How Does Gradient Direction Affect NMR Signal Characteristics?

[johnq2k7]

Suppose that you obtain a one dimension magnetic resonance image from two water-filled cubic shaped containers arranged as shown below. This diagram is a cross-section of the cubic containers in the x-y plane.

figure description:
-one of cube's is 2 cm wide, the other is 1 cm wide, and the 1cm cube is on top of the
2cm cube
-y direction, and x-direction are denoted as usual

To obtain the one-dimensional image a gradient echo MRI signal is acquired while a magnetic
field gradient of 10 mT/M in the x-direction is held on. Assume that signal (S(t)) has the form
S(t) = Sa(t) exp(-i2pi*(f_a)(t) + Sb(t) exp(-i2pi*(f_b)(t) , where Sa(t) and Sb(t) are both sinc functions.

Recall that the sinc (Fsinc(t)) defined as:

F_sinc(t)= {A*sinc(pi*(delta of frequency)(t)]/ (pi*(delta of frequency)(t)

which is the Fourier Transform of a rectangular function of frequency with width delta frequency, where A is the areaunder this rectangular function

a) Determine the time between the zeros of Sa(t) and Sb(t).
b) Determine the frequency difference |fa - fb|.
c) Suppose that another one-dimensional image is acquired of the same water-filled
cubes, but this time with the 10 mT/M gradient in the y-direction. For this gradient echo
signal, determine the time between the zeros of Sa(t) and Sb(t) and determine the frequency
difference |fa - fb|.

Please help... need a lot of help here!

 

[marcusl]

The forum rules require that you show your work or your attempt at solving the problem. Hint: Beyond one MRI fact, this problem is about Fourier transform properties.