WPCL 2BJ|x ` H   x|@  @8'@8' O  `  @  <AP IX142E OO  `  @  <AP IX142E OI (3291) I (3291)    10.HRecommendation G.722: 07 kHz AUDIOCODING WITHIN 64 KBIT/S 1. General 1.1HScope and outline description   HThis Recommendation describes the characteristics of an audio (50 to 7 000 Hz) coding system which may be used for a variety of higher quality speech applications. The coding system uses subband adaptive differential pulse code modulation (SBADPCM) within a bit rate of 64 kbit/s. The system is henceforth referred to as 64 kbit/s (7 kHz) audio coding. In the SBADPCM technique used, the frequency band is split into two subbands (higher and lower) and the signals in each subband are encoded using ADPCM. The system has three basic modes of operation corresponding to the bit rates used for 7 kHz audio coding: 64, 56 and 48 kbit/s. The latter two modes allow an auxiliary data channel of 8 and 16 kbit/s respectively to be provided within the 64 kbit/s by making use of bits from the lower subband. HFigure 1/G.722 identifies the main functional parts of the 64 kbit/s (7 kHz) audio codec as follows: Hi)  64 kbit/s (7 kHz) audio encoder comprising: a transmit audio part which converts an audio signal to a H uniform digital signal which is coded using 14 bits with H 16kHz sampling; H  a SBADPCM encoder which reduces the bit rate to 64kbit/s. Hii)  64 kbit/s (7 kHz) audio decoder comprising: H  a SBADPCM decoder which performs the reverse operation to the encoder noting that the effective audio coding bit rate at the input of the decoder can be 64, 56 or 48 kbit/s depending on the mode of operation; H  a receive audio part which reconstructs the audio signal from the uniform digital signal which is encoded using 14bits with 16 kHz sampling. HThe following two parts, identified in Figure 1/G.722 for clarification, will be needed for applications requiring an auxiliary data channel within the 64 kbit/s: H  a data insertion device at the transmit end which makes use of, when needed, 1 or 2 audio bits per octet depending on the mode of operation and substitutes data bits to provide an auxiliary data channel of 8 or 16 kbit/s respectively; H  a data extraction device at the receive end which determines the mode of operation according to a mode control strategy and extracts the data bits as appropriate. Hss 1.2 contains a functional description of the transmit and receive audio parts, ss 1.3 describes the modes of operation and the implication of inserting data bits on the algorithms, whilst ssss 1.4 and 1.5 provide the functional descriptions of the SBADPCM encoding and decoding algorithms respectively. ss 1.6 deals with the timing requirements. ss 2 specifies the transmission characteristics of the 64 kbit/s (7 kHz) audio codec and of the transmit and receive audio parts, ssss 3 and 4 give the principles of the SB ADPCM encoder respectively whilst ssss 5 and 6 specify the computational details of the Quadrature Mirror Filters (QMF) and of the ADPCM encoders and decoders respectively. HNetworking aspects and test sequences are addressed in Appendices I and II respectively to this Recommendation. HRecommendation G.725: "Systems aspects for the use of the 7 kHz audio codec within 64 kbit/s" contains specifications for inchannel handshaking procedures for terminal identification and for mode control strategy, including interworking with existing 64 kbit/s PCM terminals. 1.2HFunctional description of the audio parts HFigure 2/G.722 shows a possible arrangement of audio parts in a 64kbit/s (7 kHz) audio coding terminal. The microphone, preamplifier, power amplifier and loudspeaker are shown simply to identify the audio parts and are not considered further in this Recommendation. HIn order to facilitate the measurement of the transmission characteristics as specified in ss 2, test points A and B need to be provided as shown. These test points may either be for test purposes only or, where the audio parts are located in different units from the microphone, loudspeaker etc..., correspond to physical interfaces. HThe transmit and receive audio parts comprise either the following functional units or any equivalent items satisfying the specifications of ss 2: Hi)  transmit: H an input level adjustment device, H an input antialiasing filter, H a sampling device operating at 16 kHz, H an analoguetouniform digital converter with 14 bits and K#LL$MM$Nwith 16 kHz sampling; Hii)  receive: H a uniform digitaltoanalogue converter with 14 bits and J(#KK#LL$Mwith 16 kHz sampling, H a reconstructing filter which includes x/sin x correction, H an output level adjustment device. 