1. Receiver Bandwidth affects signal-to-noise ratio (SNR)
This is a schematic MR signal or echo, just one of the many MR signals needed to create an MR image. It is one line of k-space. It takes a certain amount of time to read out / sample this signal. We do this with the frequency encoding (readout) gradient.
affects
signal-to-noise ratio (SNR)
chemical shift artefact
(also the echo time, TE)
Don’t get confused: receiver bandwidth is different from the transmit bandwidth, which refers to the RF excitation pulse used for slice selection in a pulse sequence. The receiver bandwidth is the range of frequencies used to sample the MR signal. Generally, if someone mentions bandwidth, especially if they say “SNR” in the same breath, they mean receiver bandwidth.
Receiver bandwidth (rBW) is one of the parameters you can change on your scanner. We know that the signal-to-noise ratio (SNR) is proportional to 1/√rBW but why this is so can be a bit confusing. Hopefully, this tutorial will help.
The time it takes to sample the MR signal is related to the rBW. (This relationship refers to the sampling time. The actual number of samples taken is set with the matrix size.)
Receiver bandwidth affects the signal-to-noise ratio (SNR) and size of chemical shift artefact. If you have the TE set to shortest already, then a higher bandwidth can allow a shorter TE because the time to sample a k-space line is reduced.
Dont get confused: receiver bandwidth is different from the transmit bandwidth, which refers to the RF excitation pulse used for slice selection in a pulse sequence. The receiver bandwidth is the range of frequencies used to sample the MR signal. Generally, if someone mentions bandwidth, especially if they say SNR in the same breath, they mean receiver bandwidth.
receiver Bandwidth =
1 sampling time of echo
© D M Higgins

2. centre spatial frequency
patient signals
Here we can see a schematic representation of the signal we might measure for one line of k-space. Noise in the signal is not represented (that’s why its so smooth). This signal is digitised into a k-space line, and as you already know the central part of the signal (or echo) has more contrast information, and the edges of the signal contain edges and fine detail information.
The sampling time of the echo (Tline) the time it takes to read out this signal using the readout gradient.
NB Beware diagrams in textbooks. When discussing bandwidth, they often confuse the time domain and the frequency domain, drawing elements from both on the same axes. Watch out! They can be very confusing! (And wrong, more to the point.)
time →
centre spatial frequency
receiver Bandwidth =
1 sampling time of echo
sampling time of echo
© D M Higgins

3. centre spatial frequency
receiver Bandwidth =
1 sampling time of echo
According to this relationship, the sampling time of one MR echo is reduced by increasing the bandwidth.
increase the receiver bandwidth
patient’s signals
This slide illustrates what happens to the signal in time, when the rBW is increased. You can see here why increasing rBW allows a shorter TE to be used. If the sampling time is reduced, the whole pulse sequence can be squashed up to use up the extra time gained.
Increasing the receiver bandwidth (rBW) reduces the time it takes for the echo to be read out, as per the equation on this slide. This is because if we change the rBW (keeping the field-of-view and pixel size constant), the change occurs by use of a steeper frequency encoding (read-out) gradient in real space, across the patient.
This means that there will be a wider range of frequencies used to encode the data within each pixel in the image.
[A with-noise vs without-noise representation of the signal schematic is included on this slide for completeness.]
time →
centre spatial frequency
Ok, so maybe you can accept that changing the rBW affects the time it takes to sample the signal. But why? Its because the way a change of bandwidth is implemented (all other things being equal) is by a change of gradient strength. Read on…
sampling time of echo
© D M Higgins

4. frequency encoding gradient
patient
body
arm
arm
Increase the receiver bandwidth…
frequency
bandwidth
…and the gradient gets steeper.
frequency encoding gradient
A steeper gradient means that the rephasing it causes happens more quickly, and so the echo forms faster. I.e., the sampling time is reduced and the sampling rate is increased accordingly.
© D M Higgins

