Multiresolution Analysis and Approximation of Audio Signal: the Haar wavelet
Here we show a finite discrete signal and its multi-resolution 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
RN
=
(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.
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Audio Signal
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Basic Information
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Level 1 Approximation
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Level 1 Detail
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Level 2 Approximation
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Level 2 Detail
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Level 3 Approximation
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Level 3 Detail
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Level 4 Approximation
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Level 4 Detail
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Level 5 Approximation
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Level 5 Detail
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Level 6 Approximation
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Level 6 Detail
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Level 7 Approximation
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Level 7 Detail
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Level 8 Approximation
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Level 8 Detail
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Level 9 Approximation
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Level 9 Detail
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Level 10 Approximation
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Level 10 Detail
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