ecoendation ITU- T.6-7 (3/) Studio encoding paraeters of digital television for standard 4:3 and wide-screen 6:9 aspect ratios T Series roadcasting service (television)
ii ec. ITU- T.6-7 Foreword The role of the adiocounication Sector is to ensure the rational, equitable, efficient and econoical use of the radiofrequency spectru by all radiocounication services, including satellite services, and carry out studies without liit of frequency range on the basis of which ecoendations are adopted. The regulatory and policy functions of the adiocounication Sector are perfored by World and egional adiocounication Conferences and adiocounication Asseblies supported by Study Groups. Policy on Intellectual Property ight (IP) ITU- policy on IP is described in the Coon Patent Policy for ITU-T/ITU-/ISO/IEC referenced in Annex of esolution ITU-. Fors to be used for the subission of patent stateents and licensing declarations by patent holders are available fro http://www.itu.int/itu-/go/patents/en where the Guidelines for Ipleentation of the Coon Patent Policy for ITU-T/ITU-/ISO/IEC and the ITU- patent inforation database can also be found. Series of ITU- ecoendations (Also available online at http://www.itu.int/publ/-ec/en) Series O S T F M P A S S SA SF SM SNG TF V Title Satellite delivery ecording for production, archival and play-out; fil for television roadcasting service (sound) roadcasting service (television) Fixed service Mobile, radiodeterination, aateur and related satellite services adiowave propagation adio astronoy eote sensing systes Fixed-satellite service Space applications and eteorology Frequency sharing and coordination between fixed-satellite and fixed service systes Spectru anageent Satellite news gathering Tie signals and frequency standards eissions Vocabulary and related subjects Note: This ITU- ecoendation was approved in English under the procedure detailed in esolution ITU-. Electronic Publication Geneva, 7 ITU 7 All rights reserved. No part of this publication ay be reproduced, by any eans whatsoever, without written perission of ITU.
ec. ITU- T.6-7 Scope ECOMMENATION ITU- T.6-7 * Studio encoding paraeters of digital television for standard 4:3 and wide-screen 6:9 aspect ratios (Question ITU- /6) (98-986-99-99-994-995-7--5) This ecoendation also covers the pixel characteristics that represent a 55- or 65-line interlace digital television iage. This ecoendation specifies ethods for digitally coding video signals. It includes a 3.5 Mz sapling rate for both 4:3 and 6:9 aspect ratio iages with perforance adequate for present transission systes. Keywords STV, digital television iage, digital coding, colour difference The ITU adiocounication Assebly, considering a) that there are clear advantages for television broadcasters and prograe producers in digital studio standards which have the greatest nuber of significant paraeter values coon to 55-line and 65-line systes; b) that a worldwide copatible digital approach will perit the developent of equipent with any coon features, perit operating econoies and facilitate the international exchange of prograes; c) that an extensible faily of copatible digital coding standards is desirable. Mebers of such a faily could correspond to different quality levels, different aspect ratios, facilitate additional processing required by present production techniques, and cater for future needs; d) that a syste based on the coding of coponents is able to eet these desirable objectives; e) that the co-siting of saples representing luinance and colour-difference signals (or, if used, the red, green and blue signals) facilitates the processing of digital coponent signals, required by present production techniques, recoends that the following be used as a basis for digital coding standards for television studios in countries using the 55-line syste as well as in those using the 65-line syste. Extensible faily of copatible digital coding standards. The digital coding should allow the establishent and evolution of an extensible faily of copatible digital coding standards. It should be possible to interface siply between any ebers of the faily. * adiocounication Study Group 6 ade editorial aendents to this ecoendation in Noveber 4 and in March 7 in accordance with esolution ITU-. Standard definition television (STV).
