Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04S—STEREOPHONIC SYSTEMS 
  • H04S3/00—Systems employing more than two channels, e.g. quadraphonic
  • H04S3/02—Systems employing more than two channels, e.g. quadraphonic of the matrix type, i.e. in which input signals are combined algebraically, e.g. after having been phase shifted with respect to each other
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04S—STEREOPHONIC SYSTEMS 
  • H04S2420/00—Techniques used stereophonic systems covered by H04S but not provided for in its groups
  • H04S2420/11—Application of ambisonics in stereophonic audio systems
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04S—STEREOPHONIC SYSTEMS 
  • H04S5/00—Pseudo-stereo systems, e.g. in which additional channel signals are derived from monophonic signals by means of phase shifting, time delay or reverberation 
  • H04S5/005—Pseudo-stereo systems, e.g. in which additional channel signals are derived from monophonic signals by means of phase shifting, time delay or reverberation  of the pseudo five- or more-channel type, e.g. virtual surround

Definitions

• This invention relates to the reproduction and transmission of
• the illusory sound images are all displaced towards the nearer of the two loudspeakers.
• the illusory images also rotate in position to a lesser extent.
• stereophonic illusion This defects become particularly serious when the stereophonic sound is associated with a visual image, such as is the case with Television, video or film programmes, audiovisual and son et lumière presentations, theatrical performances with stereophonic sound effects, and amplified live musical performances. It is found empirically that angular discrepancies between the apparent directions of
• loudspeakers can either be fed with independent transmission channel signals, one for each loudspeaker system, conveying an improved stereophonic illusion, or they can be fed with signals derived from a smaller number of transmission channel signals using a mixing or matrixing process.
• This invention relates to the use of an improved matrixing process to obtain improved illusory phantom images.
• signals L and R are normally used to feed the respective left and right loudspeakers of a two-loudspeaker stereophonic system, then these can be supplemented by an additional central loudspeaker fed with the signal 1 ⁇ 2k(L+R), where k is a predetermined amplitude gain.
• k is a predetermined amplitude gain.
• loudspeakers for example, signals derived from widely spaced microphones, signals derived from
• loudspeaker method of reproduction varies considerably in its results depending on the recording technique used to produce the original stereophonic signals, and that the best value of the predetermined gain
• the total reproduced energy at a moment fed into the listening room is proportional to the sum of the squares
• stereophonic signal described in the above example does not equal, and is not proportional to, the
• the Hughes SRS method has the defect that all sounds are reproduced with equal energy from both the left and the right loudspeakers, so that any illusion of directionality is created purely by phase relationships between the loudspeaker
• stereophonic loudspeakers have given an imperfect illusion of directionality. Although the ears and brain produce a directional illusion from stimuli in a manner that is not wholly understood, many aspects of the perception of directional effect can be described reasonably well in terms of four physical quantities at the position of the head of a listener.
• acoustical pressure which is a scalar quantity
• the acoustic velocity which is a vector quantity with direction
• the acoustic energy which is a scalar quantity
• the sound intensity which is a vector quantity describing the direction and magnitude of energy flow of the sound field.
• the ratio of acoustic velocity to acoustic pressure provides a vector quantity that can be used, over any limited frequency band below a frequency of about 700 Hz, to predict the localisation of sounds
• intensity to acoustical energy can similarly be used to predict the localisation of sounds
• velocity vector localisation theories Sound localisation theories based on the ratio of acoustic velocity to acoustic pressure are termed velocity vector localisation theories, whereas those based on the ratio of sound intensity to acoustic energy are termed energy vector theories.
• energy vector theories Sound localisation theories based on the ratio of acoustic velocity to acoustic pressure are termed energy vector theories.
• loudspeakers suffer from one or more defects, which include an alteration of the recorded level-balance between sounds in a stereophonic recording, angular differences between the vector directions of acoustical velocity and of sound intensity, and an inadequate width of reproduction of the stereophonic sound stage.
• matrix methods are not only used to feed a first plurality of loudspeaker feed signals into a second larger plurality of loudspeakers, but are also used to provide third pluralities of transmission channel signals, intended for use in storage, transmission or recording of the
• the process of deriving the third plurality of transmission signals from the first plurality of loudspeaker feed signals is generally termed encoding
• the process of deriving the second plurality of loudspeaker feed signals from the third plurality of transmission channel signals is generally termed decoding.