1.3HPossible modes of operation and implications of inserting data HThe three basic possible modes of operation which correspond to the bit rates available for audio coding at the input of the decoder are defined in Table 1/G.722. HITABLE 1/G.722 HO H?Basic possible modes of operationă    Mode  7 kHz audio coding bit rate  Auxiliary data channel bit rate    1  64 kbit/s  0 kbit/s   2  56 kbit/s  8 kbit/s   3  48 kbit/s  16 kbit/s    HSee Appendix 1 for examples of applications using one or several of these modes and for their corresponding subjective quality. HThe 64 kbit/s (7 kHz) audio encoder uses 64 kbit/s for audio coding at all times irrespective of the mode of operation. The audio coding algorithm has been chosen such that, without sending any indication to the encoder, the least significant bit or two least significant bits of the lower subband may be used downstream from the 64 kbit/s (7 kHz) audio encoder in order to substitute the auxiliary data channel bits. However, to maximize the audio performance for a given mode of operation, the 64 kbit/s (7 kHz) audio decoder must be optimized to the bit rate available for audio coding. Thus, this Recommendation describes three variants of the SBADPCM decoder and, for applications requiring an auxiliary data channel, an indication must be forwarded to select in the decoder the variant appropriate to the mode of operation. Figure 1/G.722 illustrates the arrangement. It should be noted that the bit rate at the input of the 64 kbit/s (7 kHz) audio decoder is always 64 kbit/s but comprising 64, 56 or 48 kbit/s for audio coding depending on the mode of operation. From an algorithm viewpoint, the variant used in the SBADPCM decoder can be changed in any octet during the transmission. When no indication about the mode of operation is forwarded to the decoder, the variant corresponding to Mode 1 should be used. HA mode mismatch situation, where the variant used in the 64 kbit/s (7kHz) audio decoder for a given octet does not correspond to the mode of operation, will not cause misoperation of the decoder. However, to maximize the audio performance, it is recommended that the mode control strategy adopted in the data extraction device should be such as to minimize the duration of the mode mismatch. Appendix I gives further information on the effects of a mode mismatch. To ensure compatibility between various types of 64 kbit/s (7 kHz) audio coding terminals, it is recommended that, as a minimum, the variant corresponding to Mode 1 operation is always implemented in the decoder. HThe mode control strategy could be derived from the auxiliary data channel protocol (see draft Recommendation G.725). 1.4HFunctional description of the SBADPCM encoder HFigure 3/G.722 is a block diagram of the SBADPCM encoder. A functional description of each block is given below in ssss 1.4.1 to 1.4.4. 1.4.1HTransmit quadrature mirror filters (QMFs) HThe transmit QMFs comprise two linearphase nonrecursive digital filters which split the frequency band 0 to 8 000 Hz into two subbands: the lower subband (0 to 4 000 Hz) and the higher subband (4 000 to 8 000 Hz). The input to the transmit QMFs, xin, is the output from the transmit audio part and is sampled at 16 kHz. The outputs, xL and xH, for the lower and higher subbands respectively, are sampled at 8 kHz. 1.4.2HLower subband ADPCM encoder HFigure 4/G.722 is a block diagram of the lower subband ADPCM encoder. The lower subband input signal, xL after subtraction of an estimate, sL, of the input signal produces the difference signal, eL. An adaptive 60level nonlinear quantizer is used to assign six binary digits to the value of the difference , signal to produce a 48 kbit/s signal, IL. HIn the feedback loop, the