Temporal Processing and Modulation

Technical University of DenmarkDTU Electrical EngineeringØrsteds Plads, Building 3482800 LyngbyDenmarkTelephone +45 4525 3800http://www.elektro.dtu.dkTitle:Temporal Processing and ModulationCourse:31236 Auditory Signal Processingand PerceptionSpring semester 2008Project group:5Participants:Troels Schmidt LindgreenDavid Pelegrin GarciaEleftheria GeorgantiSupervisor:Torsten DauInstructor:Olaf StrelcykDate of exercise: April 3 rdSynopsis:This report deals with the ability ofa human listener to detect changes instimuli over time, referred to as temporalresolution. Two methods of measuring thetemporal resolution are examined. Themodulation detection method and the gapdetection method.Temporal resolution models are discussedand it is concluded that thepresence of a modulation filterbank canaccount for the human ability to detectamplitude modulations, independently ofthe carrier bandwidth.Pages: 19Copies: 4No part of this report may be published in any form without the consent of the writers.

IntroductionThis exercise deals with the ability of a human listener to detect changes in stimuli overtime, often called as temporal resolution. Temporal resolution can be estimated withmethods like gap detection, modulation detection and forward masking. The first twomethods are discussed in this report.In the first part of this report the detectability of sinusoidal amplitude modulation asa function of the modulation frequency is investigated, when broadband noise is used asthe carrier. The detection threshold is measured for two listeners, obtained by varying themodulation depth of the imposed amplitude modulation.In the second part the physical properties of the stimuli are examined using mathematicaltools. A Matlab function is written in order to calculate and plot the temporal waveform,the envelope and the spectrum envelope for each of the carriers that are used. Additionally,the same spectra with an imposed sinusoidal modulation are plotted and comparedqualitatively with the data measured by [Dau et al., 1997].In the last section of this report the gap detection method is examined, using differentnoise bandwidths. The gap detection threshold for 3 test subjects is determined andthe results are discussed.Technical University of Denmark, May 15, 2008Troels Schmidt Lindgreen David Pelegrin Garcia Eleftheria Georganti

Contents1 Theory 11.1 Modulation detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Examining the physical properties of the stimulus . . . . . . . . . . . . . . . 31.3 Gap Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Results 52.1 Estimation of temporal resolution . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Further investigation into temporal resolution . . . . . . . . . . . . . . . . . 72.3 Examining the physical properties of the stimulus . . . . . . . . . . . . . . . 82.4 Gap Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Discussion 133.1 Modulation detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Gap detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 Conclusion 17Bibliography 19A Matlab CodeA1

April 2008 Chapter 1. TheoryChapter 1TheoryThe information in sounds is carried in the changes over time. So, the human auditorysystem needs to account for these changes. Temporal processing in the auditory systemconsists of:• temporal resolution• temporal integrationTemporal resolution refers to the ability to detect changes in stimuli over time, e.g. todetect a brief gap in broad-band noise or that a sound is modulated in some way, whereastemporal integration is the ability to sum up information over time in order to discriminatestimuli [Dau et al., 2008, p. 2]. In this report temporal resolution will be discussed further.At this point it is important to distinguish between the rapid pressure variations in asound, which are often called the “fine structure”, and the “envelope of a signal”, whichrefers to overall changes in the amplitude of the fluctuations that appear. For the understandingof speech, the envelope of the signal plays the most important role, whereas inmusic the fine structure is more important. Temporal resolution is generally concernedwith the envelope rather than the fine structure [Moore, 2004, p. 164].The auditory cortex seems to be limited in its ability to follow fast temporal changes inthe envelope of a sound. Central processes in the brain are the limiting factor [Dau et al.,2008, p. 2].The analysis of sounds that are amplitude modulated, has been proposed to depend ona specialized part of the brain that contains an array of neurons, each of them tuned toa different modulation rate. Each neuron can be considered as a filter in the modulationPage 1

