(1) A function f(x) can be expressed in terms of a Fourier transform f(x) = 2:an neta"w". with 3e'z'l'(1 +e2i'' 2imr) 1 = 411.2112 3 5,71 =...
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屏幕快照 2019-09-23 20.11.38.jpg

(1) A function f(x) can be expressed in terms of a Fourier transform f(x) = 2::an neta—&quot;w&quot;. with 3e‘z‘l”(—1 +e2i'“ —2imr) £1 = 411.2112
3
5,71 = 0 .31th [30 points] Plotting this function poses a few challenges. First, the function is an infinite
sum. We cannot plot all the terms of the function. However. the terms for large Inl are less
important that those for small Inl, such that the function converges [almost everywhere) if
the sum is computed from n = —N to n = N, for some N. Plot the finite sums for N=3, 20,
and 100 for x = —S to x = 5. Describe in words what you see happening as N increases. [20 points] What function did I use to calculate the values for 1;? Write down the integral
that gives the value of fil quoted above.

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