• quadraphonic, surround-sound and ambisonic systems Some such systems are hierarchical in the sense that they allow for a number of different possible values for the first plurality, a number of different values for the second plurality, and a number of different values for the third plurality, while ensuring the following desirable properties: (i) when the first and second pluralities are equal and the third plurality is not less than the first plurality, the second loudpeaker feed signals are
• HDTV high definition Television
• stereophony would greatly ease the task of converting signals intended for one plurality of stereophonic loudspeakers for reproduction via another, and
• the final listener will also have the choice of which plurality of loudspeakers he or she uses.
• the UMX system of surround-sound reproduction is a known prior-art hierarchical system, but is not optimised for frontal-stage stereophony.
• the problem of designing an effective hierarchical system of stereophony has not hitherto been solved. This is because in the case of surround sound, one can
• stereophonic loudspeaker arrangements do have at least an approximate left/right symmetry, i.e.
• references to "front”, “forward”, “left” and “right” directions in this document are purely a matter of convenience, and that the "front” or “forward” direction may in fact be any chosen convenient direction in space, and the “left” and “right” directions may be any chosen opposite directions orthogonal to that direction designated as “front” or “forward”.
• One aspect of this invention provides matrix means for converting a first plurality of signals intended to feed a first plurality of
• Another aspect provides
• loudspeakers in a stereophonic arrangement into a second greater plurality of loudspeaker feed signals suitable for feeding a second plurality of loudspeakers in a second stereophonic arrangement in a manner that substantially preserves or improves the sound localisation qualities and level-balance of different sounds within the original signals.
• stereophonic loudspeakers into third pluralities m of transmission, storage or recording channels, and for decoding said third pluralities m of
• channel signals to provide second pluralities n 2 of signals suitable for reproduction via said
• a hierarchical system for transmitting, recording, or storing of first pluralities of signals intended for stereophonic reproduction via said first pluralities of loudspeakers via third pluralities of transmission, storage or recording channels, and for decoding second pluralities of signals intended for reproduction via second
• Another aspect provides means for reproducing stereophoni c signals i ntended for reproduction via two loudspeakers via three or more loudspeakers so as to achieve an improved stability of illusory phantom images near the centre of the stereophonic sound stage as the listener moves around a listening area, while retaining a wide reproduced stage width for listeners across the listening area.
• Another aspect provides means
• Another aspect provides a
• a matrix converter R n2,n1 for converting a first audio signal stereophonically encoded for reproduction over n 1 speakers into a second audio signal stereophonically encoded for reproduction over n 2 loudspeakers, when n 1 , n 2 are integers > 1 and n 2 > n 1, characterised in that the matrix converter R is an energy preserving matrix arranged substantially to preserve to within an overall constant of proportionality, which may be frequency dependent, the total reproduced energy and the directional effect of the encoded audio signal.
• the matrix converter may, for example form part of a transmission encoder, or a reproduction decoder as later described. It may be implemented by software in an appropriate digital signal processor of the type well known in the art, or by a hard-wired network in the analogue domain.
• a matrix reproduction decoding means is provided responsive to a first plurality of signals representing loudspeaker feed signals intended for reproduction via a said first plurality of loudspeakers disposed in a first stereophonic arrangement across a first sector of directions and providing a second greater plurality of output signals representing loudspeaker feed signals intended for reproduction via a said
• said matrix means being further such as to substantially preserve or improve the illusory stereophonic effect intended via said first stereophonic arrangement via said second stereophonic arrangement.
• matrix reproduction decoding means is provided responsive to a first plurality of signals representing loudspeaker feed signals intended for reproduction via a said first plurality of loudspeakers disposed in a first
• said matrix means being such as to
• means being further such as to substantially preserve, to within a second constant of proportionality that may be dependent on frequency the angular disposition, measured as the angle of the direction from a
• said matrix means being further such as to substantially preserve, to within a third constant of proportionality that may be dependent on frequency, the angular disposition of sound intensity vectors intended via said first stereophonic arrangement when
• said matrix reproduction decoding means is preferably also left/right, symmetrical, in the sense that if all left inputs and outputs were to be exchanged with their right counterparts, the results given by the matrix reproduction decoding means would remain substantially unchanged.
• said third constant of proportionality is arranged to be greater within an audio frequency band above 5 kHz than within the audio band at frequencies between 700 Hz and 3 kHz. Said increased third constant of proportionality above 5 kHz is especially desirable when said first plurality equals two.
• there is provided means for modifying the reproduced width having the effect of altering the gain of that signal component representing the difference of said first loudspeaker feed signals intended for said first stereophonic arrangement.
