| Phys 198 | May 2, 1997 |
Problem 11. What is done to a one-dimensional set of 16 data values if the Fourier transform is to be frequency shifted so that the zero frequency is in the middle of the display?
Use the frequency-shifting property of the discrete Fourier transform:
where n and m are integers representing the various frequency components and N is the number of data points. Since it is desired to center the zero frequency the desired frequency shift requires m = N/2. Putting this value into the right-hand-side of the frequency-shifting equation gives
However, looking at the quantity in square brackets in the last form of the equation and recalling that
,
it is seen that to shift the frequency spectrum by N/2, i.e., to center it, the N elements in the original data set x(k) should be multiplied in sequence by
and then the modified set is Fourier transformed in the usual way.
Send Mail or Comments: matthysd@vms.csd.mu.edu
 |
 |
Visitors to this page :