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Exercise 6.33
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Exercise 6.33
Exercise 6.33
Exercise 6.33. Show that the Discrete Fourier Transform in CN of the Fourier basis vector e; is given by the standard basis vector sj, that is, j = sj, for 0 ≤ j≤N-1. Start with the case N = 4. Although the Fourier basis is not localized at all, its Fourier trans- form is as localized as possible. We say the Fourier basis is localized in frequency, but not in space or time.
Exercise 6.33. Show that the Discrete Fourier Transform in CN of the Fourier basis vector e; is given by the standard basis vector sj, that is, j = sj, for 0 ≤ j≤N-1. Start with the case N = 4. Although the Fourier basis is not localized at all, its Fourier trans- form is as localized as possible. We say the Fourier basis is localized in frequency, but not in space or time.