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General |
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 | university closed due to weather | 3.2 | |
| - | Mar.14 | - | ||
| - | 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 |