ec. ITU- T.6-7. The digital coding should be based on the use of one luinance and two colour-difference signals (or, if used, the red, green and blue signals)..3 The spectral characteristics of the signals ust be controlled to avoid aliasing whilst preserving the passband response. Filter specifications are shown in Appendix. Specifications applicable to any eber of the faily. Sapling structures should be spatially static. This is the case, for exaple, for the orthogonal sapling structures specified in this ecoendation.. If the saples represent luinance and two siultaneous colour-difference signals, each pair of colour-difference saples should be spatially co-sited. If saples representing red, green and blue signals are used they should be co-sited..3 The digital standard adopted for each eber of the faily should perit worldwide acceptance and application in operation; one condition to achieve this goal is that, for each eber of the faily, the nuber of saples per line specified for 55-line and 65-line systes shall be copatible (preferably the sae nuber of saples per line)..4 In applications of these specifications, the contents of digital words are expressed in both decial and hexadecial fors, denoted by the suffixes d and h respectively. To avoid confusion between 8-bit and -bit representations, the eight ost-significant bits are considered to be an integer part while the two additional bits, if present, are considered to be fractional parts. For exaple, the bit pattern would be expressed as 45 d or 9 h, whereas the pattern would be expressed as 45.5 d or 9.4 h. Where no fractional part is shown, it should be assued to have the binary value..5 efinition of the digital signals Y, C, C, fro the priary (analogue) signals E, E G and E This paragraph describes, with a view to defining the signals Y, C, C, the rules for construction of these signals fro the gaa pre-corrected priary analogue signals E, E G and E. The signals are constructed by following the three stages described in.5.,.5. and.5.3. The ethod is given as an exaple, and in practice other ethods of construction fro these priary signals or other analogue or digital signals ay produce identical results. An exaple is given in.5.4..5. Construction of luinance (E Y ) and colour-difference (E E Y ) and (E E Y ) signals The construction of luinance and colour-difference signals is as follows: then: E Y.99 E.587 E G.4 E and ( E E ) E.99 E.587 E.4 E.7 E.587 E. 4 E Y G G ( E E ) E.99 E.587 E.4 E.99 E.587 E. 886 E Y G G
ec. ITU- T.6-7 3 Taking the signal values as noralized to unity (e.g.. V axiu levels), the values obtained for white, black and the saturated priary and copleentary colours are shown in Table. TAE Noralized signal values Condition E E G E E Y E E Y E E Y White lack ed Green lue Yellow Cyan Magenta..............99.587.4.886.7.43.7.587.4.4.7.587.99.587.886.886.99.587.5. Construction of re-noralized colour-difference signals (E and E C Whilst the values for E Y have a range of. to, those for (E E Y ) have a range of.7 to.7 and for (E E Y ) a range of.886 to.886. To restore the signal excursion of the colour-difference signals to unity (i.e..5 to.5), re-noralized red and blue colour-difference signals E C and E C respectively can be calculated as follows: and EC E EY.77.99E.587E.77 G.886E The sybols E C and E C will be used only to designate re-noralized colour-difference signals, i.e. having the sae noinal peak-to-peak aplitude as the luinance signal E Y thus selected as the reference aplitude..5.3 Quantization EC E EY.4.7E.587E.4.4E In the case of a uniforly-quantized 8-bit or -bit binary encoding, 8 or, i.e. 56 or 4, equally spaced quantization levels are specified, so that the range of the binary nubers available is fro to ( to FF in hexadecial notation) or to (. h to FF.C h in hexadecial notation), the equivalent decial nubers being. d to 55.75 d, inclusive. In this ecoendation, levels. d and 55.75 d are reserved for synchronization data, while levels. d to 54.75 d are available for video. G