state parts, e.g. in music and speech signals.Temporal processing in the auditory system is discussed in terms of temporal resolution (acuity)and temporal integration (summation). Temporal resolution refers to the ability to detect shortchanges in sounds, e.g., a brief gap in broad-band noise. Temporal integration refers to theability to sum up information over time in order to discriminate stimuli. This exercise focuseson temporal Chapter resolution. 1. Theory Technical University of DenmarkFigure Figure 1.1: 1.1: Illustration of fine of fine structure vs. envelope of ofa asound. The Sinusoidal dashed lineamplitude is the modulation modulationwaveform and envelope of the sounds. Left: Sinusoidal amplitude modulation of a pure-tone carrier withof a pure-tonem = 1 and fcarrier c = 10 f m .withRight:mf c = 2.51 and· f m , wheref c =f c10fdenotes m (leftthe carrierpanel)frequencyor f c =and2.5ff m is m ,thewheremodulationf c denotesthe carrier frequency. frequency From [Viemeister and f m and is the Plack, modulation 1993]. frequency. The dashed line is the modulationwaveform and envelope of the sounds. From Viemeister and Plack (1993).domain, and the array of neurons is known as “modulation filterbank” [Moore, 2004, p.It is important 183]. to distinguish between the rapid amplitude changes of sounds (the fine structure)and the slower overall amplitude changes (the envelope). Figure 1.1 illustrates this with the finestructure drawn with a solid line and the envelope drawn with a dashed line. Temporal resolutionis generally concerned with the envelope and not the fine structure.1.1 Modulation detectionAs seen in Exercise 4 (Frequency Selectivity and Masking), many aspects of human detectionperformance relating to frequency selectivity and masking can be explained in terms of veryearly stagesTemporalof auditoryprocessingprocessing,can be investigatedi.e., the propertiesby measuringof thethebasilardetectabilitymembrane.of sinusoidalWhen discussingamplituderesolution, modulation however, as a function centralof processes frequency. inSinusoidal the brainamplitude are the limiting modulation factor is defined and need totemporalbe taken as: into account. Central in this context means that stages higher than the auditory nerveare involved.In this exercise, the temporal resolution s(t) = n(t) of(1 the + m human · cos (w m auditory t)) system will be measured (1.1) usingtwo experimental paradigms: modulation detection and gap detection.For this Where: exercise, the following statements should be entered after starting Matlab in order tobe ables(t) toisaccess the signal. the provided scripts:n(t) is the carrier waveform.m is the modulation depth.cd c:\usr\course31236\TPaM % the directory of this exercisew m is the modulation frequency.startup% sets the pathcalmixer% sets the sound mixer to calibrated valuesIn figure 1.2 it can be seen that an amplitude modulated noise has sidebands that extendIf not already connected, please connect Applying the sinusoidal headphone (Sennheiser HDA 200) including thesmall black box to the soundcard (theamplitudethirdmodulationconnector from the left side).m/2-x x02-x–f m -x -x+f m x–f m x x+f m0Figure 1.2: Spectrum of a pure tone, before and after applying amplitude modulation. The spectrumbroadens after applying amplitude modulation for all types of signals and the overall power will increasebecause of the broadened spectrum. When modulating broadband noise its frequency content is alsoenriched, but in an inaudible range.Page 2Temporal Processing and Modulation

April 2008 Chapter 1. Theory± f m Hz from the edges of the passband of the unmodulated noise, where f m indicates themodulation. When a narrow-band stimuli is amplitude-modulated, the average power ofthe modulated signal is increased by 1 + m 2 /2 compared to the unmodulated signal [Dauet al., 1997].A function that relates the threshold with the modulation rate is often referred as the TemporalResolution Transfer Function (TMTF). The modulation depth is usually expressedin dB (20 log 10 m). The modulation of a sound implies a broadening in the spectrum andfor this reason broadband noise is often used as a carrier. This prevents subjects fromusing changes in the overall spectrum as a detection cue. Modulation of white noise doesnot change its long-term spectrum [Dau et al., 1997].1.2 Examining the physical properties of the stimulusThe physical properties in the time and frequency domain of a stimuli can be examinedusing the Fourier transform. A more thorough investigation of the temporal resolution ofthe stimuli can be achieved by examining the envelope of the signal. The envelope of agiven signal can be determined by means of the analytic signal.The analytic signal s a (t), when s(t) is the stimuli which is represented by a real function,equals to:s a (t) = s(t) − iS Hi [s(t)] (1.2)where S Hi [s(t)] is the Hilbert transform of the real signal. The Hilbert transform is definedas:S Hi (t) = 1 π∫ ∞−∞s(t ′ )t ′ − t dt′ (1.3)Finally, the envelope of the the waveform s(t) is defined as the absolute value of thecorresponding analytical signal s a (t):env[s(t)] = |s a (t)| (1.4)1.3 Gap DetectionAnother method to measure the time resolution of the auditory system is the gap detectionin a signal (called carrier). This is usually determined by presenting two identical signalsin two intervals, where in one of them a silence has been introduced, as seen in figure1.3 . The test subject has to choose whether the gap is in one interval or in the other.The adaptive method adjusts the duration of the gap until it corresponds to the detectionPage 3

