Here I will try to keep an updated account of what has been done so far in the course.

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)
21-23 /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 ...