4 ec. ITU- T.6-7 Given that the luinance signal is to occupy only (8-bit) or 877 (-bit) levels, to provide working argins, and that black is to be at level 6. d, the decial value of the quantized luinance signal, Y, is: Y int 9EY 6 / where takes either the value or 4, corresponding to 8-bit and -bit quantization respectively. The operator int( ) returns the value of for fractional parts in the range of to.4999 and + for fractional parts in the range.5 to.999..., i.e. it rounds up fractions above.5. Siilarly, given that the colour-difference signals are to occupy 5 (8-bit) or 897 (-bit) levels and that the zero level is to be level 8. d, the decial values of the quantized colour-difference signals, and C, are: and int 4E 8 / C The digital equivalents are tered Y, C and C. C int 4E 8 /.5.4 Construction of Y, C, C via quantization of E, E G, E C In the case where the coponents are derived directly fro the gaa pre-corrected coponent signals E, E G, E, or directly generated in digital for, then the quantization and encoding shall be equivalent to: Then: E E ( in digital for) int 9E 6 / ( in digital for) int 9E 6 G G / E ( in digital for) int 9E 6 / Y int.99e.587eg.4e / ky k k int E Y E Y 3 E G / C.7E int.587e.4 G.4E 4 8 / 9 k k k int E E 3 E G 8 /
ec. ITU- T.6-7 5 C.99E int.587e.77 G.886E 4 8 / 9 k k k int C E C E C 3 E G 8 / where k and denote the integer coefficients and the bit-lengths of the integer coefficients, respectively. The integer coefficients of luinance and colour-difference equations should be derived as per Annex. TAE Integer coefficients of luinance and colour-difference equations Coeffi cient bits enoinator uinance Y Colour-difference Colour-difference C k Y k Y k Y3 k k k 3 k C k C k C3 8 56 77 5 9 3 44 87 3 9 5 53 3 58 6 9 43 88 74 6 4 36 6 7 54 439 85 77 347 54 48 6 34 47 877 7 353 694 47 4 96 5 44 467 95 754 34 77 388 95 3 8 9 449 4 89 934 4 89 3 58 68 44 776 4 9 4 6 384 4 899 9 67 5 3 768 9 798 9 35 6 65 536 9 595 38 47 86 8 3 73 5 7 47 8 379 7 6 363 88 5 55 8 379 6 758 4 33 75 5 655 33 56 8 66 5 45 3 3 5 6 758 33 56 NOTE The bold values indicate that the values are odified fro the nearest integer values by the optiization. To obtain the 4:: coponents Y, C, C, low-pass filtering and sub-sapling ust be perfored on the 4:4:4 C, C signals described above. Note should be taken that slight differences could exist between C, C coponents derived in this way and those derived by analogue filtering prior to sapling..5.5 iiting of Y, C, C signals igital coding in the for of Y, C, C signals can represent a substantially greater gaut of signal values than can be supported by the corresponding ranges of, G, signals. ecause of this it is possible, as a result of electronic picture generation or signal processing, to produce Y, C, C signals which, although valid individually, would result in out-of-range values when converted to, G,. It is both ore convenient and ore effective to prevent this by applying liiting to the Y, C, C signals than to wait until the signals are in, G, for. Also, liiting can be applied in a way that
6 ec. ITU- T.6-7 aintains the luinance and hue values, iniizing the subjective ipairent by sacrificing only saturation..6 Colour and opto-electronic transfer characteristic Ite Characteristics Paraeter 65 55.6. Chroaticity coordinates, CIE 93 () x y x y Priaries ed.64.33.63.34 Green.9.6.3.595 lue.5.6.55.7.6. Assued chroaticity for equal priary signals eference white E EG E.37.39 x 65 y.6.3 Opto-electronic transfer characteristics before non-linear precorrection.6.4 Overall opto-electronic transfer characteristic at source 3 Assued linear E (.99.45.99) for..8 E 4.5 for.8 where: : luinance of the iage for conventional colorietry E: corresponding electrical signal. () Chroaticity coordinates specified are those currently used by 65-line and 55-line conventional systes. 3 Faily ebers The following faily ebers are defined: 4:: for 4:3 aspect ratio, and for wide-screen 6:9 aspect ratio systes when it is necessary to keep the sae analogue signal bandwidth and digital rates for both aspect ratios. 4:4:4 4 for 4:3 and 6:9 aspect ratio systes with higher colour resolution. It is recognized that a practice is now soeties used by which, when progras produced in TV are release in STV, their TV pixel ap is re-apped onto the STV pixel ap without changing the colorietry of the original progra. 3 In typical production practice the encoding function of iage sources is adjusted so that the final picture has the desired look, as viewed on a reference onitor having the reference decoding function of ec. ITU- T.886, in the reference viewing environent defined in ec. ITU- T.35. Although soe paraeters listed in ecoendation ITU- T.35 are intended for TV signal viewing, scaled viewing distances for STV signals should be used. 4 In the 4:4:4 ebers of the faily the sapled signals ay be luinance and colour difference signals (or, if used, red, green and blue signals).