Chapter 1. Theory Technical University of Denmark11Amplitude0.5Amplitude0.5t00 5 10 15 20Time [ms](a)00 5 10 15 20Time [ms](b)Figure 1.3: Two noise intervals, where in one of them a silence of duration ∆t has been introduced.threshold of the test subject.The results obtained with this method depend highly on the presented signal. The introductionof a gap implies the apparition of new spectral content (the spectrum of theoriginal signal is convolved with the spectrum of the time-gap pulse). Therefore, the detectionof the gap is done by means of spectral cues and taking advantage of the frequencydiscrimination in the human auditory system. To avoid this effect, broadband noise ispreferred compared to narrowband noise. The spectrum of broadband noise is not modifiedby the introduction of the gap, and the results are an indicator of the overall timeresolution of the auditory system.However, the duration of the gap at the threshold obtained with broadband noise doesnot provide any information about the behavior at different frequencies or bandwidths.Narrowband noise is used for this purpose. The spectral cues should be avoided usingtwo alternative strategies. The first consists of adding low amplitude broadband maskingnoise to the signals, so the spectral splatter cannot be detected by the ear. The secondstrategy consists of filtering the signal after introducing the time gap. The filtering ofhigh-frequency components will smooth the transient produced by the insertion of thegap.Page 4Temporal Processing and Modulation

April 2008 Chapter 2. ResultsChapter 2Results2.1 Estimation of temporal resolutionA temporal modulation transfer function (TMTF) experiment is performed using a bandlimitednoise carrier with a lower cut-off frequency of 1 kHz and an upper cut-off frequencyof 4 kHz. A one-up, two-down, 3-interval, 3-alternative forced choice procedure is used tomeasure six points of the TMTF for three test subjects. The modulation frequencies usedare 8, 16, 32, 64, 128, 256 Hz and the carrier level is 70 dB SPL . The results are shown infigure 2.1 together with the data obtained by Viemeister [Viemeister, 1979].Modulation depth [dB]0-5-10-15-20tldpegData by Viemeister-258 16 32 64 128 256Modulation frequency [Hz]Figure 2.1: Measured TMTF for three test subjects with 3 kHz bandwidth carrier and results from [Viemeister,1979] using a 6 kHz bandwidth carrier, as a function of the modulation frequency.It is possible to estimate a cut-off frequency from the measured results by examiningPage 5

Chapter 2. Results Technical University of Denmarkfigure 2.1, but it is quite difficult because the points do not define smooth curves. Thus, avalue of 128 Hz is assumed as a first approach for all test subjects. The cut-off frequencyfor each one is further examined by modeling results that are similar to the measured datausing Viemeister’s low-pass model with different cut-off frequencies. In figures 2.2, 2.3and 2.4, the measured results are shown together with a TMTF provided by a computermodel, fitted for each test subject, respectively. Moreover, the numeric values of the cut-offfrequencies ( f cut-off ) and the corresponding time constants measured for all test subjectsare presented in table 2.1. The time constant is calculated from equation (2.1).t =12π f cut-off(2.1)Modulation depth [dB]0-5-10-15-20dplowPassModel (100 Hz)-258 16 32 64 128 256Modulation frequency [Hz]Figure 2.2: Modulated TMTF with a cut-off frequency of 100 Hz and corresponding time constant of1.59 ms which resembles the measured data from test subject DP.Test Subject Cut-off frequency [Hz] Time constant [ms]DP 100 1.59EG 200 0.80TL 90 1.77Table 2.1: Cut-off frequencies and associated time constants measured for three test subjects, assuming alow-pass filter model in the auditory system.Page 6Temporal Processing and Modulation

