An Examination and Interpretation of ITU-R BS.1387: Perceptual Evaluation of Audio Quality

Transcription

1 An Examination and Interpretation of ITU-R BS.1387: Pereptual Evaluation of Audio Quality P. Kabal Department of Eletrial & Computer Engineering MGill University Version 2:

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3 An Examination and Interpretation of ITU-R BS.1387: PEAQ i Table of Contents 1 Introdution Time to Frequeny Domain (FFT-based Ear Model) Input Windowing Frequeny Domain Coeffiients Calibration of the Loudness Saling Fator Outer and Middle Ear Modelling Critial Band Deomposition Internal Noise Frequeny Spreading Time Domain Spreading The Filter Bank Ear Model DC Rejetion Filter Filter Bank Outer and Middle Ear Modelling Frequeny Domain Spreading Bakward Masking Internal Noise Forward Masking Pattern Proessing Exitation Pattern Proessing Modulation Pattern Proessing Loudness Calulation Calulation of the Model Output Variables Data Boundary Modulation Changes Distortion Loudness Bandwidth Masking Detetion Probability Harmoni Struture of Error Calulation of the Objetive Differene Grade Model Output Variables Basi Version Model Output Variables Advaned Version Binaural Signals...54

4 An Examination and Interpretation of ITU-R BS.1387: PEAQ ii 6.4 Saling the Model Output Variables Basi Version Saling the Model Output Variables Advaned Version Neural Network Basi Version Neural Network Advaned Version Start and End Samples Summary Referenes...61 Appix A Calibration of the Loudness Saling Fator...62 Appix B Spreading Funtion...66 Appix C Butterworth DC Rejetion Filter...68 Appix D Filter Bank...7 Appix E Error Harmoni Struture...72 E.1 Correlation Lag Values...72 E.2 Correlation Mean Removal...73 Appix F FFT-Based Ear Model Matlab Code...76 F.1 FFT Proessing...76 F.2 Critial Band Parameters...78 F.3 Critial Band Grouping...78 F.4 Spreading (DFT-Based Model)...8 Appix G Pattern Proessing Matlab Code...82 G.1 Level and Pattern Adaptation...82 G.2 Modulation Patterns...84 G.3 Loudness Calulation...84 Appix H Model Output Parameters Matlab Code...86 H.1 Modulation Differenes...86 H.2 Noise Loudness...86 H.3 Noise-to-Mask Ratio...87 H.4 Bandwidth...88 H.5 Probability of Detetion...89 H.6 Error Harmoni Struture...9

5 An Examination and Interpretation of ITU-R BS.1387: PEAQ 1 An Examination and Interpretation of ITU-R BS.1387: Pereptual Evaluation of Audio Quality This report examines the standard whih desribes a method for the objetive measure of pereived audio quality (ITU-R Reommation BS.1387). This standard uses a number of psyho-aoustial measures whih are ombined to give a measure of the quality differene between two instanes of a signal (a referene and a test signal). Many aspets of the standard are under-speified. This report examines alternate interpretations. It also looks at effiieny issues in the implementation of omputationally intensive parts of the algorithm. 1 Introdution This doument examines the Pereptual Evaluation of Audio Quality (PEAQ) as desribed in ITU-R Reommation BS.1387, Method for Objetive Measurements of Pereived Audio Quality [1]. PEAQ an be used for rating the quality of, for instane, an audio oder. Additional bakground on PEAQ an be found in [2]. The desription in BS.1387 is inadequate by itself to allow for a onforming implementation. Corretions and larifiations to BS.1387 are available [3], but they still fail to provide all of the neessary details. These have been inorporated into a Draft Revision of the standard [4]. A group of graduate students at the TSP Lab, Eletrial & Computer Engineering, MGill University implemented parts of PEAQ as part of a ourse projet. Different members of the team indepently implemented a C-language and a Matlab version. The results and assumptions used for the implementations were ompared and rationalized. However, in the resulting implementation still did not always give reasonable results. Part of the blame was put on ambiguous and poorly desribed parts of the standard. Only after the projet was finished was it disovered that some of the tables in the standard had srambled entries. (These are orreted in [4].) At the same time, F. Baumgarte (from Bell-Labs, Luent Tehnologies) and A. Lerh (now at zplane) were attempting separate implementations, but also were having trouble interpreting the intentions of the standard [5]. Lerh has implemented the ode for the Basi version of PEAQ (available on-line at one time [6]).

6 An Examination and Interpretation of ITU-R BS.1387: PEAQ 2 Problems with BS.1387 The BS.1387 standard has two options: a Basi version and an Advaned version. The Basi version uses a FFT based ear model, while the Advaned version uses that model as well as a filter bank based ear model. In both ases, model output variables are ombined using a trained neural network to give a single metri, the Objetive Differene Grade (ODG) whih measures the degradation of a test input relative to a referene input. A standard is normally written so as to unambiguously speify the operations needed for a onforming implementation. Certain parts of BS.1387 are underspeified, so that it is not possible to hoose between plausible alternatives. Some of the model output variables are poorly desribed. The EHS B model output variable is a ase in point. The desription is ambiguous. The desription of the operations for parts of the Advaned version has additional problems. Some of the speifiation is in the form of pseudo-ode. There are errors in the pseudo-ode, some of whih were orreted in [4]. It remains an open question as to whether the referene implementation also ontains these mistakes. The standard gives a table of the output quality measure for a number of test ases. However, the standard does not give values for the model output variables that lead to these values. In the Basi version of PEAQ, there are 11 model output variables that are ombined with a neural network. If these values had been given as part of the onformane tests, it might have been possible to disambiguate parts of the standard. It is the opinion of this author that a onforming implementation is not possible without aess to additional information, information whih is not provided by the standard. Goals of this Doument This doument attempts to rationalize the interpretation of ambiguous or poorly desribed setions of the standard. The goal of this present work is to use BS.1387 as a point of departure to understand the tehniques employed in the standard to evaluate audio quality. The hope is that suh an understanding will lead to use of parts of the PEAQ algorithm to guide design hoies for audio oders, first in a oneptual sense and later perhaps even in the proess of better dynamially alloating bits within the oder. One element of the examination is the effiieny of implementation of different parts of PEAQ with a view to inorporation in real-time audio oders.