• the ratio of said second constant of proportionality to said third constant of proportionality should lie within the range from one half to two.
• a conversion matrix for converting a first ambisonically encoded audio signal having components W, X and Y or linear combinations thereof into a second, stereophonically encoded signal for reproduction over n 2 loudspeakers where n 2 is an integer ⁇ 3, the conversion matrix comprising a n 2 ⁇ 2 conversion matrix means according to any preceding aspect arranged to receive at one input a first signal M dec formed from the sum of the omnidirectional component W and a first velocity component X and at the other input a signal S formed from the other velocity component Y and means for outputting a further signal component derived from the difference T dec of the said components W and X.
• said transmission channel signals represent first stereophonic loudspeaker feed signals intended to feed a first plurality of loudspeakers disposed in a first stereophonic arangement across a first sector of directions, wherein when said first plurality equals said second plurality, said transmission matrix decoding means is such that said second loudspeaker feed signals are substantially identical, to within an overall gain and equalisation, to said first stereophonic loudspeaker feed signals, and wherein when said first plurality is less than said second plurality and is not greater than said third plurality, said transmission matrix decoder means constitutes a reproduction matrix decoding means
• said transmission channel signals are such that for each first plurality not greater than said third plurality, precisely a said first plurality of transmission channel signals may be substantially nonzero, and such that for any first said first
• the transmission channel inputs to said transmission matrix decoding means for which said transmission matrix channel signals are substantially nonzero for said first said first plurality is a subset of the transmission channel inputs for which the transmission channel signals are substantially nonzero for said second said first plurality.
• a transmission matrix encoder means responsive to a plurality greater than two of signals representing loudspeaker feed signals intended to feed a said
• the decoder means according to the invention in its third aspect is in accordance with the preferred implementation of the invention in its third aspect, and the additional transmission matrix encoder means required to
• substantially nonzero representing loudspeaker feed signals intended for reproduction via a said smaller said first plurality of loudspeakers is also a transmission matrix encoder means according to the invention in its fourth aspect.
• This preferred form of the invention in its fourth aspect ensures that the different third pluralities of transmission channel signals provided in response to the different first pluralities of loudspeaker feed signals by encoding means, and the associated second pluralities of decoded loudspeaker feed signals derived from the different third pluralities of transmission channel signals derived by the inverse decoders constitutes a hierarchical system of
• a matrix system for encoding a first plurality of signals representing loudspeaker feed signals intended for reproduction via a said first plurality of loudspeakers disposed in a first stereophonic arrangement across a first sector of directions into a third plurality of transmission channel signals and for decoding said third
• a transmission matrix decoding means responsive to a third plurality of transmission channel signals and providing a second plurality of output signals representing loudspeaker feed signals intended for reproduction via a said second plurality of loudspeakers disposed in a second stereophonic arrangement across a second sector of directions intended for use with transmission channel signals provided via a transmission matrix encoding means, such that the resulting system constitutes a matrix encoding and decoding system in accordance with the invention in its fifth aspect.
• a transmission matrix encoding means responsive to one or more first pluralities of signals representing loudspeaker feed signals intended for reproduction via a said first plurality of
• loudspeakers disposed in a first stereophonic
• matrix decoding means according to the invention in its first, second, third or sixth aspects intended for use with loudspeakers (or loudspeaker systems) some of which have a more limited bass reproduction capability than the other loudspeakers, whereby said matrix decoding means is modified at low frequencies so as to provide less bass to said
• loudspeakers or loudspeaker systems which have a more limited bass reproduction capability than to said other loudspeakers.
• a matrix decoding means according to the invention in its first, second, third, sixth or eighth aspects, also incorporating or used in association with delay compensation means for output signals
• loudspeakers arrive at said listening position at a substantially identical time.
• the intended stereophonic arrangement of the reproduction loudspeakers is substantially
• left/right symmetric and said preferred listening position is disposed on the axis of left/right symmetry.
• transmission encoding means for encoding a first plurality of signals representing loudspeaker feed signals intended for reproduction via a said first plurality of loudspeakers disposed in a stereophonic arrangement across a sector of directions into a
• said encoding means providing results equivalent to a reproduction matrix decoding means according to the invention in its first, second, third, or sixth aspects responsive to said first plurality of signals providing a fourth plurality, not greater than said third plurality and larger than said first plurality, of signals
• reproduction matrix decoder means responsive to a first plurality of signals proportional to signals intended for reproduction via a said first plurality of loudspeakers disposed in a first left/right symmetric stereophonic arrangement across a first sector of directions and providing a second greater plurality of signals proportional to signals intended for reproduction via a said second plurality of loudspeakers disposed in a second left/right symmetric stereophonic arrangement across a second sector of directions,
• said matrix decoder means comprising an input sum and difference matrix means for each pair of signals
• a first linear or matrix means responsive to all said sum
• difference matrix means one associated with each
• FIGS 1a to 1g illustrate examples of loudspeaker arrangements which may be used with the invention.
