Mathematica Stack Exchange is a question and answer site for users of Mathematica. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am calculating approximations using wavelets but outside the multi resolution analysis framework; particularly, I am not using the built-in wavelet transforms.

Still, I need to calculate coefficients and therefore I am wondering how to calculate the support of a given wave in order to know where to start and stop calculating coefficients for WaveletPhi[wave] and WaveletPsi[wave] for a given resolution level. Therefore, I need to know the support for a given wavelet.

I suspect that I could use WaveletFilterCoefficients[wave,"PrimalHighpass"] and, similarly for "PrimalLowpass"; but it is just a hunch, not sure how.

Basically, I am after something along the lines of: WaveletSupport[wave] -> {a,b} support of given wavelet (For the moment just orthogonal wavelets, not biorthogonal).


share|improve this question
What families are you using ? – Sektor Jun 10 '14 at 0:16
I want to use DaubechiesWavelet. – carlosayam Jun 10 '14 at 0:37
up vote 4 down vote accepted

Both the scaling and wavelet functions of the DaubechiesWavelet are compactly supported on the interval $\left [ 0, N-1 \right ]$, where N is the number of "taps", the impulse response length or just the length of the filter. Choose the one that suits you ^^ Bear in mind that the notation in Mathematica is slightly different - The wavelets are classified by the number of vanishing moments, rather than filter lengths, so the DaubechiesWavelet[2] has 2 vanishing moments and the filter length is 4

There is another definition specifying the bounds of the support:

If the scaling function is supported on $\left [ LB, UB \right ]$ then the wavelet function is supported on $\left [ \frac{LB-UB+1}{2}, \frac{UB-LB+1}{2} \right ]$

Just a simple experiment to confirm the statement (undocumented function):

      "PrimalScalingFunction", 8, WorkingPrecision -> MachinePrecision], 
      PlotRange -> All]

Mathematica graphics

      "PrimalWaveletFunction", 8, WorkingPrecision -> MachinePrecision], 
      PlotRange -> All]

Mathematica graphics

share|improve this answer
Thanks a lot @Sektor, but the support of second graph (wavelet) seems to be around [-6,4], isn't it? This is what confuses me, because the values for $x$ where $\psi _{j,k}(x)$ is guaranteed to be zero don't seem be just outside of [0,$2^{-j}$]. – carlosayam Jun 10 '14 at 1:47
No need to ! :) Look again :) – Sektor Jun 10 '14 at 8:31
Thanks a lot @Sektor. Your comment about the "impulse response" got me thinking and I was able to arrive to something similar to yours using the "PrimalHighpass" coefficients (it is most likely the same, but I will double check with yours; fantastic.) – carlosayam Jun 10 '14 at 11:53
@caya Thank you for the question and I am glad to help :) BTW Do not hesitate to share something about wavelets or x-lets, in general - something you are working on, etc, if you can of course :) – Sektor Jun 10 '14 at 12:02

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.