two least significant bits of IL are deleted to produce a 4bit signal ILt, which is used for the quantizer adaptation and applied to a 15level inverse adaptive quantizer to produce a quantized difference signal, dLt. The signal estimate, sL is added to this quantized difference signal to produce a reconstructed version, rLt, of the lower subband input signal. Both the reconstructed signal and the quantized difference signal are operated upon by an adaptive predictor which produce the estimate, sL, of the input signal, thereby completing the feedback loop. H4bit operation, instead of 6bit operation, in the feedback loops of both the lower subband ADPCM encoder, and the lower subband ADPCM decoder allows the possible insertion of data in the two least significant bits as described in ss 1.3 without causing misoperation in the decoder. Use of a 60 level quantizer (instead of 64level) ensures the pulse density requirements as described in Recommendation G.802 are met under all conditions and in all modes of operation. 1.4.3HHigher subband ADPCM encoder HFigure 5/G.722 is a block diagram of the higher subband ADPCM encoder. The higher subband input signal, xH after subtraction of an estimate, sH, of the input signal, produces the difference signal, eH. An adaptive 4level non linear quantizer is used to assign two binary digits to the value of the difference signal to produce a 16 kbit/s signal, IH. HAn inverse adaptive quantizer produces a quantized difference signal, dH, from these same two binary digits. The signal estimate, sH, is added to this quantized difference signal to produce a reconstructed version, rH, of the higher subband input signal. Both the reconstructed signal and the quantized difference signal are operated upon by an adaptive predictor which produces the estimate, sH, of the input signal, thereby completing the feedback loop. 1.4.4HMultiplexer HThe multiplexer (MUX) shown in Figure 3/G.722 is used to combine the signals, IL and IH, from the lower and higher subband ADPCM encoders respectively into a composite 64 kbit/s signal, I, with an octet format for transmission. HThe output octet format, after multiplexing, is as follows: HIH1 IH2 IL1 IL2 IL3 IL4 IL5 IL6 where IH1 is the first bit transmitted, and where IH1 and IL1 are the most significant bits of IH and IL respectively, whilst IH2 and IL6 are the least significant bits of IH and IL respectively. 1.5HFunctional description of the SBADPCM decoder HFigure 6/G.722 is a block diagram of the SBADPCM decoder. A functional description of each block is given below in ssss 1.5.1 to 1.5.4. 1.5.1HDemultiplexer HThe demultiplexer (DMUX) decomposes the received 64 kbit/s octet formatted signal, Ir, into two signals, ILr and IH, which form the codeword inputs to the lower and higher subband ADPCM decoders respectively. 1.5.2HLower subband ADPCM decoder HFigure 7/G.722 is a block diagram of the lower subband ADPCM decoder. This decoder can operate in any of three possible variants depending on the received indication of the mode of operation. HThe path which produces the estimate, sL, of the input signal including the quantizer adaptation, is identical to the feedback portion of the lower sub band ADPCM encoder described in ss 1.4.2. The reconstructed signal, rL, is produced by adding to the signal estimate one of three possible quantized difference signals, dL,6, dL,5 or dL,4 (= dLt see note), selected according to the received indication of the mode of operation. For each indication, Table2/G.722 shows the quantized difference signal selected, the inverse adaptive quantizer used and the number of least significant bits deleted from the input codeword. HITABLE 2/G.722 HO H=Lower subband ADPCM decoder variantsă    Received  Quantized  Inverse  Number of least   indication  difference  adaptive  significant bits   of mode of  signal  quantizer  deleted from input   operation  selected  used  codeword, ILr    Mode 1  dL,6  60level  0   Mode 2  dL,5  30level  1   Mode 3  dL,4  15level  2    Note For clarification purposes, all three inverse quantizers have been indicated in the upper portion of Figure 7/G.722. In an optimized implementation, the signal dLt, produced in the predictor loop, could be substituted for dL,4. 