7 An Examination and Interpretation of ITU-R BS.1387: PEAQ 3 2 Time to Frequeny Domain (FFT-based Ear Model) 2.1 Input The PEAQ model assumes that the input signals are sampled at 48 khz. The test and referene signals are assumed to be time-aligned. Proessing ours for frames of 248 samples (43 ms). The frame advane is 124 samples, resulting in a 5% overlap of frames. The first steps in the proess of onverting from time samples to frequeny-domain samples are the same for the test and referene signals and indeed for the hannels in a stereo signal. The sampling frequeny will be denoted as F s and the frame length as data ontain samples x[ n ] with n running from to N 1, inlusive. F N F. Let a frame of 2.2 Windowing The frame of data is windowed with a Hann window. A basi disrete-time Hann window is given by 1[ 1 os ( 2π n )], n N 1, 2 N 1 F hnn [, ] F F =, otherwise, (1) where the sampling frequeny has been denoted as F s. This window is zero-valued at the points n =, and n= N F 1, meaning that this window has only NF 2 non-zero terms. 1 The sum of squared window values is h [ n, N ] = ( NF 1). (2) n= 2 3 F 8 This value an be used to sale the window suh that for DC or white noise, the energy per sample after windowing is the same as the energy per sample before windowing. 1 There are three reasonable hoies for the window length (in the notation of Eq. (1)), N F, N F + 1 or N F + 2, eah with N F or fewer non-zero oeffiients. If the window were a Hamming window (a Hann window on a pedestal), the first would be the natural hoie (giving N F non-zero values). For a Hann window, the number of non-zero samples is less by two. Consider a pure sine with a frequeny whih oinides with the entre of one of the DFT bins (frequeny kfs / N F ). Only the middle hoie of Hann window length is free of spetral leakage for those sine frequenies. The last hoie of window length gives the narrowest main lobe in the frequeny response of the window.

8 An Examination and Interpretation of ITU-R BS.1387: PEAQ 4 The atual window used in the standard is a saled version of Eq. (1), 8 hw[ n] = h[ n, NF]. (3) 3 Clearly, the window saling was meant to ompensate for the energy loss due to the taper in the window. However, the saling used is off by the fator 1 1/ N. F 2.3 Frequeny Domain Coeffiients The windowed data is onverted to the frequeny domain using a Disrete-Fourier Transform, N 1 F 1 j2 π nk/ N Xk [ ] = h[ ] [ ] F w nxne. (4) N F n= F The saling fator 1/ N is unonventional (at least in the engineering signal proessing literature). The DFT values are defined for k N F 1. However, only values for k N/ 2, orresponding to frequenies from to F s / 2 (24 khz) will be needed in the sequel. 2.4 Calibration of the Loudness Saling Fator Some of the pereptual quality fators dep on the atual sound pressure level of the test signal. A alibration step is needed to fix the mapping from input signal levels to loudness. The alulation of the saling fator is disussed in Appix A. The additional saling fator, denoted here as G L, (whih takes into aount the window saling) is equal to G L = γ f L p A 4 /2 1 3 N N 8 max ( ) ( 1) F F, (5) where L p is the sound pressure level (SPL) in db orresponding to a full-sale test sine. In the absene of other information, BS.1387 indiates that L p should be set to 92 db SPL. The parameter A max is the maximum amplitude of the sine (for instane for 16-bit data) and γ ( f ) is a fator whih varies from.84 to 1 deping on where the frequeny of the test sine falls relative to the DFT bins. For a test frequeny of Hz as suggested in BS.1387, γ ( f )

9 An Examination and Interpretation of ITU-R BS.1387: PEAQ 5 is equal to Using these values, G L is equal to The last terms in the saling fator an be omitted if one uses a standard Hann window and a standard DFT definition. The standard states: Where the normalization fator Norm is alulated by taking a sine wave of Hz and db full sale as the input signal and alulating the maximum absolute value of the spetral oeffiients over 1 frames. This measurement is unneessary, sine the appropriate gain value an be alulated analytially. The sale fators for the Hann window, the DFT and the loudness saling fator an be lumped together if desired and applied one. Appix F.1 gives Matlab ode for the operations desribed above. The alibration proedure involves setting the peak value of the DFT for a sinusoidal input to a given value. However, sound pressure level is an energy phenomenon. A more appropriate alibration would involve the total energy whih by Parseval s relationship is preserved in the frequeny domain. Suh a alibration proedure is indepent of the frequeny of the test sine. 2.5 Outer and Middle Ear Modelling The frequeny response of the weighting filter as given in BS.1387 is restated here. The response of the outer and middle ear is modelled as db khz ( ) = 1 db. 2.6( f /1 3.3) ( ) ( ) ( f )/ A ( f ) = f / e.1 f /1, W f A (6) Note that at zero frequeny, the response in db is. This response is plotted in Fig. 1. The response at 1 khz is 1.9 db and the peak value of db ours near 3.3 khz. The response in Eq. (6) is similar to that given by Terhardt [7]. The differene is in the first term whih ontrols the response at low frequenies. Terhardt uses a fator 3.64 rather than (whih is given in the standard as ) in the first term. Later in Setion 2.16 of the standard, we meet the other part of the fator ( ) as the ontribution due to internal noise. The vetor of weights (linear sale) is given by kf N N 2 s F Wk [ ] = W( ), k. (7) F

10 An Examination and Interpretation of ITU-R BS.1387: PEAQ Response (db) Frequeny (Hz) Fig. 1 Outer and middle ear response. A marker appears at 1 khz. Note that at zero frequeny ( k = ), the weight is zero. Using these weights, the weighted DFT energy (inluding the loudness sale fator) is L X [ k] = G W [ k] X[ k], k. (8) w N F Critial Band Deomposition The grouping into ritial bands uses a frequeny to Bark sale onversion, z = B( f) = 7asinh( f / 65), (9) where the units of z are Barks. The inverse mapping is f = B 1 ( z) = 65sinh( z / 7). (1) Frequeny Bands The proessing uses frequeny bands whih differ in width for the Basi version and the Advaned version of PEAQ. For the Basi version, z = 1, while for the Advaned version, z = 1 2. The frequeny bands start at f L (8 Hz) and stop at f U (18 khz). All bands but the last have the same width in Barks. 4

