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.(adsbygoogle = window.adsbygoogle || []).push({});

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!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# NMR Signal Physics Question! Please help!

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