April 2008 Chapter 2. ResultsModulation depth [dB]0-5-10-15-20eglowPassModel (200 Hz)-258 16 32 64 128 256Modulation frequency [Hz]Figure 2.3: Modulated TMTF with a cut-off frequency of 200 Hz and corresponding time constant of0.80 ms which resembles the measured data from test subject EG.0Modulation depth [dB]-5-10-15-20tllowPassModel (90 Hz)-258 16 32 64 128 256Modulation frequency [Hz]Figure 2.4: Modulated TMTF with a cut-off frequency of 90 Hz and corresponding time constant of 1.77 mswhich resembles the measured data from test subject TL.2.2 Further investigation into temporal resolutionUsing Viemeister’s low-pass model, TMTFs for carrier bandwidths of 30 Hz, 300 Hz and3 kHz are modeled and shown in figure 2.5. A time constant of 1.59 ms was used, as itwas the one that provided the best fitting for one of the test subjects (dp).Page 7

Chapter 2. Results Technical University of DenmarkModulation depth [dB]100-10-2030 Hz wide carrier300 Hz wide carrier3000 Hz wide carrier8 16 32 64 128 256Modulation frequency [Hz]Figure 2.5: TMTFs for carrier bandwidths of 30 Hz, 300 Hz and 3 kHz with a 100 Hz and correspondingtime constant of 1.59 ms.2.3 Examining the physical properties of the stimulusIn this part of the exercise, taking into account the theory described in section 1.1, thewaveforms of carriers with different bandwidths (3 Hz, 30 Hz, 300 Hz and 3 kHz) weregenerated. Additionally the envelope and the envelope spectrum for each of them wascalculated. The upper cutoff frequency was set to 4000 Hz which implies that, accordingto the Nyquist sampling theorem, the sampling frequency has to be at least 2 times thatvalue. To ensure that no aliasing effects would take place the sampling frequency was setto 10 kHz. For this reason a Matlab file, called twopointthree.m, was created and canbe found in appendix A. The results for the temporal waveforms and their envelopes canbe seen in figures 2.6, 2.7, 2.8 and 2.9, respectively.1.5500Amplitude10.50-0.5-1Envelope power density400300200100-1.50 20 40 60 80 10000 1 2 3 4 5Time [ms]Frequency [Hz](a)(b)Figure 2.6: Carrier of 3 Hz bandwidth. (a) Temporal waveform and envelope. (b) Envelope spectrum.Note that the peak at 0 Hz is not shown on the plot.Page 8Temporal Processing and Modulation

April 2008 Chapter 2. Results250Amplitude10-1Envelope power density40302010-20 20 40 60 80 10000 10 20 30 40 50Time [ms]Frequency [Hz](a)(b)Figure 2.7: Carrier of 30 Hz bandwidth. (a) Temporal waveform and envelope. (b) Envelope spectrum.Note that the peak at 0 Hz is not shown on the plot.45Amplitude20-2Envelope power density4321-40 20 40 60 80 10000 100 200 300 400 500Time [ms]Frequency [Hz](a)(b)Figure 2.8: Carrier of 300 Hz bandwidth. (a) Temporal waveform and envelope. (b) Envelope spectrum.Note that the peak at 0 Hz is not shown on the plot.40.5Amplitude3210-1-2Envelope power density0.40.30.20.1-30 20 40 60 80 10000 1000 2000 3000 4000 5000Time [ms]Frequency [Hz](a)(b)Figure 2.9: Carrier of 3000 Hz bandwidth. (a) Temporal waveform and envelope. (b) Envelope spectrum.Note that the peak at 0 Hz is not shown on the plot.Next task was to modulate the carrier waveforms using an imposed sinusoidal modula-Page 9