11 An Examination and Interpretation of ITU-R BS.1387: PEAQ 7 The bands an be speified in terms of a lower frequeny edge, a entre frequeny and an upper frequeny edge. The entre frequeny is the frequeny orresponding to the entre of the filter band on the Bark sale. The band values on the Bark sale are given as follows, z [] i = z + i z l L zl + ( i+ 1) z), i+ 1 ( zu zl)/ z zu[] i = zu, otherwise zu[] i zl[] i z[] i =, 2 (11) where z = B( f ) and z = B( f ). The orresponding band edges in frequeny are given by L using the inverse Bark mapping L U U 1 f [ i] = B ( z [ i]), l 1 f [ i] = B ( z [ i]), 1 f [ i] = B ( z [ i]). u l u (12) For the Basi version, there are 19 filter bands; for the Advaned version there are 55 bands. The band edges in Hz are given to 3 deimal plaes in tables in BS The band edges alulated using the proedure desribed above agree with the tabulated values in BS.1387 to within.3 Hz. Appix F.2 gives the Matlab ode to alulate the ritial band parameters. Grouping of Frequeny Bins The next step of proessing is to take a frame of frequeny domain samples (based on DFT bins) and group them into the frequeny bands defined above. The grouping is done as follows. DFT bin k orresponds to frequeny f [ k] = kf / N and is onsidered to be distributed over the s s F bin width, i.e., the bin exts ± F /(2 N ) from the entre frequeny. BS.1387 ontains pseudoode whih alulates the energy per frequeny band given the energy distribution in DFT bins. A more omputationally effiient proedure is to preompute tables, obviating the need for omparisons. For the i th frequeny band, the ontribution from the energy in DFT bin k is F [ ] 2k+ 1 Fs 2 1 Fs k 2 N l F 2 NF Fs N max,min( fu[ i], ) max( f [ i], ) Uik [, ] =. (13) The energy in band i for a DFT-based signal is F

12 An Examination and Interpretation of ITU-R BS.1387: PEAQ 8 k [] i u k= k [] i 2 E [] i = U[, i k] X [ k], (14) a l where Uik [, ] is non-zero over the interval k [ i] k k [ i]. Note that Uik [, ] is equal to unity when k is stritly inside the interval, leading to the simplifiation 2 l k []1 2 u i 2 2 a = l w l + w + u w u k= k []1 i + u w E [] i U [] i X [ k []] i X [ k] U [] i X [ k []] i, (15) l where U [] i = U[, i k []] i and U [] i = U[, i k []] i. Appix F.3 inludes Matlab ode to arry out l the grouping of the frequeny bands. where l A last step is to set the energy to E min is u u if it is less than this value, E [] i = max( E [], i E ), (16) b a min 2.7 Internal Noise An offset is added to the band energies to ompensate for internal noise generated in the ear, where the internal noise is modelled as E[] i = E [] i + E [], i (17) b IN INdB khz IN ( ) E ( f [ i])/1 [] = 1 INdB..8 E ( f ) = f /1, E i (18) The fator is given in the standard as , whih is the missing part of the formula given by Terhardt, referred to earlier. The response is plotted in Fig. 2. At 1 khz, the ontribution is 1.46 db. The energies E[ i ] are referred to as the pith patterns. 2 This formulation assumes k [] i > k [] i. If not then one of U [] i or U [] i should be set to zero. u l l u

13 An Examination and Interpretation of ITU-R BS.1387: PEAQ Response (db) Frequeny (Hz) Fig. 2 Internal noise ontribution. The markers indiate the entres of the frequeny bands for Basi version of PEAQ. 2.8 Frequeny Spreading The spreading operation is desribed in Appix B in terms of a ontinuous Bark spetrum. That desription is onverted here to the orresponding alulation on a disrete Bark sale used in BS The spread Bark-domain energy response is N Es[] i = [] (,, []), Bs[] i l=.4 ( E l S i l E l ) (19) where N is the number of filter bands in the frational ritial band representation (19 for the Basi version and 55 for the Advaned version). The normalizing fator is alulated for a referene level of db for eah band, 1.4 N Bs[] i = (,, ), 1.4 ( S i l E ) (2) l= where E = 1 ( db). The normalizing fator an be pre-omputed sine it does not dep on the data. The spreading funtion is

14 An Examination and Interpretation of ITU-R BS.1387: PEAQ 1 1 S (,, i l E)/1 = (21) Al (, E) (,, ) 1 db, SilE where the normalizing term is hosen to give a unit area for eah entre frequeny l. The spreading funtion in db is triangular, 3 S 27( i l) z, i l, (,, i l E) = [ log 1( E) ]( i l) z. i l, db 23 f [] l (22) The omputations involved in the evaluation of the spread energy an represent a large fration of the overall omputations needed for PEAQ. However, the form of the spreading funtion leads to a regrouping whih allows for some terms to be pre-omputed and others to be omputed reursively. SilE (,, ) z i l (1 ), i l, Al (, E) = z 23 z/ f[ l].2 z i l [(1 )(1 )( E )], i l, Al (, E) 1 i l al, i l, Al (, E) = 1 i l [ auac[ l] ae( E)], i l, Al (, E) (23) where the terms a L, a U, ac [ l ], and ae ( E ) are impliitly defined by the first part of the equation. The normalizing term A(, le ) is the sum over i of SilE (,, ) and an be expressed in losed form as 1 l N 1 l i = L + U C E l i i= ( l+ 1) 1 al 1 1 al i= l N 1 ( [ ] ( )) l auac l ae E 1 auac[ l] ae( E) A (, l E) a ( a a [] l a ( E)) 1 = + 1 (24) Consider splitting the omputation of the spread energy response in Eq. (19) into two parts, 1 E [] ( [] []) 1.4 s i = EsL i + EsU i, (25) B [] i s 3 For low frequenies, the frequeny spreading due to the time windowing of the input signal is a signifiant fration of the ritial band width. The spreading funtions an be narrowed to ompensate [9].

15 An Examination and Interpretation of ITU-R BS.1387: PEAQ 11 where and N ( L ) El [] i l EsL[] i = a, Al (, El []) (26) i 1 l= i.4.4 (( ) ) El [] i l E [] i = a a [] l a ( E[]) l. (27) su U C E l= AlEl (, []) Further omputational reorganization an be done for the lower part of the spreading funtion, E sl.4 EN [ 1] [ N 1] =, Al (, EN [ 1]).4.4 Ei [] sl L sl E [] i = a E ( i+ 1) + i= N 2,,. Al (, Ei []) (28) The term whih inludes the upper part of the spreading funtion is not quite so amenable to simplifiation. Some omputational savings arue if we ompute the power term reursively. The omputational proedure for reating the exitation patterns is shown in Appix F.4. The normalization term Bs[] i is plotted in Fig. 3. Note the hange in value at the s of the spetrum. The spreading funtions themselves (normalized by both Bs[ i ] and Al (, E ) ) are shown in Fig. 4. The plot shows every fourth spreading funtion (a spaing of 1 ritial band for the Basi version of PEAQ) for a signal level of 6 db SPL. Amplitude (db) Frequeny (Hz) Fig. 3 Normalization fator [] s B i for the Basi version of PEAQ.

