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Comment : Symmetries of the Fourier transform quiz
Comment : This quiz is designed to test your knowledge of how the Fourier transform behaves under
Comment : various transformations. The quiz is phrased so that it does not matter what your normalization
Comment : conventions are for the Fourier transform. Note: some of these questions lie outside the scope of Math 133.
Comment : All abelian groups are assumed to be amenable (if you don't know what this means, ignore it).

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Question 1: If f is a function on an abelian group G, and f is translated by a shift h, then the Fourier transform of f is

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	Shifted in the direction h.
	Shifted in the direction -h.
	Modulated by a character with frequency -h or h (depending on conventions)
	Dilated by h.
	Dilated by 1/h.
	Convolved by h.
	Multiplied by h.