1.5.3HHigher subband ADPCM decoder HFigure 8/G.722 is a block diagram of the higher subband ADPCM decoder. This decoder is identical to the feedback portion of the higher subband ADPCM encoder described in ss 1.4.3, the output being the reconstructed signal, rH. 1.5.4HReceive QMFs HThe receive QMFs shown in Figure 6/G.722 are two linearphase non recursive digital filters which interpolate the outputs, rL and rH, of the lower and higher subband ADPCM decoders from 8 kHz to 16 kHz and which then produce an output, xout, sampled at 16 kHz which forms the input to the receive audio parts. HExcluding the ADPCM coding processes, the combination of the transmit and the receive QMFs has an impulse response which closely approximates a simple delay whilst, at the same time, the aliasing effects associated with the 8 kHz subsampling are cancelled. 1.6HTiming requirements H64 kHz bit timing and 8 kHz octet timing should be provided by the network to the audio decoder. HFor a correct operation of the audio coding system, the precision of the 16 kHz sampling frequencies of the A/D and D/A converters must be better than + 50.10é6. 2.HTransmission characteristics 2.1HCharacteristics of the audio ports and the test points ,Ԍ HFigure 2/G.722 indicates the audio input and output ports and the test points (A and B). It is for the designer to determine the characteristics of the audio ports and the test points (i.e. relative levels, impedances, whether balanced or unbalanced). The microphone, preamplifier, power amplifier and loudspeaker should be chosen with reference to the specifications of the audio parts: in particular their nominal bandwidth, idle noise and distortion. HIt is suggested that input and output impedances should be high and low, respectively, for an unbalanced termination whilst for a balanced termination these impedances should be 600 ohms. However, the audio parts should meet all audio parts specifications for their respective input and output impedance conditions. 2.2HOverload point HThe overload point for the analoguetodigital and digitaltoanalogue converters should be + 9 dBmO + 0.3 dB. This assumes the same nominal speech level (see Recommendation G.232) as for 64 kbit/s PCM but with a wider margin for the maximum signal level which is likely to be necessary with conference arrangements. The measurement method of the overload point is under study. 2.3HNominal reference frequency HWhere a nominal reference frequency of 1 000 Hz is indicated below, the actual frequency should be chosen equal to 1 020 Hz. The frequency tolerance should be +2 to 7 Hz. 2.4HTransmission characteristics of the 64 kbit/s (7 kHz) audio codec HThe values and limits specified below should be met with a 64 kbit/s (7kHz) audio encoder and decoder connected backtoback. For practical reasons, the measurements may be performed in a looped configuration as shown in Figure9a/G.722. However, such a looped configuration is only intended to simulate an actual situation where the encoder and decoder are located at the two ends of a connection. HThese limits apply to operation in Mode 1. 2.4.1HNominal bandwidth HThe nominal 3 dB bandwidth is 50 to 7 000 Hz. 2.4.2HAttenuation/frequency distortion HThe variation with frequency of the attenuation should satisfy the limits shown in the mask of Figure 10/G.722. The nominal reference frequency is 1 000 Hz and the test level is 10 dBmO. 2.4.3HAbsolute group delay HThe absolute group delay, defined as the minimum group delay for a sinewave signal between 50 and 7 000 Hz, should not exceed 4 ms. The test level is 10 dBmO. 2.4.4HIdle noise HThe unweighted noise power measured in the frequency range 50 to 7000Hz with no signal at the input port (test point A) should not exceed 66dBmO. When measured in the frequency range 50 Hz to 20 kHz the unweighted noise power should not exceed 60 dBmO. 2.4.5HSingle frequency noise HThe level of any single frequency (in particular 8 000 Hz, the sampling frequency and its multiples), measured selectively with no signal at the input port (test point A) should not exceed 70 dBmO. 2.4.6HSignaltototal distortion ratio HUnder study. 