16 An Examination and Interpretation of ITU-R BS.1387: PEAQ Amplitude (db) Frequeny (Hz) Fig. 4 Spreading funtions (6 db signal level). Every fourth spreading funtion is plotted for the Basi version of PEAQ. The exitation patterns derived ( Es[ i ]) are referred to as unsmeared exitation patterns (unsmeared in time). They will be used in alulation of modulation patterns. 2.9 Time Domain Spreading The formulation until now has been based entirely on proessing a single frame. We now introdue a time spreading whih deps on multiple frames. For this purpose we add a frame index n to the spread energy in the Bark domain, Es[, in ]. Frames are updated every N F /2 samples. The frame rate is F ss Fs =. (29) N /2 To model forward masking, a frequeny depent filtering (smearing) over time is implemented, F E [, in] = α[] ie [, in 1] + (1 α[]) i E[, in], f f s E [ i, n] = max( E [ i, n], E [ i, n]). s f s (3) The parameter α [ i] ontrols the time onstant of the averaging for deaying energies. The max( ) funtion in the seond line means that E[ in, ] follows inreases in energy instantaneously.

17 An Examination and Interpretation of ITU-R BS.1387: PEAQ 13 The initial ondition for the filtering is given as Ef [,] i =. We assume that frames are indexed from n = for onsisteny with the sequel. Then, the initial ondition is atually E [ k, 1] =. The outputs E [, in] are known as exitation patterns. s f Time Constants The time onstant of the first order differene equation (in frames) is 1/ log( α[ i]). The time onstant in seonds is 1 τ [] i =, (31) F log( α [ i]) where F ss is the frame rate. The time onstant for filter band i is speified as, ss τ 1 [] i = τ min + ( 1 min ), f [] i τ τ (32) where τ 1 =.3 s and τ min =.8 s. Then α [ i] an be alulated from 1 α[] i = exp( ). (33) F τ[] i The time onstant at 1 Hz is τ 1. The lowest entre frequeny is only slightly below 1 Hz. The smallest time onstant ours at the highest entre frequeny and is lose to τ min time onstants are plotted in Fig. 5. ss. The

18 An Examination and Interpretation of ITU-R BS.1387: PEAQ Time onstant (ms) Frequeny (Hz) Fig. 5 Time onstants as a funtion of frequeny for τ min =.8 s and τ 1 =.3 s. The markers indiate the entres of the frequeny bands for the Basi version of PEAQ

19 An Examination and Interpretation of ITU-R BS.1387: PEAQ 15 3 The Filter Bank Ear Model The Advaned version of PEAQ uses a Filter bank ear model as well as the FFT-based model. The saling for the input to the filter bank is given assuming that full sale for the input is A max = More generally, the saling applied to the input is, where in the absene of other information, (16-bit data), and L p = 92 db SPL, g = Lp /2 Amax g = 1, (34) L p is assumed to be 92 db SPL. If A max is DC Rejetion Filter The signal is then passed through a 4 th order DC rejetion filter to remove subsoni signal omponents. This filter is a Butterworth highpass filter with a utoff of 2 Hz and is realized as the asade of two seond order IIR setions. The filter response is derived in Appix C. The magnitude of the frequeny response is plotted in Fig. 6. Amplitude (db) Frequeny (Hz) Fig. 6 Frequeny response of a 4'th order Butterworth highpass filter with utoff at 2 Hz. Implementing the filter with seond-order setions, x[ n] = a x[ n 1] a x[ n 2] + xn [ ] 2 xn [ 1] + xn [ 2], a 1 a 2 a x [ n] = a x [ n 1] a x [ n 2] + x [ n] 2 x [ n 1] + x [ n 2]. hp 11 hp 12 hp a a a (35)

20 An Examination and Interpretation of ITU-R BS.1387: PEAQ 16 Several memory saving approahes an be used for implementing the highpass filter. Eah setion uses the urrent and two previous inputs, and two previous outputs. Noting that the output of one setion is the input to the next, some of this memory an be shared to give an effiient implementation. 3.2 Filter Bank The filter bank uses bandpass filters at 4 entre frequenies ranging from f L = 5 Hz to f = 18.2 Hz. The entre frequenies are equally-spaed on the Bark sale with a spaing U given by B( fu) B( fl) z =. N 1 (36) The entre frequenies are 4 z [ k] = B( f ) + k z, k N 1, L 1 f [ k] = B ( z [ k]) k N 1. (37) For eah entre frequeny, there is a pair of linear phase FIR filters, an in-phase filter and a quadrature filter, f[ k] Nk I p ( π ) F 2 k h [ k, n] = h [ k, n]os 2 ( n ), n N 1, s f[ k] Nk Q p ( π ) F 2 k h [ k, n] = h [ k, n]sin 2 ( n ), n N 1, s (38) where the lowpass prototype for filter k is 4 2 n hp[ k, n] = sin ( π ), n Nk 1. (39) N N k k The prototypes have lengths as tabulated in BS See Appix D for a further disussion of the filter responses. The response of the filter bank is shown in Fig. 7. The figure shows the superimposed responses of the in-phase filters. The absissa has been warped to the Bark sale, but is labelled with frequeny in Hz. Note that the lowest frequeny bandpass filter has a signifiant response down to DC. However, the subsoni omponents up to 2 Hz have already been removed by the DC rejetion filter. 4 The results when rounded to two deimal plaes differ by at most.1 Hz from the values tabulated in BS.1387.

