A Short Wavelet Tour
Haar wavelets
Daubechies wavelets
Chord for Violin, Cello & Bass
Fragment for Wavelet Trio for Violin, Cello & Bass
Fourier performance
Wavelet performance
## [1] 5.937927 5.937927 5.937927 5.937927 5.937927 5.937927 5.937927 5.937927
## [9] 5.937927 5.937927 5.937927
Doppler example \(g(x)=\sqrt{x(1-x)}\sin\left(\frac{2.1\pi}{x+0.05}\right)\)
## [1] 3.57212 3.57212 3.57212 3.57212 3.57212 3.57212 3.57212 3.57212 3.57212
## [1] 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282
## [9] 3.506282
## [1] 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282
## [9] 3.506282
## [1] 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282
## [9] 3.506282
## MSE, universal thresholding= 1.23597 MSE, SURE thresholding= 0.4188643 MSE, smoothing spline= 0.651216
Haar wavelets
Daubechies wavelets
Chord for Violin, Cello & Bass
Fragment for Wavelet Trio for Violin, Cello & Bass
Fourier performance
Wavelet performance
## [1] 5.937927 5.937927 5.937927 5.937927 5.937927 5.937927 5.937927 5.937927
## [9] 5.937927 5.937927 5.937927Doppler example \(g(x)=\sqrt{x(1-x)}\sin\left(\frac{2.1\pi}{x+0.05}\right)\)
## [1] 3.57212 3.57212 3.57212 3.57212 3.57212 3.57212 3.57212 3.57212 3.57212
## [1] 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282
## [9] 3.506282
## [1] 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282
## [9] 3.506282
## [1] 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282 3.506282
## [9] 3.506282## MSE, universal thresholding= 1.23597 MSE, SURE thresholding= 0.4188643 MSE, smoothing spline= 0.651216