EE261 The Fourier Transform and its Applications Fall 2007 Syllabus and Schedule The following schedule is an approximation, not a contract. Use it to plan your reading, and please read the material before coming to class. September 24 Introductions Periodicity and Fourier series (Sections 1.1 – 1.4) September 26 Fourier series and orthogonality Prob Set 1 handed out September 28 Fourier series, continued Notes We won’t cover Sections 1.10, 1.11 and 1.14 – 1.18 in class; inner products, convergence of Fourier series, Gibbs phenomenon October 1 Applications of Fourier series (Section 1.13) Prob Set 2 handed out October 3 Meet the Fourier transform Prob Set 1 due October 5 Fourier transform properties and examples Pay attention to “duality.” We won’t derive all the formulas in class – but we’ll use them all. This chapter can serve as a reference October 8 Fourier transform properties and examples, cont’d Prob Set 3 handed out (Chapter 2) October 10 Convolution (Sections 3.1 – 3.3) Prob Set 2 due October 12 Convolution, filters, and differential equations (Sections 3.4 – 3.5) The last part of Section 3.5 is on diffusion of charge through a cable. We won’t cover it but there’s lots of history there. Ditto for 3.11 October 15 Convolution and the Central Limit Theorem (Sections 3.6, 3.7 We won’t do the background on probability, so read this before class!) Prob Set 4 handed out October 17 Distributions Prob Set 3 due October 19 Distributions and the Fourier transform The rigorous foundation for delta functions and the generalized Fourier transform. (Sections 1.5 – 1.9) (Chapter 2) (Chapter 4 Read through all this material over this series of lectures, but skip around as suits your tastes. We’ll treat the math with a pretty light touch. We’ll use the formulas!)October 22 Operations on distributions Prob Set 5 handed out October 24 Distributions finis Deltas and more Prob Set 4 due October 26 Deltas, diffraction and III (Section 5.1-5.3) Sections 5.8 – October 29 Sampling and interpolation (Sections 5.5-5.6) Prob Set 6 handed out October 31 Sampling and Aliasing (Section 5.9) Midterm Exam Outside of class Details TBA Prob Set 5 due November 2 The discrete Fourier transform (Section 6.1 – 6.2) We won’t cover finite sampling, Section 5.8. November 5 Applications and properties of the Prob Set 7 handed out November 7 Applications and properties of the DFT, cont’d Prob Set 6 due November 9 The FFT algorithm November 12 Linear systems (Sections 7.1 – 7.3) Prob Set 8 handed out November 14 Linear time invariant systems (Sections 7. 4 – 7.8) Prob Set 7 due November 16 Digital Filters (Section 7.13) We won’t cover Sections 7.9 – 7.12 in class; matched filters, causal signals, the Hilbert transform November 26 Higher dimensional Fourier transforms Prob Set 9 handed out November 28 Higher dimensional Fourier transforms,II Prob Set 8 due November 30 Higher dimensional Fourier transforms,III Section 8.3 is on higher dimensional Fourier series with an application to random walks December 3 III and crystallography; Intro to medical imaging (Sections 8.4, 8.5) December 5 The Radon transform & medical imaging Prob Set 9 due December 7 The Radon transform & medical imaging, II The Final Exam is Thursday, December 13, 8:30 – 11:30AM. Location TBA Thanksgiving Recess November 19 - 23 (Sections 8.1 – 8.6; omitting 8.3) (Sections 8.7 - 8.11) Chapter