21 An Examination and Interpretation of ITU-R BS.1387: PEAQ 17 Amplitude (db) Frequeny (Hz) Fig. 7 Superimposed filter bank responses. The frequeny axis is linear on a Bark sale. Note that although the filters are speified to have an even number of oeffiients, the first oeffiient of eah filter is zero. Thus they are effetively of length Nk 1. There is a middle oeffiient whih is used as a time referene for the modulation terms in Eq. (38). The filters are aligned in time relative to the middle of eah filter. This involves artifiially adding delay to the shorter branhes of the filter bank. N 2 k x [ k, n] = h [ k, m] x [ I n m D ], I I hp S k m= N 2 k x [ kn, ] = h [ kmx, ] [ I n m D], Q Q hp S k m= (4) where the filters re-indexed to omit the first (zero-valued) oeffiient and saled by g, h I[ k, n] = ghi[ k, n+ 1] n Nk 2, h [ k, n] = gh [ k, n+ 1] n N 2. Q Q k (41) The output is subsampled by the fator I S = 32. The entre oeffiient in the re-indexed filters is at index N / 2 1. For the longest filter ( k = ), the delay is set to zero, D =. The first oeffiient of this filter aligns with x [ n ] and the middle of this filter aligns with xhp [ n N /2+ 1]. The delays used to align the middle of the other filters with this same sample are k hp

22 An Examination and Interpretation of ITU-R BS.1387: PEAQ 18 D k N Nk =. (42) 2 The standard indiates that the referene implementation adds one to the delay of eah branh (inluding the branh with the longest filter). The output of eah of the filters has a sampling rate of 15 Hz in eah hannel. As noted in the standard, this redued sampling rate too small for the wider upper bands some aliasing will be inevitable for those bands. 3.3 Outer and Middle Ear Modelling The frequeny response of the outer and ear model used earlier (Eq. (6)) evaluated at the enter frequenies of the filters is used to weight the filter outputs, x [ kn, ] = W( f[ k]) x[ kn, ], Iw I x [ kn, ] = W( f[ k]) x [ kn, ]. Qw Q (43) 3.4 Frequeny Domain Spreading The filter bank outputs are spread in frequeny. The spreading funtion is level and frequeny depent. The spreading funtion is similar to that enountered earlier for the FFT model. There are differenes in the slopes of the funtion and the fat that it is applied in the magnitude domain instead of the power domain raised to the.4 exponent. The instantaneous spreading funtion in db is 31( z z), z z, SdB(, z z, E) = min[ 4, log 1 ( ) 1( E), ]( z z), z z, B z (44) where E is the energy at the entre frequeny. The instantaneous spreading funtion (in the linear domain) is S ( z [ i], z [ l], E)/2 SilE (,, ) = 1 db. (45) Time Smoothing of the Spreading Funtion The spreading funtion hanges in response to hanges in energy. The spreading funtion is smoothed to redue these variations, Siln [,, ] = αsiln [,, 1] + (1 α) SilEln (,, [, ]), (46)

23 An Examination and Interpretation of ITU-R BS.1387: PEAQ 19 where E[ ln, ] is the energy in band l at time n, 2 2 Iw Qw E[, ln] = X [, ln] + X [, ln]. (47) The smoothing parameter orresponds to a time onstant of 1 ms ( τ =.1 s), 1 α = exp( ), (48) τ where F = F /32 is the sampling rate at the output of the filter bank. ss s The smoothing of the spreading funtion with time is defined by pseudo-ode in the standard. The pseudo-ode is inonsistent with the text desription. As implemented in the pseudo-ode, the roles of α and 1 α are interhanged, resulting in an extremely short time onstant (58 µs). The omputations for frequeny spreading an be simplified using an approah analogous to that developed earlier for the FFT model spreading. In fat the pseudo-ode in the standard implements this type of reursion. F ss Spreading Applied to the Filter Outputs The spreading funtion is applied to the in-phase and quadrature omponents in eah band separately, N 1 x [ kn, ] = x [ lnskln, ] [,, ], Iw Iw l= N 1 x [ kn, ] = x [ lnskln, ] [,, ]. Qw l= Qw (49) Finally, the energy of eah hannel is omputed, 2 ( ) ( ) 2 E [ k, n ] = x Iw [ k, n ] + x Qw [ k, n ]. (5) 3.5 Bakward Masking The frequeny-spread energies are time-smeared with an FIR filter. The output of the filter is subsampled by a fator I D = 6, N B 1 b B D i= E [ km, ] = h[ ie ] [ kmi, i], (51)

24 An Examination and Interpretation of ITU-R BS.1387: PEAQ 2 where the onstant has the value.9761/6. 5 The filter hb[ i ] has N B = 12 oeffiients, 2 i ( NB /2 1) os ( π ) n NB 1, hb[] i = NB (52) otherwise. The filter pulse response is zero at n= N b 1, and so has only 11 non-zero oeffiients. The output sampling rate is F s /192 for eah hannel. 3.6 Internal Noise Internal noise is added to eah band. The internal noise funtion is given by Eq. (18) evaluated at the entre frequenies of the filters. The result is E [ kn, ] = E[ kn, ] + E [ kn, ]. (53) These are the unsmeared exitation patterns for the filter bank model. s b IN 3.7 Forward Masking Forward masking is implemented with a first order filter E [ kn, ] = α[ ke ] [ kn, 1] + (1 α[ k]) E[ kn, ], (54) s s where the differene equation oeffiients are alulated from the time onstants τ 1 =.2 s and τ min =.4 s ( F = F /192, see Setion 2.9.1) 6. The values after applying forward masking ss are the exitation patterns for the filter bank model. s 5 The origin of the value for the onstant is not lear. The filter ats on an energy signal. If the input is onstant, then setting = 2/ Nb preserves the energy level at the output. 6 In [2], the time onstant at 1 Hz is given as 5 ms.

25 An Examination and Interpretation of ITU-R BS.1387: PEAQ 21 4 Pattern Proessing The outputs of the FFT and filter bank bloks are further proessed. For this disussion, there are two input signals and the orresponding outputs: the referene signal and the test signal. Subsripts R and T will refer to signals derived from the referene and test signals, respetively. The ase of binaural signals will be disussed later in onnetion with the model output variables. For the purposes of this setion, one an onsider the two hannels (left and right, for instane) to be separate signals for whih there are referene and test instanes. 7 The proessing the FFT and filter bank outputs an be onsidered together. The FFT outputs our at a rate of F s /124, while the filter bank outputs our at a rate of F s /192. The number of entre frequenies for the FFT model is 19 for the Basi version and 55 for the Advaned version. For the filter bank (used in the Advaned version only), there are 4 entre frequenies. These parameters are summarized in Table 1. PEAQ Version Table 1 Proessing parameters Model Sampling Rate F ss No. Centre Frequenies N Basi FFT F s / Advaned FFT F s / Filter Bank F /192 4 s For the Advaned version of PEAQ, proessing has to our at two rates. For every 3 outputs from the FFT model, there are 16 outputs from the filter bank. The signals produed by the FFT model and the filter bank model are shown in Fig. 8. The figure also shows the sampling rate at different points of the proessing. 7 For the sequel, unless otherwise indiated, the index k represents frequeny band and the index n represents a frame ount.