5. Double the receiver bandwidth 1-D projection
amplitude
Double the receiver bandwidth
1-D projection
arm
body
arm
signal decrease?
Notice that the noise power spectrum (the noise levels over all the frequencies) is constant.
noise power spectrum
-32
-16 16 32
What do you notice? Increasing the rBW has stretched out the range of frequencies used for each column of pixels. As we share out the protons to a wider range of frequencies, the amount of signal from the individual frequencies in the new range must reduce. This is why the signal amplitudes on this frequency graph go down.
frequency (kHz)
When the rBW is increased, the same noise power but over a larger frequency range contaminates the signal from each voxel. Thus the total amount of noise included in each voxel is increased.
Notice also that the noise level for any one particular frequency does not change when the rBW is increased.
BUT, also notice that the area each column occupies hasn’t changed. (They may have reduced in height, but they’ve also gotten wider.) This reflects the fact that we haven’t changed the pixel size. In other words, we have the same number of protons per-voxel as before. They are just resonating at more (and different) frequencies. This is important, because it tells us that although the signal amplitudes for the range of frequencies within any particular voxel have reduced, the total amount of signal per voxel is unchanged.
If we take the central line of k-space and perform a 1-D Fourier transform (FT) on it, we get a 1-D projection of whatever was in the scanner. The FT has worked out how much signal goes into which column of pixels in the image. How the signal would be divided up into the rows is not known. Let’s double the rBW and see what happens…
the signal amplitudes decrease and change frequency
Now let’s consider what happens to the signal and the noise when the range of frequencies (rBW) used to encode the MR signal is increased.
the signal per voxel does not decrease
Now let’s consider what happens as we increase the bandwidth in image space. We’ll do this by looking at a 1-D Fourier transform of the central line in k-space. We get a 1-D projection of the object (a patient, in this case), which is digitised into sections according to the number of pixels across the image.
When the rBW is doubled, the frequency range across which these signals are encoded is doubled, by definition. Although the amplitude of signal at any particular frequency is reduced because fewer protons are encoded at that frequency the signal intensity per voxel has not changed, because we have not changed the pixel size or the field-of-view. This is an important point to remember: the signal-per-voxel does not change.
[This is shown in the slide. The amount of signal per voxel remains the same, shown by the constancy of area of the frequency vs amplitude bins in the 1-D representation.]
Notice, however, that the noise power spectrum does not reduce in amplitude when we go to a higher (wider) bandwidth. The noise levels are constant whatever frequency one considers, no matter what bandwidth is being used. Since the amplitude of the noise does not reduce like the amplitude of the signal at any particular frequency, when we add up the noise power that contributes to a voxel in the wide-bandwidth case, there is more noise than before.
[This is also shown in the slide. In the high-bandwidth case, the area of noise in each voxel bin is increased, because the voxel bin is wider, but the noise level has not dropped like the signal amplitude did.]
This is why, in an image the signal-to-noise ratio (SNR) decreases when the receiver bandwidth is increased.
the noise power per voxel is increased
We know that the SNR in the image is reduced when the rBW is increased, so either the signal is going down, or the noise is going up, or both.
…so in the image, SNR decreases
Hopefully now it will be clear what textbooks mean when they say that increasing the rBW “includes more noise”.
© D M Higgins

6. ↓ SNR ↓ chemical shift artefact ↓ TE
1 √rBW
SNR
Don’t like remembering equations? Use this handy rule:
1 rBW
chemical shift
Rule: as rBW changes, SNR, chemical shift artefact (and TE) do the opposite
↓ SNR ↓ chemical shift artefact ↓ TE
e.g. rBW ↑
You can look up the relationships between rBW and SNR or chemical shift in textbooks, but a useful rule-of-thumb is presented here.
Notice that a trade-off exists here. We may want to reduce the chemical shift artefact in an image, or reduce the echo time (TE), but can we sacrifice SNR? These decisions are made by the operator.
© D M Higgins

7. = 1.8 pixels Fixing rBW: what do you change on the scanner?
GE: rBW range (kHz)
Philips: water-fat shift (pixels)
Siemens: rBW-per-pixel (Hz/pixel)
It depends on the manufacturer. E.g.:
The relationship between these parameters is clearly shown when we work out the number of pixels of chemical shift artefact that will occur on our image:
chemical shift for your magnet
chemical shift for your magnet
Some manufacturers quote bandwidth, and you can use the equation above to work out the effect on the image. Some quote bandwidth per pixel (the bottom half of the equation). Some quote water/fat shift in pixels (chemical shift artefact), and you can use this value to work back to bandwidth, should you need it.
Notes:
Frequency matrix is usually the larger of the two numbers e.g. 256*128.
We use the Larmor equation to get from 3.5ppm to 224 Hz.
Δωcs = γδB0and so Δfcs = (γ/2π)δB0= (2.675x108rad s-1T-1/ 2π) x (3.5x10-6) x (1.5T) = 224 Hz.
224 Hz 1.5T)
3.5 ppm
= 1.8 pixels
(this is what you change on a GE scanner)
(receive) bandwidth
(receive) bandwidth
e.g. ±16 kHz
32 x 103(Hz)
256 (pixels)
= 32 kHz
(this is what you change on a Siemens scanner)
125 Hz / pixel
in this example
frequency matrix
frequency matrix
e.g. 256
(this is what you change on a Philips scanner)
© D M Higgins