• Figures 2 and 3 show schematic block diagrams of matrix reproduction decoding means in accordance with the invention.
• Figure 4 shows a reproduction decoder producing three output signals from two input signals.
• Figure 5 shows a frequency-dependent version of the decoder of figure 4.
• Figures 6 and 7 show block schematics of systems of encoding and decoding transmission signals from and to two- and three-loudspeaker reproduction signals.
• Figure 8 shows a frequency-dependent means for encoding two signals into three transmission channels and for decoding two signals into three loudspeaker signals.
• Figure 9 shows a matrix reproduction decoding means that comprises two other matrix reproduction decoding means connected in series.
• Figure 10 is a schematic indicating how stereo signals for any plurality of loudspeakers may be mixed with and decoded for stereo reproduction via any larger number of loudspeakers.
• Figure 11 is a schematic of a system of encoding and decoding stereo signals to and from transmission channel signals.
• Figure 12 shows a transmission encoder comprising the series connnection of a reproduction decoder with another transmission encoder.
• Figure 13 shows a transmission decoder comprising the series connection of another transmission decoder with a reproduction decoder.
• Figure 14 is a schematic of a hierarchy of transmission encoders accepting signals intended for different pluralities of stereo loudspeakers.
• Figure 15 is a schematic of the hierarchy inverse to that of figure 14 for decoding transmission signals into signals intended for any plurality of stereo loudspeakers.
• Figure 16 is a flow diagram indicating the procedure for designing a hierarchical system of transmission encoders and decoders in accordance with figures 14 and 15 and the invention.
• Figure 17 shows a 4 ⁇ 2 matrix reproduction decoder according to the invention.
• Figure 18 shows a schematic of a 4 ⁇ 3 matrix reproduction decoder according to the invention.
• Figure 19 shows a schematic of an n 2 ⁇ n 1 matrix
• Figure 20 shows rectangular and angular coordinates of loudspeakers with respect to a listener.
• Figures 21 to 25 show graphs of parameters describing the localisation quality of stereo images for
• Figure 26 shows the use of delay compensation means to compensate for different loudspeaker distances.
• Figure 27 shows a multispeaker stereophonic portable reproduction apparatus in accordance with the invention.
• FIGS 28 and 29 show audiovisual multispeaker
• Figure 30 is a schematic of a multispeaker stereophonic system using a preamplifier control unit incorporating a matrix decoder.
• Figure 31 is a schematic of a multispeaker stereophonic system in which a preamplifier control unit feeds a matrix decoder.
• Figure 32 shows the use of the invention in a
• Figure 33 shows a loudspeaker arrangement in a car for use with the invention.
• Figure 34a is a 3-speaker decoder for B-format signals;
• Figure 34b is a n-speaker decoder for B-format signals
• Figure 34c is a rotation matrix for use in the decoder of Figures 34a and 34b;
• Figure 35 shows the encoding to and decoding from transmission signals of a directional sound encoding system
• Figure 36 shows the relationship between conversion matrices and transmission encoding matrices
• Figure 37 shows the structure of a cascadable hierarchy for stereo and surround sound.
• FIG. 1a shows a typical monophonic loudspeaker C 1 in front of a listener (4), such as might be used for monophonic reproduction of a stereophonic signal.
• Figure 1b shows a typical monophonic loudspeaker C 1 in front of a listener (4), such as might be used for monophonic reproduction of a stereophonic signal.
• Figure 1b shows a typical monophonic loudspeaker C 1 in front of a listener (4), such as might be used for monophonic reproduction of a stereophonic signal.
• Figure 1b shows a typical
• Figure 1c shows a typical three-speaker arrangement with respective left, centre and right loudpeakers L 3 , C 3 and R 3 .
• Figure 1d shows a typica l four-speaker arrangement with respective loudspeakers L 4 , L 5 , R 5 and R 4 from left to right in front of the listener (4).
• Figure le shows a typical five-speaker arrangement with respective loudspeakers L 6 , L 7 , C 5 , R 7 , and R 6 from left to right in front of the listener (4).