26 An Examination and Interpretation of ITU-R BS.1387: PEAQ 22 x [ n] x [ n] R T F s Hann Window DC Rejetion Filter FFT X [ k] X [ k] R T Outer & Middle Ear Weighting F /124 /32 s F s Filter Bank Outer & Middle Ear Weighting Error Signal Frequeny Grouping Frequeny Grouping Internal Noise Frequeny Spreading F s /192 Bakward Masking Noise Patterns EbN [ k, n ] Frequeny Spreading E [ k, n] E [ k, n] sr st Time Spreading Forward Masking E [ k, n] E [ k, n] Exitation Patterns E [ k, n] E [ k, n] sr st Unsmeared Exitation Patterns Internal Noise E [ k, n] E [ k, n] sr sr st st Fig. 8 Output signals from the FFT model and the filter bank model. Subsripts R and T will refer to signals derived from the referene and test signals, respetively. 4.1 Exitation Pattern Proessing The inputs are the exitation patterns (frequeny spread and time smoothed): E [ kn, ] and E st [ kn, ]. These are funtions of frequeny and time. Interpretations of the following operations are given in [2,1]. sr

27 An Examination and Interpretation of ITU-R BS.1387: PEAQ 23 Time Domain Spreading The exitation patterns are time-spread again with a frequeny-depent time onstant, 1 τ[ k] = τ + ( τ τ ), min 1 min f[ k] 1 α[ k] = exp( ), F τ[ k] ss (55) where the time onstants are determined from τ 1 =.5 s and τ min =.8 s, and F ss is the sampling rate. 8 The preamble for the setion on pattern proessing in the draft revision to BS.1387 states: If not given otherwise, all variables and reursive filters are initialized to zero. The use of the phrase if not given otherwise, would lead one to expet that some filtering operations are not initialized to zero. There is no example of the otherwise in this standard (but see the omments on initialization with respet to pattern adaptation). Time-spreading ours indepently for eah frequeny band and separately for the referene and test signals, PR[ k, n] = α[ k] PR[ k, n 1] + (1 α[ k]) E sr[ k, n], P [ k, n] = α[ k] P [ k, n 1] + (1 α[ k]) E [ k, n]. T T st (56) The initial onditions for this filtering are zero. These signals are used to adjust the levels of the referene and test signals. The momentary orretion fator averaged aross frequeny bands is N 1 P [ k, n] P [ k, n] T R k= = N 1 CL[ n]. PT [ k, n] k= 2 (57) Note that the denominator is guaranteed to be positive sine an energy floor (FFT model) and an internal noise term was added. The exitation patterns are level orreted as follows, 8 Note that τ 1 is different from the value used earlier for time spreading in the FFT model.

28 An Examination and Interpretation of ITU-R BS.1387: PEAQ 24 E E LR LT E sr[ k, n]/ CL[ n] CL[ n] > 1, [ k, n] = E sr[ k, n] CL[ n] 1, E st [ k, n] CL[ n] > 1, [ k, n] = E st [ k, n] CL[ n] CL[ n] 1. (58) Pattern Adaptation The outputs are further smoothed. First a time-smoothed orrelation between the referene and test patterns for eah frequeny band is alulated. The numerator and denominator of the orrelation term are (using the same time onstants as earlier and zero initial onditions 9 ), R [ kn, ] = α[ kr ] [ kn, 1] + E [ kne, ] [ kn, ], n n LT LR R [ kn, ] = α[ kr ] [ kn, 1] + E [ kne, ] [ kn, ]. d d LR LR (59) The ratio of these terms is used to form a pair of auxiliary signals whih takes on values between and 1, 1 Rn[ kn, ] Rd[ kn, ], RR[ k, n] = Rn[ k, n] R [, ] [, ], [, ] n kn< Rd kn Rd k n Rd [ k, n] R [, ] [, ], [, ] Rn[ k, n] n kn Rd kn RT k n = 1 Rn[ kn, ] < Rd[ kn, ]. (6) Speial ases our if the denominator term is zero. If Rd [ kn, ] is zero and Rn[ kn, ] is not zero, RT [ kn, ] is set to zero and RR[ kn, ] is set to one. This ondition is automatially taken into aount when the onditions are expressed as in Eq. (6). If both denominator and numerator are zero, the values are opied from the frequeny below ( R [ kn, ] = R[ k 1, n] and R [ kn, ] = R[ k 1, n] ). T T R If there is no band below ( k = ), then both R [ kn, ] and R [ kn, ] are set to one. R T R 9 This expression does not use the fator (1 α[ k]) in front of the seond term in eah line. Suh a fator would modify the saling of eah term and would ultimately anel when the ratio is taken.

29 An Examination and Interpretation of ITU-R BS.1387: PEAQ 25 The tests are unneessary. The terms in the alulations are positive sine an energy floor was imposed during the grouping into frequeny bins (FFT model) and an internal noise term was added (FFT model and filter bank model). The auxiliary signals are smoothed in time and frequeny, to form pattern orretion fators (same time onstants; for initialization, see the omments below), P [ k, n] = α[ k] P [ k, n 1] + (1 α[ k]) R [ i, n], CR CR ar P [ k, n] = α[ k] P [ k, n 1] + (1 α[ k]) R [ i, n], CT CT at (61) where the frequeny smoothed terms are k+ M [ k] 2 1 RaR[ kn, ] = RR[ in, ], M [ k] + M [ k] i= k M [ k] 2 1 RaT [ kn, ] = RT [ in, ]. M [ k] + M [ k] i= k M [ k] 1 k+ M [ k] 1 (62) The frequeny smoothing interval is nominally from k M1 to k + M2, but is orreted at the lower and upper frequeny bands, M [ k] = min( M, k), M [ k] = min( M, N 1 k). (63) The parameters differ deping on the version and model used as shown in Table 2. PEAQ Version Table 2 Frequeny smoothing parameters Model Sampling Rate M F 1 M 2 ss No. Centre Frequenies N Basi FFT F s / Advaned FFT F s / Filter Bank F s / Finally the pattern orretion fators are applied to give the spetrally adapted patterns, E [ kn, ] = E [ knp, ] [ kn, ], PT LT CT E [ kn, ] = E [ knp, ] [ kn, ]. PR LR CR (64) These spetrally adapted exitation patterns are the final outputs of this stage of proessing. Given the omments in the preamble to the desription of the pre-proessing of the exitation patterns in the draft revision to BS.1387, the initial onditions for the pattern orretion fa-

