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
## AMSE, universal thresholding= 0.002414004 AMSE, SURE thresholding= 0.0008180944 AMSE, smoothing spline= 0.001271906
Image Compression
Lena Image
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
## AMSE, universal thresholding= 0.002414004 AMSE, SURE thresholding= 0.0008180944 AMSE, smoothing spline= 0.001271906
Image Compression
Lena Image