def plotDisplacedResponseVsBesselFunctions(azimuths, delays, ordersToShow, polarPattern) : for order in ordersToShow : print order ocolor=colors[order%len(colors)] pattern = [ polarPattern(azimuth, order) for azimuth in azimuths] spectrum = headDistortion.delayAmplitudeToSpectrum(delays, pattern, w) besselN = numpy.array([float(sympy.mpmath.besselj(order, aw*R/c)) for aw in w ]) pylab.plot(numpy.real(spectrum), ocolor+'-', label="R"+str(order)) pylab.plot(numpy.imag(spectrum), ocolor+'--', label="I"+str(order)) pylab.plot(besselN+0.01, ocolor+':', label="B"+str(order)) pylab.ylim(-1,1) pylab.grid(.3) pylab.legend() pylab.show()
plot.inDb() #plot.showPhase() plot.ylim(-40,5) delays = [ (bmaudio.sphericalHeadDelay(azimuth, R, r)-(r-R))/c for azimuth in angles ] for no in ordersToShow[:-1] : print no decoding = headDistortion.decoding3dMaxRe(no) / (no+1) decoding = headDistortion.decoding3dInPhase(no) amplitudes = [ sum( (decoding[l] * float(sh_normalization2(l,0)) * float(sympy.legendre(l,cosTheta)) * math.sin(azimuth) / nSamples for l in xrange(0,no+1) ) ) for azimuth, cosTheta in zip(angles, numpy.cos(numpy.pi/2-angles)) ] plot.addSpectrumData(headDistortion.delayAmplitudeToSpectrum(delays,amplitudes,w),spectralRange,"Order %i"%no) plot.show() def deviated3dAmbisonics(pattern, planeWaveAzimuth, ringAzimuth, slices=72) : """ Discretely integrates a ring perpendicular to the Y axis of the decoding of a plane wave planeWaveAzimuth: angle that forms the incoming wave direction and the left ear (azimuth 90) ringAzimuth: azimuth at which we are integrating the ring """ return sum( ( float(pattern(cosTheta)) for cosTheta in +math.sin(ringAzimuth)*math.sin(planeWaveAzimuth) -math.cos(ringAzimuth)*math.cos(planeWaveAzimuth)*numpy.cos(numpy.arange(0,2*pi,2*pi/slices)) )) / slices # TODO: I think that that should be cos but i get zeros.
def numericalComponent(order, w, delays) : polarPattern = polarPatternY if order&1 else polarPatternX pattern = [ polarPattern(azimuth, order) for azimuth in azimuths] return headDistortion.delayAmplitudeToSpectrum(delays, pattern, w)*2
The plot shows the difference between the numerical integration and the analytic expression of the direct sound component. It should be zero. """ azimuths = directAzimuths delays = numpy.array([headDelaySimplified(a) for a in azimuths]) off=0 # ordersToShow = xrange(0,6,1) for order in ordersToShow : print order ocolor=colors[order%len(colors)] oddOrder = order&1 polarPattern = polarPatternY if oddOrder else polarPatternX pattern = [ polarPattern(azimuth, order) for azimuth in azimuths] spectrum = headDistortion.delayAmplitudeToSpectrum(delays, pattern, w) phase = 1j**((1-(-1)**order)/2) # 1, j, 1, j... phase = 1j if order&1 else 1 besselN = numpy.array([ float(sympy.mpmath.besselj(order, aw*R/c)) for aw in w ]) otherN = sum([ numpy.sin(w*R/c*numpy.sin(a)-order*a) for a in directAzimuths ])/len(directAzimuths) # per and divided by pi hypothesis = phase*(besselN + 1j*otherN) remainder = spectrum - hypothesis pylab.plot(hypothesis+.01, label="H"+str(order)) # pylab.plot(numpy.real(remainder)+off, ocolor+':', label="R"+str(order)) # should be zero