30 An Examination and Interpretation of ITU-R BS.1387: PEAQ 26 tors are zero, sine there is no information to the ontrary. However, perhaps a more appropriate initialization for the pattern orretion fators ( PCR[ k, n ] and PCT [ k, n ]) is unity. In fat, Lerh uses this initialization [6]. The spetrally adapted exitation patterns are used for the noise loudness alulations. In that omputation, there is a.5 s delay in averaging the values. With this delay, the effet of the initial onditions will be minimal. 4.2 Modulation Pattern Proessing The unsmeared exitation patterns (spread in frequeny, but not in time) are the inputs to this alulation. The goal is to ompute averages and average differenes in an approximate loudness domain (.3 power domain). The average loudness is ( ) E [ k, n] = α[ k] E [ k, n 1] + (1 α[ k]) E [ k, n], R R sr ( ) E [ k, n] = α[ k] E [ k, n 1] + (1 α[ k]) E [ k, n]. T T st.3.3 (65) The average loudness differenes is ( ) ( ).3.3 R = α R + α ss sr sr D [ k, n] [ k] D [ k, n 1] (1 [ k]) F E [ k, n] E [ k, n 1], ( ) ( ).3.3 T = α T + α ss st st D [ k, n] [ k] D [ k, n 1] (1 [ k]) F E [ k, n] E [ k, n 1]. (66) The time onstants are the same as used in the previous setion. Zero initial onditions apply. These loudness estimates are ombined to form a measure for the modulation of the envelope (at eah frequeny), DR[ k, n] MR[ k, n] =, 1 + ER[ k, n]/.3 (67) DT [ k, n] MT [ k, n] =. 1 + E [ k, n]/.3 These modulation parameters, as well as the average loudness of the referene signal ( E [ kn),, ] will be used later in the alulation of the modulation differenes. T R 4.3 Loudness Calulation The loudness of the signals is used later to selet frames to be inluded in the noise loudness model output variables. The speifi loudness patterns are (from [11])

31 An Examination and Interpretation of ITU-R BS.1387: PEAQ Et[ k] s[ k] E sr[ k, n] NR[ k, n] = 1 s[ k] + 1, sk [ ] E Et [ k] Et[ k] s[ k] E st[ k, n] NT [ k, n] = 1 s[ k] + 1, sk [ ] E Et [ k] (68) where the threshold index is f f 2 db f = ( ) ( ) 4 16 s ( ) 2 2.5atan.75atan ( ), sk s ( f [ k])/1 [ ] = 1 db, (69) and the exitation threshold is tdb ( ) E ( f [ k])/1 [ ] = 1 tdb..8 E ( f) = 3.64 f /1, E k t (7) The threshold index is the ratio of the intensity of a just-audible test tone and the intensity of the internal noise within a ritial band. The form used is attributed to Kapust, see [1]. The exitation threshold in quiet is the low frequeny part of the outer and middle ear filtering and internal noise terms that appeared earlier. The exitation threshold and the threshold index are plotted in Fig. 9. At 1 khz, the threshold index is about 3 db. The total loudness is the sum of the speifi loudness patterns, N 1 24 NtotR[ n] = max( NR[ k, n],), N k= N 1 24 NtotT[ n] = max( NT[ k, n],). N k= (71) The fator 24 is the total number of barks in an audio signal. The term 24 / N is approximately the width of eah frequeny band.

32 An Examination and Interpretation of ITU-R BS.1387: PEAQ Response (db) Exitation theshold Threshold index Frequeny (Hz) Fig. 9 Exitation threshold and threshold index. The markers indiate the entres of the frequeny bands for the Basi version of PEAQ. The total loudness is in units of sone. A 4 db SPL sine at 1 khz should give an output of 1 sone. To get this relationship, E is set to 1 4 (4 db relative to db SPL), and is set equal to for the FFT-based ear model and equal to for the filter bank model. The above setup does not predit the loudness of a sine. If we input a 1 khz sine orresponding to 4 db SPL, the total loudness is.584 sone. The sine wave amplitude for the 1 khz L p /2 4 / 2 sine was set to A max1 /1, where L p is the alibration sound pressure level (92 db) and A max is the peak amplitude of the 92 db SPL alibration sine. Inreasing the energy of the sine by a fator of 1 (sine amplitude multiplied by 1 ) should inrease the loudness by 1 sone. In fat the total loudness inreases by.77 sone. This is onsistent with the fat that exponent (.23) has been tuned for uniform exiting noise (noise with same energy in eah ritial band).

33 An Examination and Interpretation of ITU-R BS.1387: PEAQ 29 5 Calulation of the Model Output Variables The outputs of the previous steps are generally funtions of time and frequeny for the referene signal and the test signal. Next these funtions are distilled into funtions of time. Finally, these funtions of time are averaged to give a single value, the model output variable (MOV). The proessing parameters that differ between versions and models are given again in the table below. PEAQ Version Table 3 Proessing parameters Model Sampling Rate F All of the 11 model output variables used in the Basi version are derived from the FFT model. The model output variables are named in Table 4. In the Advaned version, there are 5 model output variables, some of whih are derived from the FFT model and the rest ome from the filter bank model. For the Advaned version the situation is as shown in Table 5. ss No. Centre Frequenies N Basi FFT F s / Advaned FFT F s / Filter Bank F s /192 4 Table 4 Model Output Variables PEAQ Basi Model Output Variable Model Desription BandwidthRef B FFT Bandwidth of the referene signal BandwidthTest B FFT Bandwidth of the test signal Total NMR B FFT Noise-to-mask ratio WinModDiff1 B FFT Windowed modulation differene ADB B FFT Average blok distortion EHS B FFT Harmoni struture of the error AvgModDiff1 B FFT Average modulation differene AvgModDiff2 B FFT Average modulation differene RmsNoiseLoud B FFT Distortion loudness MFPD B FFT Maximum filtered probability of detetion RelDistFrames B FFT Relatively disturbed frames