2.5HTransmission characteristics of the audio parts HWhen the measurements indicated below for the audio parts are from audiotoaudio, a looped configuration as shown in Figure 9b/G.722 should be used. The audio parts should also meet the specifications of ss 2.4 with the measurement configuration of Figure 9b/G.722. 2.5.1HAttenuation/frequency response of the input antialiasing filter HThe inband and outofband attenuation/frequency response of the input antialiasing filter should satisfy the limits of the mask shown in Figure11/G.722. The nominal reference frequency is 1 000 Hz and the test level for the inband characteristic is 10 dBmO. Appropriate measurements should be made to check the outofband characteristic taking into account the aliasing due to the 16 kHz sampling. 2.5.2HAttenuation/frequency response of the output reconstructing filter HThe inband and outofband attenuation/frequency response of the output reconstructing filter should satisfy the limits of the mask shown in Figure 12/G.722. The nominal reference frequency is 1 000 Hz and the test level for the inband characteristic is 10 dBmO. Appropriate measurements should be made to check the outofband characteristic taking into account the aliasing due to the 16 kHz sampling. The mask of Figure 12/G.722 is valid for the whole of the receive audio part including any pulse amplitude modulation distortion and x/sin x correction. 2.5.3HGroup delay distortion with frequency HThe group delay distortion, taking the minimum value of group delay as a reference, should satisfy the limits of the mask shown in Figure 13/G.722. 2.5.4HIdle noise for the receive audio part HThe unweighted noise power of the receive audio part measured in the frequency range 50 to 7 000 Hz with a 14bit allzero signal at its input should not exceed 75 dBmO. 2.5.5HSignaltototal distortion ratio as a function of input level HWith a sine wave signal at a frequency excluding simple harmonic relationships with the 16 kHz sampling frequency, applied to test point A, the ratio of signaltototal distortion power as a function of input level measured unweighted in the frequency range 50 to 7 000 Hz at test point B, should satisfy the limits of the mask shown in Figure 14/G.722. Two measurements should be performed, one at a frequency of about 1 kHz and the other at a frequency of about 6 kHz. 2.5.6HSignaltototal distortion ratio as a function of frequency HWith a sine wave signal at a level of 10 dBmO applied to test point A, , the ratio of signaltototal distortion power as a function of frequency measured unweighted in the frequency range 50 to 7 000 Hz at test point B should satisfy the limits of the mask shown in Figure 15/G.722. 2.5.7HVariation of gain with input level HWith a sine wave signal at the nominal reference frequency of 1 000 Hz, but excluding the submultiple of the 16 kHz sampling frequency, applied to test point A, the gain variation as a function of input level relative to the gain at an input level of 10 dBmO measured selectively at test point B, should satisfy the limits of the mask shown in Figure 16/G.722. 2.5.8HIntermodulation HUnder study. 2.5.9HGo/return crosstalk HThe crosstalk from the transmit direction to the receive direction should be such that, with a sine wave signal at any frequency in the range 50 to 7 000 Hz and at a level of +6 dBmO applied to test point A, the crosstalk level measured selectively at test point B should not exceed 64 dBmO. The measurement should be made with a 14bit allzero digital signal at the input to the receive audio part. HThe crosstalk from the receive direction to the transmit direction should be such that, with a digitally simulated sine wave signal at any frequency in the range of 50 to 7 000 Hz and a level of +6 dBmO applied to the input of the receive audio part, the crosstalk level measured selectively and with the measurement made digitally at the output of the transmit audio part should not exceed 64 dBmO. The measurement should be made with no signal at test point A, but with the test point correctly terminated. 