# Unit of the frequency axis in BodePlot

I have a simple question:

What is the unit of the frequency axis in the BodePlot? I searched the documentation, but only found this:

The scaling functions can be specified as ScalingFunctions->{{magfreqscale,magscale}, {phasefreqscale,phasescale}}.

The frequency scales magfreqscale and phasefreqscale can be "Log10" or "Linear", which correspond to the base-10 logarithmic scale and linear scale, respectively.

The magnitude scale magscale can be "dB" or "Absolute", which correspond to the decibel >and absolute values of the magnitude, respectively.

The phase scale phasescale can be "Degree" or "Radian".

But it doesn't say me if the frequency axis is in Hz or rad/s or rad/min or what ever ... I'm asking because I have two BodePlots which, I'm rather shure one is in Hz and the other in rad/s.

• Radians/S, the lower-case omega is the giveaway. There's an example in the CoordinatesToolOptions section talking about coord. tool using Hz. – ciao Jan 29 '14 at 11:29
• @rasher Thanks, I found the section, but it doesn't work. I'll try to give an example. ... – Phab Jan 29 '14 at 12:41
• Works only with "Frame -> False". Sadly a bad solution for me. But with beeing sure Mma shows rad/s I'll convert it to Hz afterwards. This, unfortunately, makes my actual problem even bigger. – Phab Jan 29 '14 at 12:55
• All you have to do is look in the documentation under Options->Ticks for examples of how to display plot ticks in Hz. – david Jan 29 '14 at 17:08

The answer is that the unit of the frequency axis depends on the unit of the complex variable in the transfer function. So it could be anything $rad/s$, $Hz$, $rpm$, $cps$, etc., depending on how the transfer function was obtained.
For example, in the continuous-time system $1/(s+1)$ if the unit of $s$ is $rad/sec$, and you would like plot in $Hz$, do BodePlot[1/(s + 1) /. s -> I 2 Pi f, f]. You could also do BodePlot[TransferFunctionModel[1/(s + 1), s][2 Pi s]] because it is a continuous-time system.
To do the same thing ($rad/s$ to $Hz$) for a discrete-time system do BodePlot[tfmd/.z->Exp[I 2 Pi f T], f, SamplingPeriod->T], where $tfmd$ is the expression for the discrete-time transfer function in the complex variable $z$ and $T$ is the sampling period.
• @ModCon I know this because I'm the developer of this function and had to think through the design to handle units.:) It's documented here and here. When you realize that asking the unit of the frequency axis of BodePlot is no different than asking the unit of the x-axis in Plot[x^2, {x,0,1}], it's quite surprising and beautiful. – Suba Thomas Jun 17 at 20:32