[solution] » question in file about fourier transform f^(v)  of a function f of time. (a) (3 points)

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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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Sep 21, 2019

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