• L p is used to indicate a loudspeaker placed in a direction at an angle ⁇ p towards the (notional) left
• figure If shows an alternative preferred three-speaker arrangement with respective left, centre and right loudspeakers L 3 , C 3 and R 3 in which the three loudspeakers are at an equal distance from the listener (4), but where the two outer loudspeakers are angled in such that their axes (10) cross in front of the listener (4) as shown.
• Figure 1g shows another alternative three-speaker arrangement in which the outer loudspeakers L 3 and R 3 are angled in as before, but where the centre loudspeaker C 3 lies at the centre of a line joining L3 and R 3 , and so is closer to the listener (4).
• angles ⁇ p subtended by the loudspeakers may be chosen across a broad range of values according to convenience or the desired stage width of stereophonic presentation. However, it is generally found that if the angle
• ⁇ 3 is not more than 45° (giving a reproduced sector (3) angle of 90°); whereas wider stage widths covering sectors (3) of
• the sector (3) of reproduced directions using four or more loudspeakers will not exceed 180°, although in some cases a slightly larger angular coverage, for example 210° or 225°, may be used.
• the included angle to the rear of the listener (4) between the outermost loudspeakers is so large that stable imaging to the rear of the listener is not possible.
• the invention is applicable only to stereophonic arrangements covering a sector (3) of directions not including stable imaging of excluded angular positions, and is not applicable to loudspeaker arrangements capable of covering a 360° surround-sound stage.
• ⁇ 4 50°
• ⁇ 6 54°
• stereophonic signals capable of producing a desired directional illusion across the available sector (3) of directions via any specific stereophonic loudspeaker arrangement, such as those illustrated in figures 1b to If, can be created, recorded, stored or transmitted.
• An object of this invention is to substantially retain or improve this desired stereophonic effect via an arrangement with a larger number of loudspeakers, such as one of those shown in figures 1c to 1e.
• FIG. 2 The general method of doing this according to the invention is illustrated in figure 2, whereby an original first plurality (20) n 1 of signals from a stereophonic signal source (1), which may for example be a stereophonic microphone arrangement, the outputs from a mixing desk, the outputs from a tape or disc reproducer, a broadcast receiver or a telecommunications link, said signals representing loudspeaker feed signals suitable for a first stereophonic
• a stereophonic signal source (1) which may for example be a stereophonic microphone arrangement
• the outputs from a mixing desk the outputs from a tape or disc reproducer, a broadcast receiver or a telecommunications link
• said signals representing loudspeaker feed signals suitable for a first stereophonic
• this second plurality of signals is shown as being fed into loudspeakers (50) direct from the matrix means (2), it will be understood that generally such feeds to loudspeakers may involve necessary or desirable intermediate stages evident to those skilled in the art, such as amplification and gain adjustment stages, overall volume and tone control adjustments, equalisers for loudspeaker and room characteristics, time delays for adjusting the time of arrivals at a listener from individual loudspeakers, connecting means such as cables or infra-red links, and the like.
• the n 2 ⁇ n 1 reproduction matrix decoding means (2) causes each of the n 2 output signals to be linear combinations of the n 1 input signals (20).
• the n 2 ⁇ n 1 coefficients of these linear combinations are referred to as "matrix coefficients". These linear combinations may be
• the matrix coefficients will be complex gains that are a function of frequency. In preferred forms of the invention in the case when the matrix coefficients are frequency-dependent, the matrix coefficients will be approximately real and frequency ⁇ -independent across two or three relatively broad audio frequency bands, and will vary significantly only in the transition frequency regions between these frequency bands.
• R p 2 -1 ⁇ 2 (M p -S p ).
• signals of the form M p or C p as “sum” signals and of the form S p as “difference” signals. It is often convenient to represent two-speaker stereophonic signals L 2 and R 2 in MS form as M 2 and S 2 ; to represent three-speaker signals L 3 , C 3 and R 3 in MS form as M 3 , C 3 and S 3 ; to represent four-speaker signals L 4 , L 5 , R 5 and R 4 in MS form by M 4 , M 5 , S 4 and S 5 ; and to represent five-speaker signals L 6 , L 7 , C 5 , R 7 and R 6 in MS form by M 6 , M 7 , C 5 , S 6 and S 7 . It is sometimes convenient to describe the reproduction matrix decoding means (2) in terms of what it does to signals in MS form. By using the above MS matrix
• reproduction loudspeakers (50) will involve a
• the reproduction matrix decoding means (2) should substantially preserve the total energy of the input signals (20) fed to the intended first stereophonic arrangement when the matrix means (2) output signals (40) are reproduced via the second stereophonic arrangement (50) of loudspeakers.