ec. ITU- T.6-7 7 Annex Encoding paraeters for ebers of the faily Encoding paraeter values for the 4:: eber of the faily The specification (see Table 3) applies to the 4:: eber of the faily, to be used for the standard digital interface between ain digital studio equipent and for international prograe exchange of 4:3 aspect ratio digital television or wide-screen 6:9 aspect ratio digital television when it is necessary to keep the sae analogue signal bandwidth and digital rates. TAE 3 Paraeters 55-line, 6/., field/s systes 65-line, 5 field/s systes ) Coded signals: Y, C, C These signals are obtained fro gaa pre-corrected signals, naely: E Y, E E Y, E E Y (see.5) ) Nuber of saples per total line: luinance signal (Y) each colour-difference signal (C, C ) 858 49 864 43 3) Sapling structure Orthogonal, line, field and frae repetitive. C and C saples co-sited with odd (st, 3rd, 5th, etc.) Y saples in each line 4) Sapling frequency: luinance signal each colour-difference signal 3.5 Mz 6.75 Mz The tolerance for the sapling frequencies should coincide with the tolerance for the line frequency of the relevant colour television standard 5) For of coding Uniforly quantized PCM, 8 or bits per saple, for the luinance signal and each colour-difference signal 6) Nuber of saples per digital active line: luinance signal each colour-difference signal 7) Analogue-to-digital horizontal tiing relationship: fro end of digital active line to O 7 36 6 luinance clock periods luinance clock periods
8 ec. ITU- T.6-7 TAE 3 (end) Paraeters 55-line, 6/., field/s systes 65-line, 5 field/s systes 8) Correspondence between video signal levels and quantization levels: scale luinance signal each colour-difference signal (See.4) (Values are decial).d to 55.75 d (8-bit) or 877 (-bit) quantization levels with the black level corresponding to level 6. d and the peak white level corresponding to level 35. d. The signal level ay occasionally excurse beyond level 35. d or below level 6. d. 5 (8-bit) or 897 (-bit) quantization levels in the centre part of the quantization scale with zero signal corresponding to level 8. d. The signal level ay occasionally excurse beyond level 4. d or below level 6. d. 9) Code-word usage Code words corresponding to quantization levels. d and 55.75 d are used exclusively for synchronization. evels. d to 54.75 d are available for video. When 8-bit words are treated in -bit syste, two Ss of zeros are to be appended to the 8-bit words. Encoding paraeter values for the 4:4:4 eber of the faily The specifications given in Table 4 apply to the 4:4:4 eber of the faily suitable for television source equipent and high-quality video signal processing applications. Paraeters ) Coded signals: Y, C, C or, G, ) Nuber of saples per total line for each signal TAE 4 55-line, 6/. field/s systes 65-line, 5 field/s systes These signals are obtained fro gaa pre-corrected signals, naely: E Y, E E Y, E E Y or E, E G, E 858 864 3. Sapling structure Orthogonal, line, field and frae repetitive. The three sapling structures to be coincident and coincident also with the luinance sapling structure of the 4:: eber 4) Sapling frequency for each signal 3.5 Mz 5) For of coding Uniforly quantized PCM, 8 or bits per saple 6) uration of the digital active line expressed in nuber of saples 7) Analogue-to-digital horizontal tiing relationship: fro end of digital active line to O 7 6 clock periods clock periods
ec. ITU- T.6-7 9 Paraeters 8) Correspondence between video signal levels and quantization level for each saple: scale, G, or luinance signal () each colour-difference signal () TAE 4 (end) 55-line, 6/. field/s systes (See.4) (Values are decial) 65-line, 5 field/s systes.d to 55.75d (8-bit) or 877 (-bit) quantization levels with the black level corresponding to level 6. d and the peak white level corresponding to level 35. d. The signal level ay occasionally excurse beyond level 35. d or below level 6. d. 5 (8-bit) or 897 (-bit) quantization levels in the centre part of the quantization scale with zero signal corresponding to level 8. d. The signal level ay occasionally excurse beyond level 4. d or below level 6. d. 9) Code-word usage Code words corresponding to quantization levels. d and 55.75 d are used exclusively for synchronization. evels. d to 54.75 d are available for video. When 8-bit words are treated in -bit syste, two Ss of zeros are to be appended to the 8-bit words. () If used. Appendix to Annex efinition of signals used in the digital coding standards elationship of digital active line to analogue sync reference The relationship between the digital active line luinance saples and the analogue synchronizing reference is shown in: Figure for 65-line. Figure for 55-line. In the Figures, the sapling point occurs at the coenceent of each block. The respective nubers of colour-difference saples in the 4:: faily can be obtained by dividing the nuber of luinance saples by two. The (,3), and (6,) were chosen syetrically to dispose the digital active line about the peritted variations. They do not for part of the digital line specification and relate only to the analogue interface.
