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General |
MATH 416 , Spring 2016: Notes and Summary
| Lecture | Date | What was covered | Notes | Textbook Section |
| 1 | Jan. 26 | |
canceled due to snow | 1.1 |
| 2 | Jan. 28 | Introduction: Numbers and algebraic structures | get assignment 1 | 1.1 |
| 3 | Feb. 2 | Introduction: Functions, sequences and matrices | - | 1.2 |
| 4 | Feb. 4 | 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.11 | 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.18 | 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.25 | Fourier series: Definition, ONB, convergence, inversion. | Matlab Code | 3.1.3 |
| 11 | Mar. 1 | Fourier transform: Definition, Plancherel Theorem, Riemann-Lebesgue Lemma, Inversion | return assignment 4; get assignment 5. | 3.1.3 |
| 12 | Mar. 3 | Continuous Fourier Transform: Windowing; smoothing vs decay | 3.2 | |
| 13 | Mar. 8 | Discrete Fourier Transforms: DFT, FFT | return assignment 5 | 3.2 |
| - | Mar. 9 | REVIEW SESSION | - | Wed. Mar. 9, 3:30pm-5:00pm in CSIC 4122 |
| 14 | Mar.10 | - | First In-Class Test | - |
| 15 | Mar. 22 | Discrete Hartley Transform; Discrete Cosine Transforms | get assignment 6 | 3.2 |
| 16 | Mar.24 | Sampling: Lagrange interpolation | - | 4.1.1, 4.1.2 |
| 17 | Mar.29 | Sampling: Bandlimited functions; Shannon's sampling formula | return assignment 6; get assignment 7 | 4.1.3 |
| 18 | Mar.31 | Signal Estimation; Measurement, noise, likelihood, MLE, unbiased estimators | - | 4.2 |
| 19 | Apr. 5 | Signal Estimation: MAP and MMSE | return assignment 7; get assignment 8 | 5.1.2,5.1.3 |
| 20 | Apr. 7 | The Continuous Wavelet Transform; Scalogram; Inversion of the CWT | - | 5.2.1 |
| 21 | Apr.12 | Discrete Wavelet Transform: frames to basis; MRA (1) | return assignment 8; get assignment 9 | 5.2.1, 5.2.2, 5.2.3 |
| 22 | Apr.14 | MRA (2): Spaces Vj | - | 5.2.3 |
| 23 | Apr.19 | MRA (3): Spaces Wj | return assignment 9; get assignment 10 | 5.3 |
| 24 | Apr.21 | MRA (4): Linear Time-Invariant Filters | - | |
| 25 | Apr.26 | Synthesis Filter banks: scaling functions and wavelets | return assignment 10; get assignment 11 | |
| 26 | Apr.28 | Applications: Image analysis/synthesis | ||
| 27 | May. 3 | Application: Interplay between statistical signal processing and linear transforms | return assignment 11 | |
| - | May. 4 | REVIEW SESSION | - | Wed. May 4, 3:00pm-4:30pm in CSIC 4122 |
| 28 | May 5 | - | Second In-Class Test | |
| 29 | May.10 | Uncertainty Inequalities: Heisenberg principle; CRLB | Last Class | 4.2.2 |
| - | May.10 | REVIEW SESSION | - | Tues. May 10, 2:00pm-4:00pm in MATH B0431 |
| - | May. 12 | FINAL EXAM | FINAL EXAM | 8:00am-10:00am in CSIC 4122 |
