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

that covers the following:


  • 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.


  • 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.

  • 2
    $\begingroup$ 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. $\endgroup$ – Willie Wong Jan 30 '14 at 15:59
  • $\begingroup$ yes this is the first intro part i'll add the rest of the part now thanks @WillieWong $\endgroup$ – DeeRam Jan 30 '14 at 16:16
  • $\begingroup$ My suggestion is to stay away from Mallat. I found that book to be horribly written with very awkward and unnecessarily complicated notation. $\endgroup$ – AnonSubmitter85 Jan 31 '14 at 2:20

In that case, I recommend "A Friendly Guide to Wavelets" by Gerald Kaiser. It includes a clear introduction to linear algebra, some fundamentals of Fourier Analysis and Windowed Fourier Transform, and a presentation of wavelets for those who had not heard of that.


How about learning the subject from Wavelets and Filter Banks, by Gilbert Strang and Truong Nguyen. The legendary MIT Professor has a great knack of explaining stuff.


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