• the matrix means (2) output signals (40) are reproduced via the second stereophonic arrangement (50) of loudspeakers.
• all loudspeakers have identical characteristics and a flat frequency response, so that the signals fed to the loudspeakers are identical, to within a constant of gain, to the signals emitted by the
• the total energy emitted into the room at each moment is the sum of the squares of the separate loudspeaker feed
• reproduced energy is that many different recording and mixing techniques may be used to prepare the original stereo effect, and that a reproduction matrix decoding means (2) that substantially departs from preserving total energy by giving some stereophonic signal
• a reproduction matrix decoding means (2) should be substantially energy preserving, although it will be understood that overall adjustments of gain or tonal quality affecting all component stereo signals
• variations at any frequency produced by use of the reproduction matrix decoder means (2) between different components of the stereo signal should not exceed about 3 dB, and it is desirable that such variations of gain should be less than 2 dB, and ideally be less than 1 dB for high quality results.
• L 3 (1 ⁇ 2sin ⁇ )(L 2 + R 2 ) + 1 ⁇ 2w(L 2 -R 2 )
• R 3 (1 ⁇ 2sin ⁇ )(L 2 + R 2 ) - 1 ⁇ 2w(L 2 -R 2 )
• reproduction matrix decoding means (2) is energy-preserving.
• Figure 4 shows a schematic of a 3 ⁇ 2 reproduction matrix decoding means (2) satisfying the above 3 ⁇ 2 matrix means decoding means equations.
• An initial MS matrix means (31) receives the input signals L 2 (21) and R 2 (22) to produce signals M 2 and S 2 ; the difference signal S2 is given an optional width gain adjustment (32) w to provide any desired adjustment of reproduced stage width, producing a signal S 3 ; the sum signal M 2 is passed into a network (33) such as a constant-power pair of gain adjustments or a sine/cosine potentiometer or gain adjustment producing two outputs with respective gains costf and sin ⁇ whose squares add up to one.
• This network (33) may consist of a fixed pair of gain
• adjustment stages or a fixed resistor network for a fixed value of the parameter ⁇ can comprise an adjustable network giving constant power output.
• the signal C 3 with gain cos ⁇ can be used as the centre loudspeaker feed signal (42), and the signal M3 with gain sintf is fed with S 3 to a second MS matrix means (39) to provide signals L 3 (41) and R 3 (43) suitable for feeding the outer loudspeakers of a three-speaker stereophonic arrangement (50) such as shown in figures 3, 1c, 1f or 1g.
• the stability of central images is determined mainly by frequencies between around 300 Hz and 5 kHz, whereas the frequencies above 5 kHz are important for creating a sense of wide stage width.
• the degree of angular image movement with respect to loudspeaker directions with change of listener position is reduced by a factor of about three for central illusory images, and the
• FIG. 5 shows one realisation of a frequency-dependent matrix version of the invention.
• MS versions M 2 and S 2 of the input signals L 2 (21) and R 2 (22) are produced by an MS matrix means (31), and the difference signal S 2 is passed via a direct connection (37) through an optional width gain adjustment (32) as before.
• the sum signal M 2 is passed through a bandsplit filter (3-4) that divides the signal into two sets of frequency components; typically this may consist of a low-pass filter (34a) and a high-pass filter (34b) whose outputs sum to their input M 2 .
• these filters may be complementary first-order or RC filters with a cross-over frequency at around 5 or 6 kHz, although a sharper transition rate can be achieved by using second-order or higher-order filters.
• the high-pass signal component of M 2 from bandsplit means (34b) is fed to a constant-power gain adjustment means (33b) to produce gains COS ⁇ H and sin ⁇ H as shown, where ⁇ H is the desired high-frequency value (typically around 55°) of the angle parameter ⁇ , and the low-pass signal component from the bandsplit filter means (34a) is fed to another constant-power gain adjustment means (33a) to produce gains cos ⁇ M and sin ⁇ r ⁇ as shown, where ⁇ M is the desired mid and low frequency value (typically around 35°) of the parameter ⁇ .
• R3 (43) are loudspeaker feed signals suitable for use with the three-speaker arrangements of figures 3, lc, If or Ig.
