#Calm radio bandwidth full#

The maximum detectable frequency is still 1/2t d, but we can now distinguish positive from negative frequencies in that range.Īnother topic ignored in the above discussion is the concept of frequency oversampling.

#Calm radio bandwidth full#

The full usable bandwidth is therefore BW = + 1/2t d − (−1/2t d) = 1/t d. The bandwidth we can actually represent is only from 0 to 1/2t d.Ĭollecting both the real and imaginary data allows us to distinguish + 1/2t d from − 1/2t d. We would be able to detect signals over the the range − 1/2t d to + 1/2t d, but would be unable to distinguish positive from negative frequencies within this range. If we only sampled a single real signal (as is done in some older NMR spectrometers and very old MRI scanners), then the true BW would be only 1/2t d.

The answer is that in MRI we sample in complex mode, collecting both real and imaginary data for each point. So it would seem the proper equation should be BW=1/2t d. The Nyquist criterion requires that a sinusoid must be sampled at least twice per cycle to determine its true frequency. You might wonder why our definition of BW=1/t d isn't in conflict with the Nyquist criterion from sampling theory. At 3.0T the chemical shift difference is about 440 Hz, so the Philips BW at this field would be reported as 2.2 pixels. Continuing the example above, a BW of 195 Hz/pixel at 1.5T would be reported by Philips as 220/195 = 1.1 pixels (Px). This is known as the chemical shift artifact and will be explained much more completely in a future Q&A. At 1.5T the resonant frequencies of fat and water protons differ by about 220 Hz causing them to refocus in slightly different positions in the image.

Philips has a somewhat obtuse way of prescribing bandwidth - the 'fat/water shift' in pixels. So for N f = 256 they would report the BW to be 50,000/256 or 195 Hz/Px.

Siemens and Toshiba would calculate BW on a per pixel basis. In the example above, GE would report a rBW = 50 kHz regardless of the spatial resolution chosen. GE Healthcare uses the total bandwidth across the entire image, while Siemens and Canon use bandwidth per pixel (Px). MR manufacturers have slightly different methods for defining receiver bandwidth.