Question

7.5 Discrete Fourier Decomposition - By Hand 5 pts You now sample the same f(t) at 4-Hz (i.e., ?t = 0.25), starting with f? = 0 at t? = 0, and getting four discrete points (tj, fj) over one period ? a) Write out the values (tj, fj) of these four points. What's N and 2N? b) Use the four points in (a) to calculate (by-hand) the DFT for f(t): i. Calculate all the Fourier coefficients A? and B?, for 0 ? k ? N, ii. Substitute the values of the coefficients into the discrete Fourier Series representation of the earthquake function f(t) = B? + ?(... etc. ...) and express in a simplified form.

          7.5
Discrete Fourier Decomposition - By Hand
5 pts
You now sample the same f(t) at 4-Hz (i.e., ?t = 0.25), starting with f? = 
0 at t? = 0, and getting four discrete points (tj, fj) over one period ?
a) Write out the values (tj, fj) of these four points. What's N and 2N?
b) Use the four points in (a) to calculate (by-hand) the DFT for f(t):
i. Calculate all the Fourier coefficients A? and B?, for 0 ? k ? N,
ii. Substitute the values of the coefficients into the discrete Fourier Series representation
of the earthquake function f(t) = B? + ?(... etc. ...) and express in a simplified form.

7.5
Discrete Fourier Decomposition - By Hand
5 pts
You now sample the same f(t) at 4-Hz (i.e., ?t = 0.25), starting with f? =
0 at t? = 0, and getting four discrete points (tj, fj) over one period ?
a) Write out the values (tj, fj) of these four points. What's N and 2N?
b) Use the four points in (a) to calculate (by-hand) the DFT for f(t):
i. Calculate all the Fourier coefficients A? and B?, for 0 ? k ? N,
ii. Substitute the values of the coefficients into the discrete Fourier Series representation
of the earthquake function f(t) = B? + ?(... etc. ...) and express in a simplified form.

Added by Bradley S.

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