Chapter 2. Results Technical University of Denmarktion of 16 Hz. In order to achieve this, equation (1.1) was used and the results for themodulation spectra of the generated stimuli can be seen in figure 2.10. The modulationEnvelope power density40200-20-40-603 Hz30 Hz300 Hz3 kHz-8010 1 10 2 10 3Frequency [Hz]Figure 2.10: Modulation spectra of the generated stimuli when 3 Hz, 30 Hz, 300 Hz and 3000 Hz bandwidthof the carrier is used, with an imposed sinusoidal modulation of 16 Hz.spectra present low pass characteristics with cut-off frequencies equal to the bandwidth ofthe carriers. Additionally, a peak at 16 Hz appears in all the spectra and corresponds tothe frequency of the sinusoidal modulation.2.4 Gap DetectionThe threshold for gap detection was measured for three test subjects (dp, eg and tl). Thecarriers were band-limited noise of bandwidths (BW) 30, 100, 300, 1000 and 3000 Hz. Allof them had an upper cut-off frequency of 4 kHz. This means that the spectrum of thesignal was contained in the frequency range [4 kHz-BW, 4kHz]. Their level was 70 dBSPL. A three-interval, three-alternative forced choice procedure was used, in connectionto a one-up two down rule. The results of this experiment are presented in figure 2.11.Page 10Temporal Processing and Modulation

April 2008 Chapter 2. Results10050Gap threshold [ms]201052dpegtl130 100 300 1000 3000Bandwidth [Hz]Figure 2.11: Measurement of the gap detection threshold for different carrier bandwidths.Page 11

Chapter 2. Results Technical University of DenmarkPage 12Temporal Processing and Modulation

April 2008 Chapter 3. DiscussionChapter 3Discussion3.1 Modulation detectionIn figure 2.1 on page 5, the measured values of TMTF for three test subjects are comparedwith the data obtained by Viemeister. The values obtained by Viemeister presentlower thresholds than the test subjects, but all the curves have a similar behavior. Thus,the threshold increases with increasing modulation frequency. These results could lead tomodel the temporal processing of the auditory system as a low-pass filter, but it is necessaryto measure thresholds with different carrier bandwidths and modulations in order toextract a general conclusion.Assuming the low-pass filter as a first approach, the cut-off frequencies (and the timeconstants) were estimated to be about 128 Hz for all test subjects. Figures 2.2, 2.3 and2.4 show that the three test subjects have different cut-off frequencies. These frequenciesare 90 Hz, 100 Hz and 200 Hz, whereas the cut-off frequency estimated by Viemeister is64 Hz (time constant of 2.5 ms). The temporal resolution of the test subjects’ auditorysystem seems to be much faster than the one predicted by Viemeister. A possible explanationfor this is that the background noise, when measuring the thresholds for the threetest subjects, affected the curves, especially for the lower modulation frequency thresholds.Because of the changes in the curve, the cut-off frequency is shifted toward highfrequencies and the calculated time constant is too low.In figure 2.5 on page 8, it can be seen that the low-pass model cannot detect full modulationfor modulation frequencies above 16 Hz with a 30 Hz wide carrier. Full modulationcorresponds to a value of m = 1 in equation (1.1), which corresponds to a value of20 log 10 m = 0 dB. This behavior is also observed for a 300 Hz wide carrier at modulationPage 13

Chapter 3. Discussion Technical University of Denmarkfrequencies above 256 Hz and it is likely to obtain the same results at higher modulationfrequencies for the 3000 Hz wide carrier. However, these results do not correspond tothe measurements from [Dau et al., 1997], shown in figure 3.1, where different frequencycharacteristics appear. E.g. at very narrow carrier widths, there is high-pass filter characteristics.The low-pass model cannot account for the observed effects with narrowbandcarriers.Figure 3.1: Temporal modulation transfer functions obtained using narrowband noise carriers with 3 Hz,31 Hz, 314 Hz. The center frequency of the carrier was 5 kHz. Data from [Dau et al., 1997].In figure 2.6 (a) the carrier noise waveform of 3 Hz bandwidth appears to be deterministic.The envelope lies on top of the carrier producing very slow fluctuations compared to thefine structure of the noise. The envelope spectrum of the same carrier appears in figure2.6 (b). It can be seen that the magnitude decreases with respect to the frequency andafter 3 Hz goes to zero. In figures 2.7, 2.8 and 2.9 a similar effect can be observed forthe carriers of 30 Hz, 300 Hz and 3 kHz bandwidths, respectively. The magnitude againdecreases with the frequency and falls to zero for frequencies above the carrier bandwidth.The rapidity of the inherent random amplitude fluctuations (i.e. the envelope) in the noisecarriers increases with increased bandwidth [Moore, 2004, p. 185].The envelope spectra in figures 2.6, 2.7, 2.8 and 2.9 have triangle-like shape, which isin accordance with the literature [Dau, 2008, p. 28]. It should be noted that there areenvelope power density peaks at 0 Hz which are not shown in the figures.From figure 3.2 it can be seen that the curves that define the thresholds are related to thePage 14Temporal Processing and Modulation

