# Perform calculations on y-axis values?

Posted 2 months ago
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 Sometimes when plotting functions, you want to do some operation on the y-axis. This comes up when you want to plot say decibels vs. frequency. It is not clear how you can do an operation like performing 10 Log10 on the y-axis values. Is there a straight forward way to do this? Incidentally, LogPlot just gives you the y-axis in log form.
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Posted 2 months ago
 Below are two methods. Here the function applied to the y data is Log, but any other will do as well. Also, have a look at LogLogPlot and LogLinearPlot. xyData = RandomReal[{.1, 10}, {5, 2}] (* {{3.7863585396010766,2.0525620539014238},{5.685398066640987,4.\ 020348266453116},{7.6771838544964695,9.879694699280535},{4.\ 361245849573017,1.6275433819822656},{7.313321495705271,6.\ 484234251087724}} *) (* mapping a pure function *) oneWay = {#[[1]], Log[#[[2]]]} & /@ xyData (* {{3.7863585396010766,0.7190887952133352},{5.685398066640987,1.\ 3913685323245182},{7.6771838544964695,2.290481610399797},{4.\ 361245849573017,0.48707175034119526},{7.313321495705271,1.\ 8693737307790999}} *) (* applying a rule *) anotherWay = xyData /. {x_, y_} -> {x, Log[y]} (* {{3.7863585396010766,0.7190887952133352},{5.685398066640987,1.\ 3913685323245182},{7.6771838544964695,2.290481610399797},{4.\ 361245849573017,0.48707175034119526},{7.313321495705271,1.\ 8693737307790999}} *) 
Posted 2 months ago
 ScalingFunctions
Posted 2 months ago
 I think scaling functions can be used to scale the plot, but the values indicated will be the original. In cases like dB, you really want to plot 10 Log(power). Am I wrong on this?
Posted 2 months ago
 David's approach is interesting, but it does not give me what I am looking for. What I ultimately want is the y-axis to be linear in decibels is 10 decibel increments. Matlab can readily do this. Attachments:
Posted 2 months ago
 TimeSeries are also useful for this even if the x's are not times.
 If you want the y-axis linear in dB, then convert gain to dB using the appropriate function and plot the y-axis using a linear scale. For power gain, the gain in dB is 10 Log10(gain). (For voltage or current gain, 20 Log10(gain).) For most control theory and electronics design purposes, a graph which is logarithmic in frequency and linear in dB is common. Using the Butterworth high pass in your notebook: tfhpb = ButterworthFilterModel[{"Highpass", {1000, 4000}, {40, .1}}]; Plot[10 Log10[Abs[tfhpb[I \[Omega]]]], {\[Omega], 0, 10000}, Frame -> True, PlotRange -> {-60, 10}, GridLines -> {Automatic, Range[-100, 100, 20]}, ScalingFunctions -> {"Log10", None}, FrameLabel -> {"Frequency (Hz)", "Gain (dB)"}, LabelStyle -> 14] You might also look at BodePlot.