date 
what we did 
comments 
29/10  1/11 
 We have mostly worked on Ch. 1 in Bergh: Notes on
generalized functions.
 definition and some properties of the Fourier transform
 the inversion formula
 the class S
 convolution and autocorrelation
 the tempered distributions, S' ,
differentiation, multiplication by functions, the Fourier transform.
 some examples: Dirac measure, the finite part of
x^{3/2} H(x)


5/11  8/11 
 We have finished Chapter 1 in Bergh
 Most of the relevant details in Bracewell: ch1 ch10.
Some more about power spectra, and some inequalities related
to Fourier analysis remain.


12/11 
 Rules for computing DFT
 The fast Fourier transform


14/11 
 Cost of computing the FFT
 The uncertainty relation
 Fourier transforms and tempered distributions in higher
dimension.
 tensor products of tempered distributions


15/11 
 Tensor products of tempered distributions
 Some formulas related to mulitdimensional fourier
transforms
 The Hankel transform (in 2 and more dimensions)


19/11 
 A little about the assignement 1: How to experiment
with filters and audio signals from e.g. music.
 The Abel transform
 The Radon transform: its definition, and the inversion
theorem (without proof so far)


2123 /11 
 note that there only lectures this week.
 The Radon transform: proof of the inversion formula
 The Hilbert transform and the analytical signal
 The fourier transform of homogeneous distributions, and
in particular of (z)^{1/2}
 The Uncertainty principle
 A little about probability theory: a proof of the
central limit theorem
 Tempered measures, positive measures and positive
definite distributions.
 Beginning of discrete filter theory: linear time invariant and
causal filters, FIR and IIR ...