April 2008 Chapter 3. DiscussionFigure 3.2: Temporal modulation transfer functions obtained using narrowband noise carriers with 3 Hz,31 Hz, 314 Hz. Additionally, the envelope spectra of Gaussian noise corresponding to the noise carriersare plotted. Data from [Dau, 2008, p. 30].bandwidth of the envelope spectrum for each carrier, at least for the 3 Hz and the 31 Hzwide carriers.For the case of the modulation spectra of the noise carriers with an imposed sinusoidalmodulation of 16 Hz the results can be seen in figure 2.10. Looking at the spectrum of thecarrier with 3 Hz bandwidth, there is a peak appearing at 16 Hz, because of the imposedsinusoidal modulation. The peak is very high in comparison to the rest of the spectrum forthe 3 Hz carrier bandwidth. This implies that the detection threshold for a tone e.g. 16Hz, when a noise carrier with 3 Hz bandwidth is used, should be low. For 30 Hz bandwidthcarrier the detection threshold should be higher, as the peak at 16 Hz is much lower incomparison to the intrinsic fluctuations of the spectrum. The observations described herewere experimentally verified by [Dau et al., 1997] and the results can be seen in figure 3.1.At 314 Hz, a different behavior is observed. In this case, the threshold increases withincreasing frequency. This could be explained if the presence of a modulation filterbankis assumed. These filters are assumed to be bandpass filters of increasing bandwidth withincreasing frequency. With these considerations, the amount of envelope noise in a certainfilter increases with increasing frequency and this would result in a higher threshold(worse). The hypothesis of the presence of a modulation filterbank also accounts for theresults with 3 Hz and 31 Hz wide carriers.Page 15

Chapter 3. Discussion Technical University of Denmark3.2 Gap detectionThe results from the gap detection experiment are compared in figure 3.3 with the onesFigure 3.3: Comparison of the measured gap detection thresholds with the data from [Dau, 2008, p. 13].The dashed line indicates the time constant obtained by [Viemeister, 1979]provided by [Dau, 2008, p. 13]. It can be seen that they all have the same behavior, sothe threshold versus bandwidth presents an approximately linear decay when both magnitudesare plotted in a logarithmic scale. This is, the threshold decreases with increasingbandwidth of the carrier. This may be explained because the noise has inherent fluctuationsthat depend on its bandwidth. Thus, narrowband noise has slower fluctuations thanbroadband noise, and the gaps might be confused with dips in these fluctuations. [Moore,2004, p. 169]The value of temporal resolution obtained by the gap detection method at the highestmeasured bandwidth (3 kHz) is the closest to the one obtained by modulation detection.However, it is not possible to obtain a single time constant from figure 3.3 because the valuesdo not converge to a specific time constant. In order to find convergence and therebyobtain a time constant, more results are needed with higher bandwidths.Page 16Temporal Processing and Modulation

April 2008 Chapter 4. ConclusionChapter 4ConclusionIn this exercise, the temporal processing properties of the human auditory system, andconcretely the temporal resolution, were investigated using two different methods: amplitudemodulation and gap detection.By analyzing the results, the main conclusions are:The low-pass filter model of temporal resolution in the auditory system accounts forthe detection of sinusoid modulations using broadband noise carriers. The modeldoes not account for the human ability to detect amplitude modulations with narrowbandcarriers (bandwidths below 300 Hz).The presence of a modulation filterbank accounts for the human ability to detectamplitude modulations, independently of the carrier bandwidth.A time constant has not been accurately determined. In the amplitude modulation experiment,the presence of background noise resulted in a shift of the apparent cut-offfrequency. In the gap detection experiment, the time constant presented decreasingvalues with increasing bandwidths of the carrier. However, further measurementsare needed to observe convergence in the time constant values.Page 17

