question in file about fourier transform f^(v) of a function f of time.
(a) (3 points) The Fourier transform f?(? ) of a function f of time is shown in Figure
2. Suppose that the function f is sampled once per second. Sketch the Fourier
transform of the sampled function on the graph. Figure 2: Fourier transform for question 9
(b) (2 points) What should the sample rate be so that the original function can be
recovered from the samples with no error? Assume the units for frequency are
Hertz. Briefly justify your answer. f(t) = t on [??, ?] = 2[(-1)n+1/n sint
2[(-1)n+1/n sinpi - 2[(-1)n+1/n sin(-pi) = 2[(-1)n+1/n(sinpi -sin(-pi)) = 0.22*(-1)n+1/n
but, i = (-1)1/2
Thus, 0.22*(-1)n+1/n =0.22i2(n+1)/n
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Oct 14, 2020EXPERT
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