Course handouts:
 Course Organization .html.
 Course Survey: .pdf.
Lectures:
 Lecture 1: Timeinvariant
(linear) operators, convolutions, continuoustime Fourier transform
 Lecture 2: Fourier inversion
formula, convolution theorem, central limit theorem via Fourier
transforms
 Lecture 3:
ParsevalPlancherel theorem, Fourier transform of squareintegrable
functions, Fourier transform of distributions, Fourier transform in
higher dimensions
 Lecture 4: The (Weyl) Heisenberg uncertainty principle
and its interpretation in quantum mechanics
 Lecture 5: Poisson
summation formula, sampling and the aliasing formula, Shannon's
sampling theorem
 Lecture 6: Discrete
convolutions, Fourier series, another look at Shannon's sampling
theorem
 Lecture 7: Numerical
accuracy of the trapezoidal rule, Fourier transform of finite signals, FFTs
 Lecture 8: Xray tomography, Xray
propagation and Beer's law
 Lecture 9: Xray
tomography, Radon transform, backprojection, Radon inversion formula
 Lecture 10: Xray
tomography, illposedness of the inverse problem, regularized
inversion
 Lecture 11: Nonuniform fast
Fourier transforms (NUFFTs)
 Lecture 12: Magnetic
Resonance Imaging (MRI), nuclear magnetic resonance (NMR), Bloch
phenomenological equations, relaxation times
 Lecture 13: Magnetic
Resonance Imaging (MRI), simple imaging experiment, signal equation
 Lecture 14: Magnetic
Resonance Imaging (MRI), roles of relaxation times, selective excitation
Lecture 15: Wave optics,
the phenomenon of diffraction, history, FresnelKirchhoff integral formula
 Lecture 16:
RayleighSommerfeld diffraction theory, Fresnel diffraction,
Fraunhoffer diffraction, examples
 Lecture 17: Lenses, thin
lenses, Fourier transform properties of thin lenses
 Lecture 18: Image
formation, relation between object and image, effects of diffraction
 Lectures 19:
The Wiener filter: KarhunenLoeve decomposition of stochastic
processes, stationary processes, estimation of Gaussian processes
