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Exercise 4

Due Date: 8th June 2011 (till 23:59)

For the theoretical parts of the solutions either type them and send them as a pdf file, or write them down as a hard copy and deliver it in the box near the lecture room (48-462), the box is labelled "Exercises / AG. Prof. Breuel".  

Thomasson-Lanczos-Cooley-Tukey-Gauss Lemma (30 points)

State and prove the TLCTG Lemma.

Fourier Transform of a Gaussian (30 points)

Derive the mean and variance of the Fourier transform of a Gaussian.

Translation (30 points)

Given a signal s(x), assume it is translated by an amount d.  This corresponds to a change in phase in the corresponding Fourier transform F[s](k).  Derive the transformed signal.