rf.js Examples

• Basics
• Interferometry
• Spectrograms

Basics

rf.js (source) is a set of javascript functions for doing signal processing with jsroot TGraph's. It is intended for web monitoring applications for detectors trying to detect ultra-high-energy neutrinos via radio emission, but might be useful for others as well.

Most operations assume your waveforms are stored as TGraph's. All operations are part of the RF object. Here is a basic example showing a few things that can be done.

// RF.range will generate a 512 values starting at 0 with a step of 0.5 var N = 512; var ts = RF.range(0,N,0.5); // Generate a waveform of some sort var ys = RF.randomGaussian(N); for (var i =0; i < N; i++) { var t = ts[i]; ys[i]+= 5*Math.sin(0.09*t*2*Math.PI) + 3*Math.cos(0.03*t*2*Math.PI); } //Make a graph and draw it var g= JSROOT.CreateTGraph(N, ts,ys); g.InvertBit(JSROOT.BIT(18)); g.fTitle="A waveform and its envelope and a filtered versinon;ns;V"; JSROOT.draw('c1', g); //now draw its hilbert enveope var h = RF.hilbertEnvelope(g); h.InvertBit(JSROOT.BIT(18)); h.fLineColor = 3; //different color to differentiate JSROOT.draw('c1',h); //now lets get a filtered version. the filtering is in place. var f = JSROOT.CreateTGraph(N,ts,ys); f.InvertBit(JSROOT.BIT(18)); //some IIR coefficients corresponding to a 2nd order butterworth lowpass //in the future might implement filter design var b= [0.020083,0.040167,0.020083]; var a= [1.00000,-1.56102,0.64135]; RF.IIRFilter( f, b,a); f.fLineColor = 2; //different color to differentiate JSROOT.draw('c1',f); // take the power spectrum and draw it var G = RF.makePowerSpectrum(g); var F = RF.makePowerSpectrum(f); F.fLineColor=2; G.fTitle = "Spectra!; GHz; dBish"; JSROOT.draw('c2',G); JSROOT.draw('c2',F);

c1

c2

Interferometry

One of the main applications of rf.js is correlating waveforms from multiple antennas together and making interferometric maps. Here are some examples of cross-correlation, 1-D interferometric maps, and 2d interferometric map using some synthetic data.

In this case, we consider 3 vertical strings of 4 antennas. Figure c3 shows the graphs, generated by taking a white noise with a gaussian signal on top run through an IIR filter bandpass filter. The time delays for each signal are calculated according to a known plane wave angle. Figure c4 shows the cross-correlation between the first two graphs. Figure c5 shows the average cross-correlation for a given elevation angle within a vertical tring. Figure c6 shows the entire array cross-correlation in terms of elevation and azimuth. Finally, c7 shows the coherent waveform. It starts at the correct angle, but clicking on the 2D map will compute the coherent sum at that angle.

// setup JSROOT.gStyle.AutoStat=false; JSROOT.gStyle.Palette = 87; JSROOT.gStyle.fNumberContours=255; var N = 512; //number of samples var Nant = 12; //number of antennas var tmin = -50; //minimum time for each waveform var dt =0.5; //time step var filter_b = [0.16718,0,-0.66872,0,1.00308,0,-0.66872,0,0.16718]; var filter_a = [1,0,-0.7821,0,0.67998,-0,-0,0.18268,-0,0.030119]; var noise = 5; var dist = 5; var signal_amp = 100; var signal_width = 1; var c = 0.3; //speed of light //coordinates of antennas var pt = dist*Math.sqrt(3)/2; var xant = [0,0,0,0,dist,dist,dist,dist,pt,pt,pt,pt]; var yant = [0,0,0,0,0,0,0,0,pt,pt,pt,pt]; var zant = [0,dist,2*dist,3*dist,0,dist,2*dist,3*dist,0,dist,2*dist,3*dist]; //incoming direction var phi = 30; var theta = -10; //done with settings var cos_phi = Math.cos(phi*Math.PI/180); var sin_phi = Math.sin(phi*Math.PI/180); var cos_theta = Math.cos(theta*Math.PI/180); var sin_theta = Math.sin(theta*Math.PI/180); // direction vector var k = [ cos_phi*cos_theta,sin_phi*cos_theta,sin_theta]; var gs = []; var ts = RF.range(tmin, N,dt); var ants = []; for (var i = 0; i < Nant; i++) { // figure out the correct time at this antenna, t=0 at 0,0,0 var X = [xant[i],yant[i],zant[i]]; var t_signal = -RF.dotProduct(X,k)/c; //start with some noise var ys = RF.randomGaussian(N,0,noise); //now add the signal for (var j = 0; j < N; j++) { ys[j] += signal_amp * Math.exp( -Math.pow(ts[j]-t_signal,2)/signal_width); } var g = JSROOT.CreateTGraph(N, ts,ys); g.InvertBit(JSROOT.BIT(18)); //now filter RF.IIRFilter(g,filter_b, filter_a); gs.push(g); //needed for angle mapper ants.push(RF.Antenna(xant[i],yant[i],zant[i])); g.fLineColor=1+i; g.fName='g'+i; g.fTitle='graphs;ns;V'; } var mg = JSROOT.CreateTMultiGraph.apply(0,gs); mg.fTitle = "The graphs;ns;V"; JSROOT.draw('c3', mg,'al'); //great, now we have our examples! First let's draw a cross-correlation graph var xcorr = RF.crossCorrelation(gs[0],gs[1]); xcorr.fTitle = "Cross-Correlation 0 vs 1;ns;correlation"; JSROOT.draw('c4',xcorr,"l"); //setup elevation mapper for first 4 antennas var mapper_elev = RF.ElevationMapper(zant.slice(0,4),c); var map_elev = new RF.InterferometricMap(mapper_elev, 180,-90,90); map_elev.setTitle("String 1 Elevation Map"); map_elev.compute(gs.slice(0,4)); console.log(map_elev.getMaxes()); JSROOT.draw('c5', map_elev.hist); //set up angle mapper for all antennas var mapper_ang = RF.AngleMapper(ants,c); var map_ang = new RF.InterferometricMap(mapper_ang, 360,-180,180,180,-90,90,true,false); map_ang.setTitle("Array Angle Map"); map_ang.compute(gs.slice(0,Nant)); console.log(map_ang.getMaxes()); JSROOT.draw('c6', map_ang.hist,"colz", function(painter) { painter.ConfigureUserClickHandler( function(info) { var binx = info.binx; var biny = info.biny; var clicked_h = info.obj; var x = clicked_h.fXaxis.GetBinCenter(binx); var y = clicked_h.fYaxis.GetBinCenter(biny); JSROOT.cleanup('c7'); var coh = mapper_ang.coherentSum(gs,[x,y]); coh.fTitle='Coherent sum at phi='+x+',theta='+y+';ns;sum'; JSROOT.draw('c7',coh,"l"); }); }); //now let's construct the coherent waveform at the known location var coh = mapper_ang.coherentSum(gs,[phi,theta]); coh.fTitle='Coherent sum at phi='+phi+',theta='+theta+';ns;sum'; JSROOT.draw('c7',coh,"l");	c3
	c4
	c5
	c6
	c7

Spectrograms