Homework-3: FTs are your friend.

  1. What is the Fourier transform of the quadrature signal from a 63 MHz sine wave? (Assume there are equal real 63 MHz cosine and imaginary 63 MHz sine components.)

  2. What is the Fourier transform of a 33 ms long square pulse?

  3. What is the Fourier transform of the 63 MHz sine wave of Question 1 which is turned on for only 33 ms?

  4. What is the width of this function in Hz and in ppm when this signal is greater than 90% of its maximum value? Why is this result significant in NMR and MRI?

  5. What quadrature sampling rate is necessary to accurately record the FID from a 500 Hz wide NMR spectrum?