ec. ITU- T.6-7 FIGUE 6:9 or 4:3 at 3.5 Mz 65 O Analogue line n Analogue line n uinance saples 4::, chroo saples C igital line n igital blanking T 3 T igital line n 77 78 79 7 7 73 73 73 733 86 863 359 36 365 366 43 4::, chroo C saples 359 36 365 366 49 T : luinance sapling period T.6- Analogue line n FIGUE 6:9 or 4:3 at 3.5 Mz 55 O Analogue line n igital line n uinance saples 4::, chroo saples C 4::, chroo C saples igital blanking 6 T T igital line n 77 78 79 7 7 734 735 736 737 856 857 359 36 367 368 48 359 36 367 368 48 T : luinance sapling period T.6-
ec. ITU- T.6-7 Appendix to Annex Filtering characteristics Soe guidance on the practical ipleentation of the filters In the proposals for the filters used in the encoding and decoding processes, it has been assued that, in the post-filters which follow digital-to-analogue conversion, correction for the (sin x/x) characteristic is provided. The passband tolerances of the filter plus (sin x/x) corrector plus the theoretical (sin x/x) characteristic should be the sae as given for the filters alone. This is ost easily achieved if, in the design process, the filter, (sin x/x) corrector and delay equalizer are treated as a single unit. The total delays due to filtering and encoding the luinance and colour-difference coponents should be the sae. The delay in the colour-difference filter (Figs 4a) and 4b)) is typically double that of the luinance filter (Figs 3a) and 3b)). As it is difficult to equalize these delays using analogue delay networks without exceeding the passband tolerances, it is recoended that the bulk of the delay differences (in integral ultiples of the sapling period) should be equalized in the digital doain. In correcting for any reainder, it should be noted that the saple-and-hold circuit in the decoder introduces a flat delay of one half a sapling period. The passband tolerances for aplitude ripple and group delay are recognized to be very tight. Present studies indicate that it is necessary so that a significant nuber of coding and decoding operations in cascade ay be carried out without sacrifice of the potentially high quality of the 4:: coding standard. ue to liitations in the perforance of currently available easuring equipent, anufacturers ay have difficulty in econoically verifying copliance with the tolerances of individual filters on a production basis. Nevertheless, it is possible to design filters so that the specified characteristics are et in practice, and anufacturers are required to ake every effort in the production environent to align each filter to eet the given teplates. The specifications given in Appendix were devised to preserve as far as possible the spectral content of the Y,, C signals throughout the coponent signal chain. It is recognized, however, that the colour-difference spectral characteristic ust be shaped by a slow roll-off filter inserted at picture onitors, or at the end of the coponent signal chain.
ec. ITU- T.6-7 5 4 FIGUE 3 Filter teplate for a luinance, G or 4:4:4 colour-difference signal 4 d (d) 3 d 3 4 5 6 7 8 9 3 4 5 5.75 6.75 3.5 Frequency (Mz) a) Teplate for insertion loss/frequency characteristic.5 (d)..5. d.5 3 4 5 6 Frequency (Mz) 5.5 5.75 b) Passband ripple tolerance 5 ns (ns) 4 ns 6 ns 5 3 4 5 6 Frequency (Mz) 5.75 c) Passband group-delay tolerance Note The lowest indicated values in b) and c) are for kz (instead of Mz). T.6-3
ec. ITU- T.6-7 3 5 FIGUE 4 Filter teplate for a 4:: colour-difference signal 4 4 d 3 (d) 6 d 3 4 5 6 7.75 3.375 6.75 Frequency (Mz) a) Teplate for insertion loss/frequency characteristic..5 (d).. d.5. 3 Frequency (Mz).75 b) Passband ripple tolerance (ns) 4 ns 8 ns ns 4 ns 3 Frequency (Mz).75 c) Passband group-delay tolerance 3 d loss frequency Note The lowest indicated values in b) and c) are for kz (instead of Mz). T.6-4
4 ec. ITU- T.6-7 6 5 FIGUE 5 igital filter teplate for sapling-rate conversion fro 4:4:4 to 4:: colour difference signals 55 d (d) 4 3 See Note 3 6 d 3 4 5 6 7.75 3.375 6.5 6.75 Frequency (Mz) a) Teplate for insertion loss/frequency characteristic..5 (d).5. d. 3 Frequency (Mz).75 b) Passband ripple tolerance T.6-5
