Resolving reduced resolution issues in WSMLink

Question

I have been attempting to evaluate Wolfram System Modeler (WSM) and it has not been going smoothly. It looks like some of the Modelica Models (combiTable1D for instance) supplied are not complete or not functional in WSM. I am working with Wolfram Support to get some clarification on that, but after days of trying I have been unable to get a simple output=input model working.

What I am trying to do as a first step is to just get an audio file into simulation and to port this straight through to an output to verify that it got in with reasonable accuracy. To do this I start with a very simple model:

model AudioProcessing
  Modelica.Blocks.Interfaces.RealInput u=5;
  Modelica.Blocks.Interfaces.RealOutput y;
equation 
  connect(u,y) 
end AudioProcessing;

Here I have set the input to the constant 5 just to see if I can run the simulations without error and indeed this works fine.

In order to bring in the .WAV file I have tried many things, but the best results I get so far is to use WSMLink and the WSMInputFunctions option of WSMSimulate to provide and interpolated version of the .WAV to the simulation. For instance:

Needs["WSMLink`"]
rawAudio = Import["C:\\Users\\vandel\\Desktop\\Mathematica\\Guitar_Sample.wav"]
samplePeriod = N[1/First[rawAudio][[-1]]];
sampleData = First[rawAudio][[1, 1]];
audioTimeSeries = Table[{n*samplePeriod, sampleData[[n + 1]]}, {n, 0, Length[sampleData] - 1}];
audiofunction = Interpolation[audioTimeSeries];
Plot[audiofunction[t], {t, 0, 10}, PlotRange -> All]

This plot looks fine and I can generate reasonable audio using the interpolation function.

Now I try to bring that into WSM as follows:

M = WSMSimulate[audioSignal, {0, 10}, WSMInputFunctions -> {"u" -> (audiofunction[#] &)}];

This runs fine but when I plot this as follows:

WSMPlot[M,"y", PlotRange -> All]

The resolution is so reduced that the sound can not be reproduced. The same takes place with the variable u and when I use the returned interploation table to build a new signal with higher time resolution such as:

{outputVector} = M[{"u"}];
testPlot = Table[outputVector[t], {t, 0, 10, .00001}];
ListPlot[testPlot, PlotRange -> All]

The plot from this looks just like the earlier plot.

I have tried using different solver methods and high numbers of InterpolationPoints and InterpolationOrder to no avail.

Any insight would be appreciated and if there is a better way to get a real world signal sample into the application I'd be happy to look at that as well.

Answer 1

(Disclosure: I work at Wolfram Research developing Wolfram SystemModeler)

SystemModeler (and WSMLink in particular) does have some trouble with high frequency data, however, there are some things that can be done.

Using InputFunctions relies on automatic sampling of you input. As you know what frequency you want to sample the function at, using the "ModelicaCombiTimeTable" and the corresponding export format may be better. The model would look like this:

    model AudioProcessing
      Modelica.Blocks.Interfaces.RealOutput y;
      Modelica.Blocks.Sources.CombiTimeTable combiTimeTable1(fileName="C:\\Dev\\temp\\audio.txt", tableOnFile=true, tableName="invar");
    equation 
      connect(combiTimeTable1.y[1],y);
    end AudioProcessing;

Using the "audioTimeSeries" variable from your post, export to an input file, which will be read by the "ModelicaCombiTimeTable" component above:

Export["C:\\Dev\\temp\\audio.txt", {{"invar", audioTimeSeries}}, "ModelicaCombiTimeTable"]

For the given example, a fixed step solver may be better suited, as we know we want to sample at a given frequency. Set the step size to the known sample period. Also reduce the interpolation order to 1.

m = WSMSimulate["AudioProcessing", {0, 1.5},
     Method -> {"Euler", "StepSize" -> samplePeriod}, InterpolationOrder -> 1];

When plotting high frequency functions, it is sometimes required to increase the number of initial sample points using PlotPoints. Use PerformanceGoal -> "Speed" to speed the plotting up (removes tooltips, for example):

WSMPlot[m, "y", PlotRange -> All, PerformanceGoal -> "Speed", PlotPoints -> 200]

Using a sample sound from ExampleData ("ExampleData/rule30.wav"), I was able to get a good result when playing the simulation result with the given sample rate:

Play[m[{"y"}, t][[1]], {t, 0, 1.5}, SampleRate -> 1/samplePeriod]

The slowness in reading high frequency simulation results remains, but is somewhat improved by these steps.