From the course: Wavelet Analysis: Concepts with Wolfram Language
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Discrete wavelet data - Wolfram Language Tutorial
From the course: Wavelet Analysis: Concepts with Wolfram Language
Discrete wavelet data
So now let us look at some of the theory that goes behind the discrete wavelet transform. Recall that, associated with the scaling function, we have the low-pass filter coefficients which are denoted by the term a, and the high-pass filter coefficients are associated with the term b. When this is used with the original time series signal and a convolution is performed, you end up performing the decomposition. So a discrete wavelet transform takes the original signal and breaks it down into a set of coarse coefficients and detail coefficients. The coarse coefficients are due to a convolution with the low-pass filter coefficients, and the detail coefficients are due to the high-pass filter coefficients. Furthermore, the coefficients taken at a certain level can be decomposed to a j + 1 and a d + 1, the coarse and detail coefficients at level j + 1, and this analysis eventually leads to what is called as the multi-resolution analysis. The difference between discrete wavelet transform and…
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