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Jan 02, 2025
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EE 7733 - Time Frequency Analysis and Wavelet Signal Processing and Applications
Good knowledge of Fourier transforms, properties, basic DSP: sampling, DTFT, and discrete time filtering (grad DSP course EE6713) required. Structured to cover two areas: the broad area of time-frequency (TF) analysis, and the focused application of wavelets to various signal processing tasks. In TF analysis, covers the fundamental need for this type of analysis, the uncertainty principle, densities, characteristic functions, and mathematical representations, the short-time Fourier transform and Spectrogram, the Wigner distribution, other TF distributions, and some TF distribution construction methods. Various examples will be used to illustrate the power and challenges of TF analysis. In the wavelet section, connects TF analysis to the use of wavelets, and covers multiresolution analysis, 1D and 2D compression of signals and images, noise reduction, and signal modulation. MATLAB Wavelet Toolbox used to implement, study, and visualize the operation of wavelet filter banks.
Requisites: EE 6713
Credit Hours: 3
Repeat/Retake Information: May not be retaken.
Lecture/Lab Hours: 3.0 lecture
Grades: Eligible Grades: A-F,WP,WF,WN,FN,AU,I
Learning Outcomes:
- Ability to apply the lifting algorithm implementation of integer-to-integer wavelet transforms.
- Ability to compute the STFT and Wigner distributions.
- Ability to derive marginal distributions from joint distributions, and compute multiple types of averages.
- Ability to determine when conventional Fourier analysis is inadequate and TF analysis needed for non-stationary signals.
- Ability to distinguish between dyadic wavelet and wavelet packet decomposition of signals and images, and apply them in lossless and loss data compression techniques.
- Ability to generate TF distributions via the characteristic function and kernel methods.
- Ability to implement and apply the discrete wavelet transform using quadrature-mirror filter banks.
- Ability to represent signals in analytic form.
- Ability to understand and apply the signal uncertainty principle.
- Ability to use wavelet basis functions as an alternative to Fourier bases.
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