Outline

Reminder

• Linear signal decomposition
• Optimal linear transform: KLT, principal component analysis

Discrete cosine transform

• Definition, properties, fast implementation

Review of multi-rate signal processing

Wavelet and filter banks

• Aliasing cancellation and perfect reconstruction
• Spectral factorization: orthogonal, biorthogonal, symmetry
• Vanishing moments, regularity, smoothness
• Lattice structure and lifting scheme
• M-band design – Local cosine/sine bases

Detail here Lecture