ec. ITU- T.6-7 5 Annex erivation of integer coefficients of luinance and colour-difference equations for the conventional colour gaut syste igital systes ay introduce coputation errors in the luinance and colour-difference signals due to the finite bit-length of the equation coefficients. Also, digital luinance and colour-difference signals ay take slightly different values depending on the signal processing sequence, i.e. the discrepancy between signals quantized after analogue atrixing and signals digitally atrixed after quantization of G signals. To iniize such errors and discrepancies, the integer coefficients for the digital equations should be optiized. The optiization procedure and the resultant integer coefficients for several bit-lengths are given in the following. igital equations In the following, and n denote the bit-lengths of the integer coefficients and digital signals, respectively. The digital luinance equation for the conventional colour gaut syste is described as follows: Y INT.99.587. 4 () G r Y r Y r INT Y 3 G () k Y k Y k INT Y 3 G (3) where r' and k' denote the real values of the coefficient and the integer coefficients, respectively, given below: Y.99 k Y INTr Y r Y.587 k Y INTr Y r Y 3.4 k Y 3 INTr Y 3 r The digital colour-difference equations for the conventional colour gaut syste are described as follows:.99.587.886 4 INT G n C.77 9 (4) r INT k INT C C r C r C3 G k C k C3 G n n (5) (6)
6 ec. ITU- T.6-7.7.587.4 4 INT G n.4 9 (7) where: r INT k INT.99 4 r.77 9 r r 3 G k k 3 G n n C k C INTr C.587 4 r.77 9 C k C INTr C.886 4 r.77 9 C 3 k C 3 INTr C 3.7 4 r.4 9 k INTr.587 4 r.4 9 k INTr.4 4 r.4 9 3 k 3 INTr 3 (8) (9) Optiization procedure Equation (3) shows the digitally atrixed luinance signal which includes coputation errors due to the finite bit-length of the integer coefficients. When the coefficient bit-length is increased, the arguent (the value in [ ]) of equation (3) gets close to that of equation (), resulting in the reduced errors or discrepancies between the equations. Therefore, the difference between the arguents of equations () and (3) can be regarded as a easure of the integer coefficient optiization. As the difference of arguents depends on input G signals, east Square Error optiization is defined, in which the integer coefficients are adjusted in such a way that the su of the squared difference over all inputs falls into the iniu value, that is, the value of equation () is iniized. ε Y for all G k Y k Y k G Y 3 r Y r Y r G Y 3 () In addition to providing the iniu r..s. errors, this SE optiization autoatically iniizes the peak error that takes place at a particular input colour (a particular cobination of input G signals), as well as the discrepancy between different signal processing sequences (analogue-atrixing and digital-atrixing).
ec. ITU- T.6-7 7 The optiization procedure is as follows: Step : For the initial value of each integer coefficient r Yj (j,, 3), take the nearest integer to the real value of the coefficient r Yj. Step : With the initial integer coefficients, calculate the r..s. errors or the squared difference su (equation ()) over the input G signal range, e.g., 6 through 35 for an 8-bit syste (a siple calculation ethod without using suation is described in 3). Step 3: Exaine the r..s. errors when increasing/decreasing each integer coefficient by one. 7 ( 3 3 ) cobinations ust be evaluated in total, because each coefficient can take three values, i.e. increased, decreased and unchanged fro the initial value. Step 4: Select the cobination of the coefficients that gives the iniu r..s. error. This cobination is the resultant optiized one. The sae procedure is applied for the colour-difference equations, using equations () and (). ε C kc k C k n C 3 G for all G r 3 C r C r n C G () ε k k k n 3 G for all G r 3 r r n G () 3 Siple calculation ethod for squared difference su y expressing the difference between integer and real coefficients value as ij k'ij r'ij, and the digital G signals as j, the su of the squared differences of equations () to () can be written as the following: εi 3 i (3) i i3 3 where and denote the lower and upper boundaries of the input signal range, respectively, for which the integer coefficients are to be optiized. As and are constant in the digital syste under consideration, the suations for j are also constant. Then equation (3) can be expressed as a function only of ij. N i N 3 (4) i i i i3 i3 i i i i
8 ec. ITU- T.6-7 where: N 3 3 3 )/6} ( ) ( )/6 ( ) ( { ) ( N 3 3 3 3 3 / } ) ( )/ ( ) { ( Thus the calculation of r..s. errors or equations () to () can be siply perfored by equation (4).