Let's talk about the concept of frequency encoding.

Again, please keep in mind that with respect to spatial encoding,

the coordinate in case space at a certain time

is determined by the integral area of gradient as a function of time along each axis.

So integral area of gradient

determines location on the frequency domain or called K-space.

So k_x corresponds to gamma hat g_x t_x and k_y correspond to gamma hat g_y t_y.

So this is linear multiplication of time and gradient.

It's actually corresponding to the integral area of the gradient.

Okay, so let me give you an example of pulse sequence shown here.

So this is g_x and g_y.

So this is right after slide let's assume like that then the location one,

at the location time 0.1,

there is no gradient is applied.

So there is a gradient g_x but there's no time so the integral area is going to be zero.

So that is going to start from the center of the frequency domain. So it's zero.

But at the time point of two,

so there is integral area along x direction,

so it's going to move to the location two.

So if we sample a data at number

one and that can be used to fill the case-based center as shown here,

and the if we sample another point at time point number two,

then it can be used to sample a point here.

Okay, it's going to move along x direction.

For instance, and then number three case,

there's time integration along y direction but the polarities minus so it's going

to move downward along y direction and it can be used to

sample a point here if we sample a data as number three.

Then number four and then there's a narrative gradient along g_x and then

the area is a little bit bigger so it's going to be moved or folder.

So it can be used to sample a point number four as shown here.

Therefore, the number of five case,

both g_x and g_y,

they are applied all together and then it's going to move in

this direction because both x and y accumulate as a function of time.

So it's going to move all the way along there.

Then for the number five,

it'll be used to sample here and

the number six and so x direction

and it's with a negative polarity it going to move left.

Then number six, from number six number to number seven.

So both gradient, x and the y direction, is turned on.

So it's going to move along this direction,

minus x, minus y.

Then folder number seven to eight,

at the number eight positive gradient along

x direction so it's going to move along this direction

and negative gradient along y direction is going to move along this direction.

So it's going to move like that and return back to original case-based center.

So as shown in this example,

summation of integral area of

gradient determines the location on the frequency domain for the sampled data.