Week  Topics  Study Materials  Materials 
1 
Fundamentals of Linear Algebra: Vector spaces, Bases, Orthogonality, Orthonormality, Projection, Functions and function spaces, Orthogonal functions, Orthonormal functions, Orthogonal basis functions, Signal Representation in Fourier domain, Fourier series, Orthogonality, Orthonormality and the method of finding the Fourier coefficients, Complex Fourier series, Orthogonality of complex exponential bases


Insight into wavelets, Chapter 2

2 
Mathematical preliminaries for continuous and discrete Fourier transform, Limitations of Fourier domain signal processing


Insight into wavelets, Chapter 3

3 
Short Time Fourier Transform (STFT): Signal representation with continuous and discrete STFT, Concept of timefrequency resolution, Resolution problem associated with STFT, Heisenberg's uncertainty principle and time frequency tiling


Insight into wavelets, Chapter 3

4 
Why wavelet transform? Introduction to wavelet transform: The origins of wavelets, Wavelets and other wavelet like transforms, Different families of wavelets, Continuous wavelet transform: Continuous timefrequency representation of signals, Properties of wavelets used in continuous wavelet transform, Continuous versus discrete wavelet transform


Insight into wavelets, Chapter 3

5 
Discrete wavelet transform: Haar scaling functions and function spaces, Translation and scaling of phi(t), Orthogonality of translates of phi(t), Function space V0 , Finer Haar scaling functions, Concepts of nested vector spaces, Haar wavelet function, Scaled and translated Haar wavelet functions


Insight into wavelets, Chapter 4

6 
Orthogonality of phi(t) and psi(t), Normalization of Haar bases at different scales, Refinement relation with respect to normalized bases, Support of a wavelet system, Daubechies wavelets, Plotting the Daubechies wavelets


Insight into wavelets, Chapter 4

7 
Other wavelet Families



8 
Designing orthogonal wavelet systems (A direct approach): Refinement relation for orthogonal wavelet systems, Restrictions on filter coefficients, Unit area under scaling function, Orthonormality of translates of scaling functions, Orthonormality of scaling and wavelet functions


Insight into wavelets, Chapter 5

9 
Approximation conditions (Smoothness conditions), Designing Daubechies orthogonal wavelet system coefficients, Constraints for Daubechies' 6 tap scaling function.


Insight into wavelets, Chapter 5

10 
Discrete wavelet transform and relation to filter banks: Signal decomposition (Analysis), Relation with filter banks


Insight into wavelets, Chapter 6

11 
Frequency response, Signal reconstruction: Synthesis from coarse scale to fine scale, Downsampling, upsampling and filtering, Perfect reconstruction filters, QMF conditions, Computing initial sj+1 coefficients, Concepts of MultiResolution Analysis (MRA)


Insight into wavelets, Chapter 6

12 
Biorthogonal Wavelets: Biorthogonality in vector space, Introduction to biorthogonal Wavelet Systems, Signal representation using biorthogonal wavelet system


Insight into wavelets, Chapter 8

13 
Biorthogonal synthesis, Construction of biorthogonal wavelet system, BSplines


Insight into wavelets, Chapter 8

14 
Applications of wavelets: Applications of wavelets in signal and image processing and other related engineering fields


