scaling_function function

scaling function and the wavelet function

Computes the scaling function and the wavelet function (for compactly supported wavelet) using the cascade algorithm on the grid of dyadic integer $2^{-J}$

scaling_function(filter,J)

Arguments

• filter: wavelet filter as obtained with scaling_filter.
• J: value of the largest scale.

Returns

• phi: Scaling function.

• psi: Wavelet function.

References

G. Fay, E. Moulines, F. Roueff, M. S. Taqqu (2009) Estimators of long-memory: Fourier versus wavelets. Journal of Econometrics, vol. 151, N. 2, pages 159-177.

S. Achard, I. Gannaz (2016) Multivariate wavelet Whittle estimation in long-range dependence. Journal of Time Series Analysis, Vol 37, N. 4, pages 476-512. http://arxiv.org/abs/1412.0391.

S. Achard, I Gannaz (2019) Wavelet-Based and Fourier-Based Multivariate Whittle Estimation: multiwave. Journal of Statistical Software, Vol 89, N. 6, pages 1-31.

Author(s)

S. Achard and I. Gannaz

See Also

DWTexact, scaling_filter

Note

This function was rewritten from an original matlab version by Fay et al. (2009)

Examples

res_filter <- scaling_filter('Daubechies',8);
filter <- res_filter$h
scaling_function(filter,J=6)