2.6HTranscoding to and from 64 kbit/s PCM HFor compatibility reasons with 64 kbit/s PCM, transcoding between 64kbit/s (7 kHz) audio coding and 64 kbit/s PCM should take account of the relevant specifications of Recommendations G.712, G.713 and G.714. When the audio signal is to be heard through a loudspeaker, more stringent specifications may be necessary. Further information may be found in Appendix 1. 3.HSBADPCM encoder principles HA block diagram of the SBADPCM encoder is given in Figure 3/G.722. Block diagrams of the lower and higher subband ADPCM encoders are given respectively in Figures 4/G.722 and 5/G.722. HMain variables used for the descriptions in ssss 3 and 4 are summarized in Table 3/G.722. In these descriptions, index (j) indicates a value corresponding to the current 16 kHz sampling interval, index (jl) indicates a value corresponding to the previous 16 kHz sampling interval, index (n) indicates a value corresponding to the current 8 kHz sampling interval, and index (nl) indicates a value corresponding to the previous 8 kHz sampling interval. Indices are not used for internal variables, i.e. those employed only within individual computational blocks. 3.1HTransmit QMF HA 24coefficient QMF is used to compute the lower and higher subband signal components. The QMF coefficient values, hi, are given in Table 4/G.722. HThe output variables, xL(n) and xH(n), are computed in the following way: HxL(n) = xA + xB (1) xH(n) = xA xB (2) where 11 HxA = $ h2i.xin(j 2i) (3) i=0 11 HxB = $ h2i+1.xin(j 2i 1) (4) i=0 3.2HDifference signal computation HThe difference signal, eL(n) and eH(n), are computed by subtracting predicted values, sL(n) and sH(n), from the lower and higher subband input values, xL(n) and xH(n): HeL(n) = xL(n) sL(n) (5) HeH(n) = xH(n) sH(n) (6) HITABLE 3/G.722 HO H0Variables used in the SBADPCM encoder and decoder descriptionsă Note Variables used exclusively within one section are not listed. Subscripts L and H refer to lower subband and higher subband values. Subscript Lt denotes values generated from the truncated 4bit codeword as opposed to the nontruncated 6bit (encoder) or 6/5/ or 4bit (decoder) codewords. HITABLE 4/G.722 HO H:Transmit and receive QMF coefficient valuesă 3.3HAdaptive quantizer HThe difference signals, eL(n) and eH(n), are quantized to 6 and 2 bits for the lower and higher subbands respectively. Tables 5/G.722 and 6/G.722 give the decision levels and the output codes for the 6 and 2bit quantizers respectively. In these tables, only the positive decision levels are indicated, the negative levels can be determined by symmetry. mL and mH are indices for the quantizer intervals. The interval boundaries, LL6, LU6, HL and HU, are scaled by computed scale factors, L(n) and H(n) (see ss 3.5). Indices, mL and mH, are then determined to satisfy the following: HLL6(mL).L(n)  eL(n) < LU6(mL).L(n) (7) HHL(mH).H(n)  eH(n) < HU(mH).H(n) (8) for the lower and higher subbands respectively. HThe output codes, ILN and IHN, represent negative intervals, whilst the output codes, ILP and IHP, represent positive intervals. The output codes, IL(n) and IH(n), are then given by:  ILP(mL) , if eL (n)  0 HIL (n) =  (9)  ILN(mL) , if eL (n) < 0 H  IHP(mH) , if eH (n)  0 IH (n) =  (10)  IHN(mH) , if eH (n) < 0 for the lower and higher subbands respectively. 3.4HInverse adaptive quantizers 3.4.1HInverse adaptive quantizer in the lower subband ADPCM encoder HThe lower subband output code, IL(n), is truncated by two bits to produce ILt(n). The 4bit codeword, ILt(n), is converted to the truncated quantized difference signal, dLt(n), using the QL4é1 output values of Table7/G.722, and scaled by the scale factor, L(n): HdLt(n) = QL4é1(ILt(n)).L(n).sgn(ILt(n)) (11) where sgn (ILt(n)) is derived from the sign of eL(n) defined in equation 9. HThere is a unique mapping, shown in Table 7/G.722, between four adjacent 6bit quantizer intervals and the QL4é1 output values. QL4é1(ILt(n)) is determined in two steps: first determination of the quantizer interval index, mL, corresponding to IL(n) from Table 5/G.722, and then determination of QL4é1(mL) by reference to Table 7/G.722. 