Can I perform DWT with B-spline?

[Ahmed Torky]

Hello,

I am a bit puzzled and I hope I can get some insight.

Multi-level signal decomposition is possible on time discrete data with discrete wavelet transforms using wavelets. I have been using sym, coif and dmey families. However, in analysis of seismic wave, B-spline of order 4 have been used. In an article of earthquake engineering it is stated that "The B-spline with an order of 4 was applied to the mother wavelet."

I have tried coding the following:

(a, d) = pywt.dwt(signal, 'fbsp4-1.0-1.0')

Unfortunately, I get the obvious error:

ValueError: A ContinuousWavelet object was provided, but only discrete Wavelet objects are supported by this function.

Is there an obvious way to use Frequency B-Spline wavelets with dwt for multi-level signal decomposition?

Do I have to make custom wavelets that approximate the B-spline of order 4?

I would appreciate any support.

Thank you.

Ahmed

[aama...@gmail.com]

Hi

Hope anyone could shed some light on this post pretty please!

Thank you

Ahmed

[Gregory Lee]

On Mon, Aug 31, 2020 at 9:18 PM aama...@gmail.com <aama...@gmail.com> wrote:

Hi

Hope anyone could shed some light on this post pretty please!

Thank you

Ahmed

I think the b-spline wavelets are infinite impulse response, so are better implemented in the Frequency domain. However PyWavelets DWT is only implemented using time-domain (or spatial domain) convolution. It might be possible to implement a finite length approximation to these wavelets as in https://doi.org/10.1137/S0036141092234086, for example, but there is no built-in PyWavelets function for these wavelets.

 

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