• bandplitting filters (34) may be implemented subsequently to the constant-power gain adjustment stages (33) rather than
• Bandsplitting filters (34) may be used whose outputs substantially sum to an all-pass response rather than to their input signal, in which case a parallel all-pass filter (37) with a substantially identical all-pass characteristic should be placed in series with the S 2 signal path, for example as shown in figure 5, in order that the phase relationships between the parallel signal paths remain substantially unaffected.
• filters (34a), (34b) and (37) that have identical phase characteristics in order that all interpath phase differences be
• first order all-pass network (37) with low-pass means (34a) comprising two cascaded first-order low ⁇ -pass stages, and high-pass means (34b) comprising two cascaded first-order high-pass stages with a polarity inversion, all stages and filters having identical time constants.
• the frequency-dependent version of the invention may be extended to the case where the bandsplit network (34) comprises filter means giving three or more outputs that substantially sum to its input or to an all-pass response, which feed a corresponding number three or more of constant-power gain adjustment stages (33) whose sine gain outputs are fed to summing means (36) to produce a signal M 3 and whose cosine gain outputs are fed to another summing means (35) to produce a signal C 3 .
• Such a version of the invention may be used to choose one value ⁇ L of the parameter ⁇
• the value of ⁇ L may be adjusted in the range 0° to 90° to achieve a satisfactory result taking into account the
• ⁇ L near 90° may be used to minimise bass fed to the centre loudspeaker. If instead only the centre loudspeaker has an extended bass response, a value ⁇ L near 0°
• phase-adjustment means at the outputs (41), (42) and (43) of the 3 ⁇ 2 reproduction matrix decoding means in order to compensate for
• the low-pass filter means (34a) in figure 5 may be replaced by a bandpass means for
• the high-pass filter means (34b) may be replaced by a
• This system encodes two (21b, 22b) or three (21c, 22c, 23c) signals from a respective two- or three-speaker stereo source (1b or 1c respectively) via transmission matrix encoding means (7 or 7b) to produce transmission channel signals (60), which are transmitted via transmission channels (8) which may for example consist of wire, broadcast or telecommunications channels, tape or disc recording and playback channels, digital storage channels or the like, and which are then decoded using transmission matrix decoding means (9 or 9b) to produce two-speaker signals (41b and 42b) or three-speaker feed signals (41c, 42c and 43c).
• Figure 6 shows a 3 ⁇ 3 transmission matrix encoding means (7) receiving three-speaker feed signals L 3 , C 3 and R 3 and producing transmission channel signals L, R and T transmitted via transmission means (8) and 3 ⁇ 3 transmission matrix decoding means (9) producing
• the resulting 3 ⁇ 2 reproduction matrix decoding means (2) should be a 3 ⁇ 2 decoder according to the 3 ⁇ 2 matrix decoding equations described above.
• the 3 ⁇ 3 transmission matrix decoding means (9) should be inverse to the 3 ⁇ 3 transmission matrix encoding means (7), so that three-speaker feed signals are recovered substantially unaltered after 3-channel transmission.
• the angle parameters ⁇ * and ⁇ " are preferably between 15° and 75°
• the width parameter w' is preferably equal to one and in any case greater than sin ⁇ '
• the third channel gain parameter k' may equal 1 or any other predetermined non-zero value.
• angle parameters ⁇ ' which determines the 3 ⁇ 2 reproduction decoding matrix
• FIG. 7 shows the schematic of the hierarchical transmission system according to the invention when MS transmission channel signals are used.
• transmission signals generally have the simplest appearance in MS form.
• transmission encoding and decoding equations is that the decoding of two channels via three loudspeakers does not have an optimum frequency-dependent form. While it is possible to use frequency-dependent encoding parameters, this has two disadvantages: (i) that the two-channel transmitted signal L and R is frequency-dependent and so not of optimum compatibility with two-speaker reproduction, and (ii) a standardisation of the frequency-dependence does not allow of any future modification that may improve subjective results further.
• the transmission decoding matrix may be switched or
• the two-speaker stereo signals L 2 and R 2 may first converted to three-speaker form by means of a 3 ⁇ 2 matrix reproduction decoding means such as shown in figure 5, and then fed into the 3 ⁇ 3 encoding matrix (7) to produce three transmission signals.
• the decoded signals L 3 , C 3 and R 3 obtained after transmission matrix decoding (9) will be the same as if a frequency-dependent matrix reproduction decoder such as that of figure 5 had been used by the final listener.