Chapter 4. Conclusion Technical University of DenmarkPage 18Temporal Processing and Modulation

April 2008BibliographyBibliography[Dau, 2008] Dau, T. (2008). Temporal processing in the auditory system. Slide show.[Dau et al., 1997] Dau, T., Kollmeier, B., and Kohlrausch, A. (1997). Modeling auditoryprocessing of amplitude modulation. i. detection and masking with narrow-band carriers.Journal of the Acoustical Society of America, 102(5):2892–905.[Dau et al., 2008] Dau, T., Strelcyk, O., and Buchholz, J. (2008). Temporal processingand modulation guide. 1.2.1 edition.[Moore, 2004] Moore, B. C. J. (2004). An introduction to the psychology of hearing.[Viemeister, 1979] Viemeister, N. (1979). Temporal modulation transfer functions basedupon modulation thresholds. J. Acoust. Soc. Am, 66:1364–1380.[Viemeister and Plack, 1993] Viemeister, N. and Plack, C. (1993). Human Psychophysics.Chapter: Time analysis.Page 19

BibliographyTechnical University of DenmarkPage 20Temporal Processing and Modulation

Project group 5 April 2008Appendix AMatlab Code✞1 clear a l l ;2 clc ;3 close a l l ;456 % out = b p n o i s e ( len , flow , f h i g h , f s ) ;78 % l e n = output l e n g t h in samples9 % f l o w = lower c u t o f f f r e q in Hz10 % f h i g h = upper c u t o f f f r e q in Hz11 % f s = sampling r a t e in Hz1213 % out = output v e c t o r1415 m = 0.1;16 fhigh = 4000; % Upper c u t o f f f r e q .17 fs = fhigh *2.5;18 N = 100* fs;192021 % C a r r i e r s22 % 3 , 30 , 300 , 3000 Hz23 noise3 = bpnoise (N, fhigh -3 , fhigh , fs);24 noise30 = bpnoise (N, fhigh -30 , fhigh , fs);25 noise300 = bpnoise (N, fhigh -300 , fhigh , fs);26 noise3000 = bpnoise (N, fhigh -3000 , fhigh , fs);2728 envelope3 = abs( hilbert ( noise3 ));29 envelope30 = abs( hilbert ( noise30 ));30 envelope300 = abs( hilbert ( noise300 ));31 envelope3000 = abs( hilbert ( noise3000 ));3233 % P l o t temporal waveforms and e n v e l o p e s3435 figure ;36 t =[1/ fs :1/ fs :0.1];☎Page A1

APPENDIX37 plot (t *1000 , noise3 (1: length(t)),’-’,’Color ’ ,[.5 .5 .5]) ;38 hold on39 plot (t *1000 , envelope3 (1: length(t)),’-k’,’ LineWidth ’ ,2);40 xlim ([0 100]) ;41 xlabel (’Time [ms]’);42 ylabel (’Amplitude ’);43 nicefigure ;444546 figure ;47 plot (t *1000 , noise30 (1: length(t)),’-’,’Color ’ ,[.5 .5 .5]) ;48 hold on49 plot (t *1000 , envelope30 (1: length(t)),’-k’,’ LineWidth ’ ,2);50 xlim ([0 100]) ;51 xlabel (’Time [ms]’);52 ylabel (’Amplitude ’);53 nicefigure ;5455 figure ;56 plot (t *1000 , noise300 (1: length(t)),’-’,’Color ’ ,[.5 .5 .5]) ;57 hold on58 plot (t *1000 , envelope300 (1: length(t)),’-k’,’ LineWidth ’ ,2);59 xlim ([0 100]) ;60 xlabel (’Time [ms]’);61 ylabel (’Amplitude ’);62 nicefigure ;6364 figure ;65 plot (t *1000 , noise3000 (1: length(t)),’-’,’Color ’ ,[.5 .5 .5]) ;66 hold on67 plot (t *1000 , envelope3000 (1: length(t)),’-k’,’ LineWidth ’ ,2);68 xlim ([0 100]) ;69 xlabel (’Time [ms]’);70 ylabel (’Amplitude ’);71 nicefigure ;7273 % e n v e l o p e spectrum74 [P3 ,w1 ]= pwelch ( envelope3 ,5* fs);75 [P30 ,w2 ]= pwelch ( envelope30 ,2* fs);76 [P300 ,w3 ]= pwelch ( envelope300 ,fs);77 [ P3000 ,w4 ]= pwelch ( envelope3000 ,fs /2) ;787980 % P l o t t h e e n v e l o p e power spectrum81 figure ;82 f=w1/ pi *fs /2;83 plot (f,P3 ,’-k’);84 xlim ([0 5]) ;85 ylim ([0 1500]) ;86 xlabel (’Frequency [Hz]’);87 ylabel (’Envelope power density ’);88 nicefigure ;8990 figure ;Page A2Temporal Processing and Modulation

