information

Level 1 Approximation

Level 1 Detail

Level 2 Approximation

Level 2 Detail

Level 3 Approximation

Level 3 Detail

Level 4 Approximation

Level 4 Detail

Level 5 Approximation

Level 5 Detail

Level 6 Approximation

Level 6 Detail

Level 7 Approximation

Level 7 Detail

Level 8 Approximation

Level 8 Detail

Level 9 Approximation

Level 9 Detail

Level 10 Approximation

Level 10 Detail
