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Frequency Directivity Plot

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Importing MLSSA frequency response files into a contour graph

This series of VACS screen-shots demonstrates the import of MLSSA sound pressure frequency response files and subsequent down-sampling and smoothing.

Download example files

Select file-group in the file-dialog or drag from File-Manager.

VACS-Screenshots-Importing MLSSA Contour

Each data-set gets assigned a record of parameters. Decide which parameter forms the y-axis of the contour, here "Axial angle". Also we provide the measurement distance, which is 1m and the driving voltage, which is 4Vpeak (P = Ueff2/R » Ueff = sqrt(P·R) = 2.828Veff = 4Vpeak).

VACS-Screenshots-Importing MLSSA Contour Param

Ready. The import gets named and organized in the tree-list and you may add details of the measurement in edit-box on page Doc.

VACS-Screenshots-Importing MLSSA Contour Naming

The sibling curve-graphs allow for projections. The projection onto the x-Graph shows the frequency response at any angle. For in between angles the continuous phase interpolation technique is used, which allows for correct interpolation between two complex-valued functions. The green curve is a power-integration over all data-sets at each frequency (see Processing > A-Power and Rms).

VACS-Screenshots-Importing MLSSA Contour xGraph

The other projection yields the polar-plot. The red curve shows the SPL at 2.5kHz and the the blue curve is a power-integration over a 3rd octave at this frequency (see Processing > A-Power and Rms).

VACS-Screenshots-Importing MLSSA Contour yGraph

The property dialog informs about details and integrals of the data-sets. For example it tells us that each spectrum has 4096 points on a linear grid.

VACS-Screenshots-Importing MLSSA Contour Prop

VACS-Screenshots-Importing MLSSA Contour ProcMenu Often it is useful to down-sample such data to more manageable size. VACS offers resampling and smoothing tools. For transfer functions we select Smoothing response, which comfortably does both.

We resample to 400 points on a log-grid and sub-sequentially smooth with a window of 6th of an octave relative width. The dialog reports also the point distribution of the original as well as the re-sampled data-sets, ie 400 points corresponds to 33.25 points per octave.

VACS-Screenshots-Importing MLSSA Contour Smoothing

Clicking Apply starts the calculation in the background and yields the result as a new page with contour-graph and curve-siblings. For comparison the original curve has been overlayed (copy-paste or drag and drop).

VACS-Screenshots-Importing MLSSA Contour Smoothed

Now let's see what is in the box. VACS maintains the complex-valued nature during the integrations of down-sampling and smoothing by applying the Continuous Phase Technique. If you double-click into the graph-area the Range-Dialog opens, where we set Real part as Bode-type and ArSinh as Axis-type, the latter for both the x-axis and the z-axis. ArSinh is a novel kind of mapping which allows to plot linearly and logarithmically [more...]. Also we alter the x-axis range to 50 ... 10kHz.

VACS-Screenshots-Importing MLSSA Contour RangeDialog

The real part of sound pressure measurements are usually wavy due to the presents of delay caused by the traveling time from the source to the microphone. The plot demonstrates that the original curve with 4096 points and the down-sampled curve with 400 points are almost identical thanks to the Continuous Phase Technique.

VACS-Screenshots-Importing MLSSA Contour RealPart

Using Processing > Calculate curves n->1 we can calculate the relative error between the original and the sampled curves. The formula used is "100*(C1 - C2)/C2", with C1 the log-sampled and smoothed curve and C2 the original curve. The calculation mode is set to Real + Imaginary". If you set the calculation mode to Amplitude then, of course, the error is diminished.

VACS-Screenshots-Importing MLSSA Contour RelError