So, let me try to remind you of the concept of sampling again.

So, we have a signal, one dimensional signal,

and this is impulse stream for the sampling.

Then sample the signal,

we'll have spectrum slightly different from the previous one.

So, this is the spectrum and this is the original signal intensity on the spatial domain.

So let's say this is frequency distribution of this signal,

original signal, and this is sampling for impulse stream.

So, its Fourier transform is another impulse stream

with longer distance than the previous impulse stream.

Then these two sampling means,

there's convolution between these two signals,

which means, the original spectrum is going to be repeated on the frequency domain.

If there is aliasing between these spectrums,

and we cannot recover the signal completely.

But if this sampling frequency is high enough,

so that sampling frequency determines the distance between these two events.

So, that means distance between these two repeated spectrum,

this repeated spectrum distance is longer,

bigger than the maximum bandwidth or

twice the maximum bandwidth of the signal or the full range of the spectrum.

One side represents maximum frequency or bandwidth of the signal.

So, the full range is twice the bandwidth of the signal.

So, if twice the bandwidth of the signal

is smaller than the sampling frequency

which determines the distance between these two spectrum,

then there will be no aliasing.

So, that is the concept of micro Sampling Theorem.

The sampling frequency, the distance between the repeated spectrum should

be bigger than the twice the maximum bandwidth

of the signal or the full range of the spectrum.

So, we can apply for low pass filter to the sampled version

of the signal to recover the original signal completely.

So, this low pass filter bandwidth or antialiasing filter bandwidth or placebo bandwidth,

and the sampling frequency are different,

but often in MR imaging they represent almost the same thing, considered the same.

Sometime they are used interchangeable way.

They present definitely different things,

but they sometimes are used to represent the same thing.