3.4.2HInverse adaptive quantizer in the higher subband ADPCM encoder HThe higher subband output code, IH(n) is converted to the quantized difference signal, dH(n), using the Q2é1 output values of Table 8/G.722 and scaled by the scale factor, H(n): HdH(n) = Q2é1(IH(n)).H(n).sgn(IH(n)) (12) HITABLE 5/G.722 HO H,Decision levels and output codes for the 6bit lower subband quantizeră Note If a transmitted codeword for the lower subband signal has been transformed, due to transmission errors to one of the four suppressed codewords "0000XX", the received code word is set at "111111". HO HITABLE 6/G.722 HO H+Decision levels and output codes for the 2bit higher subband quantizeră    mH  HL  HH  IHN  IHP    1  0  1.10156  01  11         2  1.10156    00  10    HITABLE 7/G.722 HO HOutput values and multipliers for 6, 5 and 4bit lower subband inverse quantizers HITABLE 8/G.722 HO H-Output values and multipliers for the 2bit higher subband quantizeră    mH  Q2é1  WH    1  0.39453  0.10449       2  1.80859  0.38965    where sgn (IH(n)) is derived from the sign of eH(n) defined in equaltion (10), and where Q2é1(IH(n)) is determined in two steps: first determine the quantizer interval index, mH, corresponding to IH(n) from Table 6/G.722 and then determine Q2é1(mH) by reference to Table 8/G.722. 3.5HQuantizer adaptation HThis block defines L(n) and H(n), the scaling factors for the lower and higher subband quantizers. The scaling factors are updated in the log domain and subsequently converted to a linear representation. For the lower sub band, the input is ILt(n), the codeword truncated to preserve the four most significant bits. For the higher subband, the 2bit quantizer output, IH(n), is used directly. HFirstly the log scaling factors, L(n) and H(n), are updated as follows: L(n) = B. L(n1)WL(ILt(n1)) (13) H(n) = B. H(n1)WH(IH(n1)) (14) where WL(.) and Wy(.) are logarithmic scaling factor multipliers given in Tables7/G.722 and 8/G.722, and B is a leakage constant equal to 127/128. HThen the log scaling factors are limited, according to: 0  L(n)  9 (15) 0  H(n)  11 (16) HFinally, the linear scaling factors are computed from the log scaling factors, using an approximation of the inverse log2 function: L(n) = 2( L(n)2)min (17) H(n) = 2 H(n)min (18) where min is equal to half the quantizer step size of the 14 bit analogueto digital converter. 3.6HAdaptive prediction 3.6.1HPredicted value computations HThe adaptive predictors compute predicted signal values, sL(n) and sH(n), for the lower and higher subbands respectively. HEach adaptive predictor comprises two sections: a secondorder section that models poles, and a sixthorder section that models zeroes in the input signal. HThe second order pole sections (coefficients aL,i and aH,i) use the quantized reconstructed signals, rLt(n) and rH(n), for prediction. The sixth order zero sections (coefficients bL,i and bH,i) use the quantized difference signals, dLt(n) and dH(n). The zerobased predicted signals, sLz(n) and sHz(n), are also employed to compute partially reconstructed signals as described in ssĠ3.6.2. 4.HSBADPCM decoder principles HA block diagram of the SBADPCM decoder is given in Figure 6/G.722 and block diagrams of the lower and higher subband ADPCM decoders are given respectively in Figures 7/G.722 and 8/G.722. HThe input to the lower subband ADPCM decoder, ILr, may differ from IL even in the absence of transmission errors, in that one or two least significant bits may have been replaced by data. 4.1HInverse adaptive quantizer 4.1.1HInverse adaptive quantizer selection for the lower subband ADPCM I"Jdecoder HAccording to the received indication of the mode of operation the number of least significant bits which should be truncated from the input codeword ILr, and the choice of the inverse adaptive quantizer are determined, as shown in Table 2/G.722. HFor operation in mode 1, the 6bit codeword, ILr(n), is converted to the quantized difference, dL(n), according to QL6é1 output values of Table7/G.722, and scaled by the scale factor, L(n): HdL(n) = QL6é1(ILr(n)).L(n).sgn (ILr(n)) (39) where sgn (ILr(n)) is derived from the sign of IL(n) defined in equation (9). HSimilarly, for operations in mode 2 or mode 3, the truncated codeword (by one or two bits) is converted to the