# Need to learn wavelet, suggest steps and resources

I am looking for a good introduction to wavelets and wavelet transforms.

that covers the following:

Basics

• Vector Spaces – Properties– Dot Product – Basis – Dimension, Orthogonality and Orthonormality
• Relationship Between Vectors and Signals – Signal Spaces
• Concept of Convergence
• Hilbert Spaces for Energy Signals
• Fourier Theory: Fourier series expansion, Fourier transform, Short time Fourier transform, Time-frequency analysis.

Multi-resolution analysis

• Definition of Multi Resolution Analysis (MRA)
• Haar Basis
• Construction of General Orthonormal MRA
• Wavelet Basis for MRA
• Continuous Time MRA Interpretation for the DTWT
• Discrete Time MRA
• Basis Functions for the DTWT
• PRQMF Filter Bank

Continuous wavelet transforms

• Wavelet Transform – Definition and Properties – Concept of Scale and its Relation with Frequency
• Continuous Wavelet Transform (CWT)
• Scaling Function and Wavelet Functions (Daubechies-Coiflet, Mexican Hat, Sinc, Gaussian, Bi Orthogonal)
• Tiling of Time – Scale Plane for CWT

Discrete wavelet transform

• Filter Bank and Sub Band Coding Principles
• Wavelet Filters
• Inverse DWT Computation by Filter Banks
• Basic Properties of Filter Coefficients; Choice of Wavelet Function Coefficients
• Derivations of Daubechies Wavelets
• Mallat's Algorithm for DWT
• Multi Band Wavelet Transforms Lifting Scheme
• Wavelet Transform Using Polyphase Matrix Factorization
• Geometrical Foundations of Lifting Scheme
• Lifting Scheme in Z –Domain.

Applications

• Wavelet methods for signal processing
• Image Procession: Compression Techniques: EZW–SPHIT Coding; Denoising Techniques: Noise Estimation – Shrinkage Rules – Shrinkage Functions – Edge Detection and Object Isolation, Image Fusion, and Object Detection.

Please suggest the steps,resources and materials to do the same. And the time frame to master in this.

• Your detailed list of "covered material" has relatively little to do with wavelets per se. The first third of your list is covered in any linear algebra textbook/course; the middle third seems to be about signal processing; and the last third is applied Fourier theory. I would say the list you gave are more like prerequisites for starting to study wavelets. – Willie Wong Jan 30 '14 at 15:59
• yes this is the first intro part i'll add the rest of the part now thanks @WillieWong – DeeRam Jan 30 '14 at 16:16
• My suggestion is to stay away from Mallat. I found that book to be horribly written with very awkward and unnecessarily complicated notation. – AnonSubmitter85 Jan 31 '14 at 2:20