General Home

MATH 416 , Spring 2017: Notes and Summary

 Lecture Date What was covered Notes Textbook Section 1 Jan. 26 Introduction: Numbers and algebraic structures get assignment 1 1.1 2 Jan. 31 Introduction: Functions, sequences and matrices - 1.2 3 Feb. 2 Vector Spaces, Linear Independence, Spanning, Basis - 2.1 4 Feb. 7 Vector Spaces, Linear Independence, Spanning, Basis return assignment 1; get assignment 2 2.1 5 Feb. 9 Vector spaces: Basis theorem; Norms and Banach space - 2.1 6 Feb.14 Scalar products and Hilbert spaces; Cauchy-Schwarz inequality; Schauder basis; Orthonormal basis;Gramm-Schmidt orthonormalization; biorthogonal basis. - 2.2 7 Feb.16 Subspaces, Linear transformations, Matrix representation, Matrix Algebra return assignment 2; get assignment 3. 2.2 8 Feb.21 The adjoint operator; orthogonal projections - 2.2 9 Feb.23 Projections onto range and kernel of linear operators; direct sums and orthogonal decompositions return assignment 3; get assignment 4 2.2 10 Feb.28 Fourier series: Definition, ONB, convergence, inversion. Matlab Code 3.1.3 11 Mar. 2 Fourier series: Parseval and Plancherel Theorems, Inversion; Examples return assignment 4; get assignment 5. 3.1.3 12 Mar. 7 Continuous Fourier Transform/Fourier Integrals: Plancherel Theorem and Inversion; translation and modulation; smoothing vs decay 3.1.3 13 Mar. 9 Discrete Fourier Transforms: DFT, FFT return assignment 5; get assignment 6 3.2 14 Mar.14 Discrete Hartley Transform; Discrete Cosine Transforms university closed due to weather 3.2 - Mar.14 - REVIEW SESSION 5:30pm-7:30pm in CSIC 4122 - Mar.15 - REVIEW SESSION 3:00pm-5:00pm in MATH 0402 15 Mar.16 - First In-Class Test - - Mar.20-24 - SPRING BREAK - 16 Mar.28 Discrete Cosine Transforms (I-IV) - 3.2 17 Mar.30 Sampling: Lagrange interpolation - 4.1.1, 4.1.2 18 Apr. 4 Sampling: Bandlimited functions; Shannon's sampling formula return assignment 6; get assignment 7 4.1.3 19 Apr. 6 Signal Estimation; Measurement, noise, likelihood, MLE, unbiased estimators - 4.2 20 Apr.11 Signal Estimation: MAP and MMSE return assignment 7; get assignment 8 5.1.2,5.1.3 21 Apr.13 Noise Reduction in Speech Processing using the Wiener Filter - Matlab code 22 Apr.18 The Continuous Wavelet Transform; Scalogram; Inversion of the CWT return assignment 8; get assignment 9 5.1 23 Apr.20 Example of a CWT; Multi Resolution Analysis: Spaces Vj - 5.1,5.2 24 Apr.25 MRA (2): Spaces Wj return assignment 9; get assignment 10 5.2 25 Apr.27 MRA (3): Linear Time-Invariant Filters - 5.2 26 May 2 Synthesis Filter banks: scaling functions and wavelets return assignment 10; get assignment 11 5.2 27 May 4 Low-pass and high-pass filters. 5.2 - May 4 REVIEW SESSION 3:30pm-5:30pm in CSIC 4122 28 May 9 Applications: Image analysis/synthesis. Uncertainties: Heisenberg Principle and CRLB return assignment 11 4.2.2 29 May 11 - Second In-Class Test - May 12 - REVIEW SESSION 11:00am-1:00pm in CSIC 4122 - May 13 - FINAL EXAM 8:00am-10:00am in CSIC 4122