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The slice selection gradients, as well as the phase and frequency, in MRI imaging are traditionally represented by on/off box or rectangular symbols:

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or

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My question is what is the mathematical name for these functions - it would be the equivalent of multiple rectangle functions, periodic or not. For example:

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or

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  • $\begingroup$ that is a square wave. $\endgroup$
    – JEB
    Commented Aug 26, 2018 at 20:13
  • $\begingroup$ @JEB Right! Here it is. Thank you. $\endgroup$
    – Antoni Parellada
    Commented Aug 26, 2018 at 20:19
  • $\begingroup$ @JEB Would "step function" be a more generic name to include all possible arrangements of rectangle / box functions - periodic and non periodic? $\endgroup$
    – Antoni Parellada
    Commented Aug 27, 2018 at 6:32
  • $\begingroup$ the "Heaviside Step Function" is different. What you drew is a square wave--I'm sure it's an option on your synth: youtube.com/watch?v=j2uB4nKzGlg $\endgroup$
    – JEB
    Commented Aug 27, 2018 at 15:15

1 Answer 1

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They are usually simply called trapezoidal waveforms or trapezoidal gradients. The vertical edges are not possible, the maximum change in gradient strength with respect to time (dG/dt) is called the slew rate. In modern MRI systems it is on the order of 200 mT/m/ms

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  • $\begingroup$ Do you have any link? Are any of these on/off oscillating functions called "trapezoidal" regardless of the context? $\endgroup$
    – Antoni Parellada
    Commented Aug 26, 2018 at 19:39
  • $\begingroup$ I cannot tell you about other contexts. I have only seen these waveforms in the context of MRI gradients. Here is an example in the context of reducing peripheral nerve stimulation: onlinelibrary.wiley.com/doi/pdf/10.1002/mrm.1910320213 $\endgroup$
    – Dale
    Commented Aug 26, 2018 at 20:14
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    $\begingroup$ I like your answer a lot because of your comment on the fact that the slew rate prevents a completely square morphology in real life. However, I think that the right answer just came in a comment to the OP: "square wave." $\endgroup$
    – Antoni Parellada
    Commented Aug 26, 2018 at 20:18
  • $\begingroup$ Yes, good point. The waves as drawn are square waves. Square waves are not used for the gradients in MRI due to hardware limitations, but in that sense I didn’t answer the question asked but rather changed the question and answered that. I hope that is ok. $\endgroup$
    – Dale
    Commented Aug 26, 2018 at 20:24

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