Project group 5 April 200891 f=w2/ pi *fs /2;92 plot (f,P30 ,’-k’);93 xlim ([0 50]) ;94 ylim ([0 100]) ;95 xlabel (’Frequency [Hz]’);96 ylabel (’Envelope power density ’);97 nicefigure ;9899 figure ;100 f=w3/ pi *fs /2;101 plot (f,P300 ,’-k’);102 xlim ([0 500]) ;103 ylim ([0 10]) ;104 xlabel (’Frequency [Hz]’);105 ylabel (’Envelope power density ’);106 nicefigure ;107108 figure ;109 f=w4/ pi *fs /2;110 plot (f,P3000 ,’-k’);111 xlim ([0 5000]) ;112 ylim ([0 1.0]) ;113 xlabel (’Frequency [Hz]’);114 ylabel (’Envelope power density ’);115 nicefigure ;116117118 close a l l ;119 % Modulation o f 16 Hz120121 t =[1/ fs :1/ fs:N/fs ];122 cos16 = cos (2* pi *16* t);123 s3 = noise3 ’.*(1+ m* cos16 );124 s30 = noise30 ’.*(1+ m* cos16 );125 s300 = noise300 ’.*(1+ m* cos16 );126 s3000 = noise3000 ’.*(1+ m* cos16 );127128 envelopes3 = abs( hilbert (s3));129 envelopes30 = abs( hilbert ( s30 ));130 envelopes300 = abs( hilbert ( s300 ));131 envelopes3000 = abs( hilbert ( s3000 ));132133 [Ps3 ,w]= pwelch ( envelopes3 ,5* fs);%,10∗ f s ) ;134 [Ps30 ,w]= pwelch ( envelopes30 ,5* fs);135 [ Ps300 ,w]= pwelch ( envelopes300 ,5* fs);136 [ Ps3000 ,w]= pwelch ( envelopes3000 ,5* fs);137138 f=w/ pi *fs /2;139140 % P l o t t h e e n v e l o p e power spectrum141 figure ;142 semilogx(f ,10* log10( Ps3 ),’-k’);143 hold on;144 semilogx(f ,10* log10( Ps30 ),’:k’);% , ’ Color ’ , [ . 2 5 .25 . 2 5 ] ) ;Page A3

APPENDIX145 semilogx(f ,10* log10( Ps300 ),’-’,’Color ’ ,[.5 .5 .5]) ;146 semilogx(f ,10* log10( Ps3000 ),’-’,’Color ’ ,[.75 .75 .75]) ;147 %148 % xlim ( [ 2 4550]) ;149 % x l a b e l ( ’ Frequency [ Hz ] ’ ) ;150 % y l a b e l ( ’ Envelope power d e n s i t y ’ ) ;151 % l e g e n d ( ’ Carrier BW 3 Hz ’ , ’ Carrier BW 30 Hz ’ , ’ Carrier BW 300 Hz ’ , ’ Carrier BW 3000Hz ’ )152 % n i c e f i g u r e ;153 %154 xlim ([2 50]) ;155 xlabel (’Frequency [Hz]’);156 ylabel (’Envelope power density ’);157 set (gca,’XTick ’ ,[2 5 10 20 50]) ;158 legend(’3 Hz wide carrier ’,’30 Hz wide carrier ’,’300 Hz wide carrier ’,’3000 Hz widecarrier ’,’ Location ’,’ SouthWest ’);159 nicefigure ;✝✆Page A4Temporal Processing and Modulation