## Frequency and amplitudes in k-space

Dave Higgins
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Joined: Fri Sep 02, 2005 2:21 pm
Location: Leeds, UK
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### Frequency and amplitudes in k-space

Hi Lauren,

On the ReviseMRI.com feedback form, you asked
I am confused about amplitude and frequency. Signals in the edges of k-space are generally high frequency / low amplitude or are they low frequency / high amplitude signals?
The answer is: higher (spatial) frequency, lower (average) amplitude.

Frequency
Signals at the centre of k-space are represent a low spatial frequency in the image - large waves.
Signals at the periphery of k-space are represent a high spatial frequency in the image - fine, narrow waves.

Amplitude
The amplitudes in k-space could be anything - that depends on what's in the magnet. A particular spatial frequency may not be present (low amplitude - a small value in k-space), or it may be very strong (high amplitude - a large value in k-space).

When we spatially encode the MRI signal which is emitted from the patient, we use magentic field gradients which result in a variation of the precessional (Larmor) frequency in the patient. However, it's important to remember that when we talk about k-space frequency, we are no longer talking about precessional frequency. We are talking about spatial frequencies which refer to image content.

It is not surprising that the low spatial frequency data in k-space (at the centre) has higher amplitude than the rest of k-space (on average - any particular point still could take any value within reason) because that's the type of data needed to "draw" the main contrast of an image (see the first k-space tutorial on this site).

Regards
Dave

PS I have referred to "values" in k-space in this discussion. Actually each "value" in k-space is a complex number with a real and imaginary part. (Not that the "imaginary" part is in any way made up - we do measure it!)

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