34 An Examination and Interpretation of ITU-R BS.1387: PEAQ 3 Table 5 Model Output Variables PEAQ Advaned Model Output Variable Model Desription RmsModDiff A Filter Bank Modulation hanges RmsNoiseLoudAsym A Filter Bank Distortion loudness Segmental NMR B FFT Noise-to-mask ratio EHS B FFT Harmoni struture of the error AvgLinDist A Filter Bank Linear distortions The Advaned version uses two MOV s from the FFT-based model, Segmental NMR A whih is used only in the Advaned version and EHS B whih is used in both versions. For binaural signals, for most MOV s, the alulation is done separately for hannel 1 and hannel 2. The orresponding MOV s for the hannels are then averaged. For two MOV s used in the Basi version, MFPD B and ADB B, the hannels are ombined frequeny by frequeny before time averaging. The figure below shows the inputs and outputs for the pattern proessing of the previous setion and whih are used in this setion. Exitation Patterns E [ k, n] E [ k, n] sr st Unsmeared Exitation Patterns E [ k, n] E [ k, n] sr st Exitation Patterns Loudness Modulation EPR[ k, n] EPT [ k, n] NtotR[ n] NtotT[ n] Spetrally Adapted Exitation Patterns Total Loudness M [ kn, ] M [ kn, ] R T Modulation Measures ER [ k, n ] Modified Exitation Patterns Fig. 1 Inputs and outputs from the pattern proessing step. The model output variables use the outputs of the pattern proessing step and sometimes other signals as well. The relationships are shown in Fig. 11.

35 An Examination and Interpretation of ITU-R BS.1387: PEAQ 31 E sr [ k, n ] EPR[ k, n] EPT [ k, n] M R[ kn, ] MT[ kn, ] ER[ k, n ] M R[ kn, ] MT[ kn, ] NtotR[ n] NtotT[ n] Modulation Differenes Distortion Loudness Averaging Averaging 2 2 T X [ k] X [ k] R E [ k, n] E [ k, n] bn sr Bandwidth Noise-to-Mask Ratio Averaging Averaging E [ k, n] E [ k, n] sr st Probability of Detetion 2 2 T X [ k] X [ k] R Error Harmoni Struture Energy Threshold Averaging Averaging Fig. 11 Inputs to the model output variable alulations. 5.1 Data Boundary The parameters that will be time averaged to beome the model output variables are subjet to a data boundary hek. The draft revision to BS.1387 states that the data boundary riterion applies to all MOV s. Low level frames at the beginning or of the input sequene are identified. The test for the beginning or of data is determined from the referene signal and is desribed as follows.

36 An Examination and Interpretation of ITU-R BS.1387: PEAQ 32 The beginning or of data is defined as the first loation, sanning from the start or of the file, where the sum of the absolute values over five sueeding samples exeeds 2, in one of the orresponding audio hannels. Frames whih are fully outside of this range are subsequently ignored. One assumes that the threshold value is given for 16-bit signed integer data. The threshold for a signal with maximum amplitude A max is Amax A thr = 2. (72) The implementation alls for a sliding window of L = 5 samples. The test is that the average magnitude of the samples in a window be greater than A thr / L (equal to 4 for 16-bit signed integer data). Interpretation: The data boundary start orresponds to the first sample of the first group of five samples to satisfy the riterion. Similarly for the of the file, the data boundary orresponds to the last sample of the last group of five samples whih satisfies the riterion. In terms of frames, the start frame is the first frame ontaining the start-of-data sample and the frame is the last frame ontaining the -of-data sample. It is an open question how to apply the data boundary ondition for the Advaned version of PEAQ. For the Advaned version, in the filter bank proessing, a definition of frame is somewhat more elusive than for the FFT proessing. In the subsequent desriptions, the frame index n will start ounting from zero at the start frame and the number of frames N will ount the frames up to the frame. 5.2 Modulation Changes The temporal envelopes for eah frequeny band are ombined into several model output variables. The differenes between the modulation patterns for the test and referene signals are first alulated for eah frequeny band and then averaged over frequeny bands. WinModDiff1 B (Basi version, FFT model) The instantaneous modulation differene for this MOV is given by M diff1 B MT[ kn, ] MR[ kn, ] [ k, n] =. 1 + M [ k, n] R (73)

37 An Examination and Interpretation of ITU-R BS.1387: PEAQ 33 The saled average over the bands is N 1 1 M diff1 [ n] = B Mdiff1 [ k, n]. (74) B N k= The final MOV is given by the sliding window average with L = 4 (85 ms), Delayed averaging is applied. N L diff1 [ ]. (75) 1 1 MWdiff1 = M n i B N L 1 L B + n= L 1 i= Delayed Averaging For delayed averaging, the values alulated during the first.5 seonds are omitted. The number of frames skipped is Ndel = τdel F ss, (76) where τ del =.5 s. Speifially, the frame index n inludes only the frames whih our after the initial delay and the total number of samples N that is used in the average, ounts only those values. Our interpretation is that the omputation of the delay in frames should give a delay of at least.5 seonds. AvgModDiff1 B (Basi version, FFT model) The instantaneous modulation differene is given by Eq. (73). The average over bands is given by Eq. (74). The differene for this MOV omes in the form of the averaging used. The final MOV is given by a temporally weighted time average, M = N 1 n= B Adiff1B N 1 W [ n] M [ n] 1 diff1 n= W 1 B [ n] B, (77) where the temporal weighting is determined by modulation pattern loudness for the referene signal (see Eq. (65)) and an internal noise term (see Eq. (18)),

38 An Examination and Interpretation of ITU-R BS.1387: PEAQ 34 W N 1 ER[ k, n] [ n] =. (78) E [ k, n] + 1 E [ k] 1B.3 ( ) k= R IN Again delayed averaging is used, see Setion AvgModDiff2 B (Basi version, FFT model) The instantaneous modulation differene is given by M diff2 B MT[ k, n] MR[ k, n] MT[ kn, ] MR[ kn, ],.1 + MR[ k, n] [ k, n] = MR[ k, n] MT[ k, n].1 MT[ kn, ] < MR[ kn, ]..1 + MR[ k, n] (79) The average over bands is N 1 1 M diff2 [ n] = B Mdiff2 [ k, n]. (8) B N k= The final MOV is given by a temporally weighted time average, M = N 1 n= B Adiff2B N 1 W [ n] M [ n] 2 diff2 n= W 2 B [ n] B, (81) where the temporal weighting is determined by modulation pattern loudness for the referene signal (see Eq. (65)) and an internal noise term (see Eq. (18)), W N 1 Delayed averaging is used, see Setion ER[ k, n] [ n] =. (82) E [ k, n] + 1 E [ k] 2B.3 ( ) k= R IN RmsModDiff A (Advaned version, Filter bank model) The instantaneous modulation differene is given by M diff A MT[ kn, ] MR[ kn, ] [ k, n] =. 1 + M [ k, n] R (83) The average over bands is