wolfrain
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One quick question about the wavelet shape of CWT and DWT...
Here we go:
I can't really intuitively understand what's the relations between the Shape of the wavelet of CWT and DWT. What should be the correlation between the Wavelet in continuous form (Wavelet function) and the discrete points of the high-pass filter of that particular wavelet.
How should we link them together? Or, how should we 'derive' DWT form based on the CWT form of a particular wavelet.
1. To give you some examples on my confusion:
I use Matlab -> Toolbox -> Wavelet Toolbox -> Wavelet Display, where it shows you different types of wavelet/scaling functions and (if applicable) its corresponding Decomposition high/low-pass filters.
========================
Here is Haar wavelet.
Haar is a piecewise function, where 1 in [0 0.5] and -1 in (0.5 1], as shown in continuous case (wavelet function). However, in discrete case, it is -1 and then 1. To me, the shape of these two cases are opposite, intuitively. This is one confusion.
========================
Secondly, we have Symlets 2.
Again, decomposition high-pass filter looks like opposite to the wavelet function....
========================
Thirdly, we have Symlets 3.
Again, looks like opposite to each other...
========================
However, if I take a look at db 2.
They look not quite opposite, but similar...
========================
and db 3...
They looks similar again...
////////////////////////////////////////////////
After that, then what's the problem?
1. Why some of them looks opposite to each other, and some of them don't? What is the reason behind this?
2. Am I thinking in a wrong way? Can I actually think in terms of an intuitive relation between continuous and discrete cases of the wavelet?
3. If not, then how should we link them two together? Is it related to any mathematical properties? Any related materials explain about this relation?
Thanks for your time in reading this.
regards,
wolfrain
Here we go:
I can't really intuitively understand what's the relations between the Shape of the wavelet of CWT and DWT. What should be the correlation between the Wavelet in continuous form (Wavelet function) and the discrete points of the high-pass filter of that particular wavelet.
How should we link them together? Or, how should we 'derive' DWT form based on the CWT form of a particular wavelet.
1. To give you some examples on my confusion:
I use Matlab -> Toolbox -> Wavelet Toolbox -> Wavelet Display, where it shows you different types of wavelet/scaling functions and (if applicable) its corresponding Decomposition high/low-pass filters.
========================
Here is Haar wavelet.
Haar is a piecewise function, where 1 in [0 0.5] and -1 in (0.5 1], as shown in continuous case (wavelet function). However, in discrete case, it is -1 and then 1. To me, the shape of these two cases are opposite, intuitively. This is one confusion.
========================
Secondly, we have Symlets 2.
Again, decomposition high-pass filter looks like opposite to the wavelet function....
========================
Thirdly, we have Symlets 3.
Again, looks like opposite to each other...
========================
However, if I take a look at db 2.
They look not quite opposite, but similar...
========================
and db 3...
They looks similar again...
////////////////////////////////////////////////
After that, then what's the problem?
1. Why some of them looks opposite to each other, and some of them don't? What is the reason behind this?
2. Am I thinking in a wrong way? Can I actually think in terms of an intuitive relation between continuous and discrete cases of the wavelet?
3. If not, then how should we link them two together? Is it related to any mathematical properties? Any related materials explain about this relation?
Thanks for your time in reading this.
regards,
wolfrain