psi_hat_exact {multiwave}

discrete Fourier transform of the wavelet

Description

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.

Usage

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.

Value

psih

Values of the discrete Fourier transform of the wavelet.

grid

Frequencies where the Fourier transform is evaluated.

Author(s)

S. Achard and I. Gannaz

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.

See Also

DWTexact, scaling_filter

Examples

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