National University of Sciences and Technology
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EE-933 Time Frequency Analysis
Campus MCS
Programs PG
Session Spring Semester 2017
Course Title Time Frequency Analysis
Course Code EE-933
Credit Hours 3+0
Pre-Requisutes Signals and System, Laplace Transform, Fourier series, Fourier Transform, matrix algebra
Course Objectives To familiarize the students with the basic principles of digital signal processing and the signal analysis tools in time and frequency domains.
Detail Content Review of Linear spaces, Hilbert spaces, Banach Spaces, Projection theorem, Parseval’s theorem, Review of Transform Analysis, Fourier analysis and Z-Transform Gabor Transform, spectrogram Time and Frequency Joint Perspective and ideal behavior The Uncertainty Principle and Time frequency bandwidth Product Wavelet Transform in General Time Frequency Plane & its Tilings Proof that a non-zero function cannot be both time and band-limited Haar Wavelet and Multire solution Analysis Frequency domain analysis of Haar Multirate Digital Signal Processing Filter Bank Analysis, Synthesis and Perfect Reconstruction Mallat Algorithm Daubechies Family of MRA Reconstruction & Admissibility The Theorem of Multiresolution Analysis JPEG 2000 5/3 Filter Bank& Spline MRA Orthogonal Multiresolution Analysis with Splines Building Piecewise Linear Scaling Function, Wavelet The Wavelet Packet Transform The Lifting Structure & Polyphase Matrices/ approach Modulation Analysis and Filter Bank, Applications Vanishing moments and regularity Geometric Wavelets. Wavelet Applications; Singularity detection, de-noising, embedded coding, shrinkage and sparse representation of images and videos.
Text/Ref Books
  1. S. Mallat, “A wavelet Tour of Signal Processing,” Academic press, 2nd Edition.
  2. G. Strang and T. Q. Nguyen, “wavelets and filter banks,” Wellesley-cambridge Press, revised Edition, 1988.
  3. L. Cohen, “Time Frequency Analysis,” Prentice Hall, 1995.
Time Schedule Spring Semester 2015
Faculty/Resource Person Dr. Imran Touqir, PhD