ExtraWindows

Extension

Introduction

ExtraWindows provides additional windowing functions to the ones already available in the Signal class methods. It also overrides some of the original class methods to provide an extra parameter - sym - controlling the window's symmetric or periodic property.

Documentation on the methods can be found here: Signal: Windows from ExtraWindows Quark

The README of the repository can be found here: https://github.com/khoin/ExtraWindows

Comparison of different Windows

Run this code below to display an interface to compare between different windows( var size = 2048; var drawnSize = (size/32).asInteger; // 16th of bandwidth var minDb = -120.0; // minimum dB to display var genCol = Signal.listOfWindows.size.collect { |i| Color.hsv(i/Signal.listOfWindows.size, 0.6, 1, 1) }; var avBounds = Window.availableBounds; var left, mid, windowPlot, right, transferPlot; var boxes = [], sliders = Dictionary.new; var layout = HLayout([ left = VLayout(StaticText().string_("List of Windows").maxHeight_(50).align_(\topLeft)), stretch: 1 ], [ VLayout( mid = CompositeView(), StaticText().string_("Time Domain").maxHeight_(50).align_(\center) ), stretch: 2 ], [ VLayout( right = CompositeView(), StaticText().string_("Frequency Domain").maxHeight_(50).align_(\center) ), stretch: 2 ]); var window = Window( "ExtraWindows Comparison", Rect().width_(avBounds.width*4/5).height_(avBounds.height/2).center_(avBounds.center) ).layout_(layout).front; var boxAction = { var rangeMap = (\tukeyWindow: 1); var windows = []; var transfers = []; var magNorm = (Array.with(1/size) ++ Array.fill(size/2 - 1, { 2/size })).keep(drawnSize); // fft mag normalisation boxes.do({ |b| if(b.value, { var range = rangeMap.atFail(b.string.asSymbol, { 12 }); var win = Signal.performKeyValuePairs(b.string.asSymbol,[ \size, size, \sym, false, \a, range * sliders.at(b.string.asSymbol).value ]); var trans = ((win.fft(Signal.newClear(size), Signal.fftCosTable(size)).magnitude).keep(drawnSize) * magNorm).ampdb.max(minDb); windows = windows.add(win); transfers = transfers.add(trans); }); }); if(windows.isEmpty, {transfers = windows = (0..1)}); windowPlot.value = windows; transferPlot.value = transfers; transferPlot.specs = ControlSpec(minDb, 0, \lin); // variable minDb transferPlot.domainSpecs = ControlSpec(0, drawnSize, 4, 1, 440, units: "bin"); [windowPlot, transferPlot].do({ |p| p.plots[0].plotColor_(genCol) .backgroundColor_(Color.black) .fontColor_(Color.white) .font_(Font.sansSerif(12, true)); p.refresh; }); }; Signal.listOfWindows.asArray.sort.do({ |name| var box = CheckBox().string_(name); var slider = Slider(); slider.orientation = \horizontal; slider.value = 0.25; slider.action = boxAction; sliders.add(name.asSymbol -> slider); box.action = boxAction; boxes = boxes.add(box); left.add(HLayout([box, s:1], [slider, s:1])); }); windowPlot = Plotter(parent: mid).superpose_(true); transferPlot = Plotter(parent: right).superpose_(true); windowPlot.value = (0..1); transferPlot.value = (0..1); )

Converting Gaussian window from Scipy to ExtraWindow's parameterization

Scipy's implementation of their Gaussian window (scipy.signal.gaussian) is different from ExtraWindow's. Here is the converting function:~pyGaus2ew = { |pyLength = 512, pyAlpha = 3, pySym = true, padding = 0| var ewAlpha = (2*pyAlpha).reciprocal * (pyLength-1); Signal.gaussianWindow(pyLength, padding, ewAlpha, pySym); }; ~pyGaus2ew.(10, 5); // Matching Python Code: // // from scipy import signal // window = signal.gaussian(10, 5, True) // print(window)

Testing

This Quark comes with its Unit Test. We should expect no failure when we run the test:TestExtraWindows.new.run;

References

ExtraWindows was made with referneces to these sources:

1. Smith, J.O. Spectral Audio Signal Processing, http://ccrma.stanford.edu/~jos/sasp/, online book, 2011 edition, accessed 2019.
2. J. Kaiser and R. Schafer, "On the use of the I0-sinh window for spectrum analysis," in IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 28, no. 1, pp. 105-107, February 1980. doi: 10.1109/TASSP.1980.1163349 http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1163349&isnumber=26144
3. Heinzel, G.; Rüdiger, A.; Schilling, R., "Spectrum and spectral density estimation by the Discrete Fourier transform (DFT), including a comprehensive list of window functions and some new flat-top windows" Max Planck Institute (MPI) für Gravitationsphysik / Laser Interferometry & Gravitational Wave Astronomy. http://edoc.mpg.de/395068