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Show that the Fourier transform map defined by (10.7) is linear map; that is, show that and ? (a) Show that the functions e2πi fn t are orthogonal over the interval 0 ≤ t ≤ T ; that is, show that
(b) Now suppose that Multiply each side by e−2πi fn t and then integrate both sides over the interval 0 ≤ t ≤ T . Use part (a) above to conclude that