psi_hat_exact function

discrete Fourier transform of the wavelet

Computes the discrete Fourier transform of the wavelet associated to the given filter using scaling_function. The length of the Fourier transform is equal to the length of the grid where the wavelet is evaluated.

psi_hat_exact(filter,J=10)

Arguments

• filter: wavelet filter as obtained with scaling_filter.
• J: 2^J corresponds to the size of the grid for the discretisation of the wavelet. The default value is set to 10.

Returns

• psih: Values of the discrete Fourier transform of the wavelet.

• grid: Frequencies where the Fourier transform is evaluated.

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

Examples

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