quantized difference signal, dL(n), according to QL5é1 or QL4é1 output values of Table 7/G.722 respectively. HThere are unique mappings, shown in Table 7/G.722, between two or four adjacent 6bit quantizer intervals and the QL5é1 or QL4é1 output values respectively. HIn the computations above, the output values are determined in two steps: first determination of the quantizer interval index, mL, corresponding to ILr(n) from Table 5/G.722, and then determination of the output values corresponding to mL by reference to Table 7/G.722. HThe inverse adaptive quantizer, used for the computation of the predicted value and for adaptation of the quantizer and predictor, is described in ss 3.4.1, but with IL(n) replaced by ILr(n). 4.1.2HInverse adaptive quantizer for the higher subband ADPCM decoder HSee ss 3.4.2. 4.2HQuantizer adaptation HSee ss 3.5. 4.3HAdaptive prediction 4.3.1HPredicted value computation HSee ss 3.6.1. 4.3.2HReconstructed signal computation HSee ss 3.6.2. HThe output reconstructed signal for the lower subband ADPCM decoder, rL(n), is computed from the quantized difference signal, dL(n), as follows: HrL(n) = SL(n) + dL(n) (40) 4.3.3HPole section adaptation HSee ss 3.6.3. 4.3.4HZero section adaptation HSee ss 3.6.4. 4.4HReceive QMF HA 24coefficient QMF is used to reconstruct the output signal, xout(j), from the reconstructed lower and higher subband signals, rL(n) and rH(n). The QMF coefficient values, hi, are the same as those used in the transmit QMF and are given in Table 4/G.722. HThe output signals, xout(j) and xout(j+1), are computed in the following way: (41) (42) (43) (44) H:Attenuation/frequency response of the inpută HFantialiasing filteră H9Attenuation/frequency response of the outpută H6reconstructing filter (including x/sinx correction)ă H<Signaltototal distortion ratio as a ă HEfunction of frequencyă 7I(3291) CCITT\APIX\DOC\142E8.TXS 77I(3291) CCITT\APIX\DOC\142E8.TXS 7 X  5.HComputational details for QMF 5.1HInput and output signals HTable 9/G.722 defines the input and output signals for the transmit and receive QMF. All input and output signals have 16bit wordlengths, which are limited to a range of 16384 to 16383 in 2's complement notation. Note that the most significant magnitude bit of the A/D output and the D/A input appears at the third bit location in XIN and XOUT, respectively. 5.2HDescription of variables and detailed specification of subblocks HThis section contains a detailed expansion of the transmit and receive QMF. The expansions are illustrated in Figures 17/G.722 and 18/G.722 with the internal variables given in Table 10/G.722, and the QMF coefficients given in Table 11/G.722. The wordlengths of the internal variables, XA, XB and WD, must be equal to or greater than 24 bits (see Note 1). The other internal variables have a minimum of 16 bit wordlengths. A brief functional description and the full specification is given for each subblock. HThe notations used in the block descriptions are as follows: H>>n  denotes an nbit arithmetic shift right operation (sign H8"II"Jextension), H+ denotes arithmetic addition with saturation control which J(#KK#Lforces the result to minimum or maximum representable value ; <<=in case of underflow or overflow, respectively, H denotes arithmetic subtraction with saturation control which M$NN%Oforces the result to minimum or maximum representable value <==>in case of underflow or overflow, respectively. H* denotes arithmetic multiplication which can be performed with N%OO%Peither truncation or rounding, H< denotes the "less than" condition as x < y; x is less than y, H> denotes the "greater than" condition, as x > y; x is greater M$NN%Othan y, H=  denotes the substitution of righthand variable for lefthand N%OO%Pone. Note 1 Some freedom is offered for the implementation of the accumulation process in the QMF: the wordlengths of the internal variables can be equal to or greater than 24 bits, and the arithmetic multiplications can be performed with either truncation or rounding. It allows a simplified implementation on various types of processors. The counterpart is that it excludes the use of digital test sequence for the test of the QMF.