Arun K. Tangirala

1. Introductory Lecture

   1. Part I (bird's eye view of multi scale systems; Fourier, Short-Time Fourier and Wigner-Ville distributions)

   2. Part II (brief non-mathematical tour of wavelet transforms)

2. Basic Definitions and Concepts

   1. Part I (deterministic and stochastic signals, periodic signals,sampling)

   2. Part II (power and energy signals; cross- and auto-covariance functions for deterministic signals)

   3. Part III (signal representations and linear algebra)

3. Fourier Series and Transforms

   1. Continuous-time Fourier series

   2. Continuous-time Fourier transforms

   3. Discrete-time Fourier series

   4. Discrete-time Fourier transforms

   5. Properties of Fourier transforms

   6. Discrete Fourier transform and Periodogram

4. Time-Frequency Analysis

   1. Duration and Bandwidth

   2. Bandwidth equation and Instantaneous frequency

   3. Instantaneous frequency and Analytic signals

   4. Duration-Bandwidth principle

   5. Requirements of time-frequency analysis techniques

   6. Joint energy density

5. Short-time Fourier Transform (STFT)

   1. STFT: Concepts and Definition

   2. Properties of STFT​​​​​

   3. Practical aspects of STFT

   4. Closing remarks (on STFT)

6. Wigner-Ville Distributions (WVD)

   1. WVD: Concepts and Definition​​

   2. Properties of WVD - Part I

   3. Properties of WVD - Part II

   4. Discrete WVD

   5. Pseudo- and smoothed WVD

   6. Cohen's class and smoothed WVD

   7. Cohen's class and Ambiguity functions

   8. Affine class and Closing remarks

7. Wavelet Transforms

   1. Continuous wavelet transforms (CWT)

   2. Scale to Frequency

   3. Computational aspects of CWT

   4. Scalogram and MATLAB demo

   5. Scaling function

   6. Wavelets

   7. Applications of CWT

8. Discrete wavelet transform (DWT)​​

   1. DWT: Concept and Definition

   2. Orthogonal scaling function bases and multi-resolution analysis (MRA)

   3. Wavelet filters and fast DWT algorithm

   4. Wavelets ​​for DWT

   5. Applications of DWT

9. Closing Remarks and Road Ahead

   1. Glimpses of advanced topics​

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