• R 3 1 ⁇ 2 ( s i n ⁇ - 1)L 2 + 1 ⁇ 2 ( s i n ⁇ + 1)R 2
• R 1 ⁇ 2(cos( ⁇ - ⁇ '))(L 2 + R 2 ) - 1 ⁇ 2(L 2 - R2)
• T (2-1 ⁇ 2sin( ⁇ - ⁇ '))(L 2 + R 2 ) .
• input stereo signals L 2 and R 2 are passed into an MS matrix (31) and the difference signal S 2 is (optionally) passed through an optional width gain control (32) to provide an (optionally) modified difference signal S (62).
• the sum signal M 2 from the MS matrix (31) is used to provide a signal M (61) and also passed to the filter means (38) discussed above to provide a third signal T (63).
• the three signals M, S, T are three-channel transmission signals in MS form which may be used to feed a transmission system in accordance with the invention with signals derived from a two-speaker stereo source when psycho ⁇ -acoustic frequency-dependence and (optional) width control is desired.
• figure 8 constitutes a 3 ⁇ 2 transmission encoding matrix in accordance with the invention.
• all-pass filters may be placed in the M and S (or L and R) signal paths (61,62) to provide a desired phase difference with the output of the T-channel filter means (38).
• a three-speaker transmission matrix decoding means (9) is provided for the M, S and T signals (61-63) to provide three-speaker stereo signals (41-43) suitable for feeding L3, R3 and C3 loudspeakers such as shown in figures 1c, 1f and 1g
• figure 8 constitutes an alternative frequency-dependent 3 ⁇ 2 reproduction matrix decoding means to that shown in figure 5 according to the invention.
• the means shown in figure 8 may also incorporate switching (not shown) in the signal paths (61-63) to accept as inputs two- and 3-channel transmissions in MS form as an alternative to inputs (21,22) in L 2 ,R 2 form.
• the T signal path (63) only may be switchable to accept a third channel signal T from a three-channel transmission source L,R,T as an alternative to the synthesised third channel signal at the output of the filter (38) derived from a two-channel input.
• a frequency-dependent n ⁇ 2 reproduction matrix decoding means producing loudspeaker feeds for n greater than 3 loudspeakers according to the invention may be achieved by substituting in figure 8 an n ⁇ 3 transmission matrix decoder means of the type described subsequently for the 3 ⁇ 3 decoder means (9) shown in figure 8.
• n 2 ⁇ n 1 reproduction matrix decoders there are many possible n 2 ⁇ n 1 reproduction matrix decoders in accordance with the invention, and explicitly describing every case one wishes to consider would be extremely laborious. It is therefore convenient and useful to consider "composite" decoders contructed by series connection of simpler ones. If one has three successively larger pluralities n 1 , n 3 and n 2 , and one has an n 3 ⁇ n 1 reproduction matrix decoder (2a) in accordance with the invention, as shown in figure 9, and also an n 2 ⁇ n 3 reproduction matrix decoder (2b) also in accordance with the invention, then the result of cascading the two decoders, so that n 1 input signals (20) from a stereo source (1) are converted into
• n 3 signals (20a) by n 3 ⁇ n 1 matrix (2a) and then
• signals (40) constitutes an n 2 ⁇ n 1 reproduction matrix decoder (2) in accordance with the invention.
• each component decoder (2a) and (2b) preserves the total energy of the pluralities of signals passing through them, then so does the composite
• each of the component decoders (2a) and (2b) substantially preserves or improves the intended stereo effect, so does the composite decoder (2), and if each of the component decoders (2a) and (2b)
• a composite decoder based on two known decoders need not be implemented by physically implementing and connecting together the two known component decoders, but can alternatively be implemented as a single matrix circuit or means designed, by methods evident to those skilled in the art, to achieve the same end-result as a
• R n3n1 and the matrix coefficients of the n 2 ⁇ n 3 matrix decoder (2b) are represented by the n 2 ⁇ n 3 matrix R n2n3 then the matrix coefficients of the composite decoder
• R n2n1 R n2n3 R n3n1
• an n 2 ⁇ n 1 reproduction matrix decoder according to the invention can be designed so long as one knows for each plurality n how to design an (n+1) ⁇ n reproduction matrix decoder according to the invention, by series connection for increasing n such as shown in the schematic of figure 10.
• This shows successive signals sources (1a to 1e) intended to feed the respective loudspeaker layouts shown in figures la to le. (We have included the monophonic case for completeness).
• Figure 10 also indicates schematically how mixing or adding means may be used to mix signals originated for different numbers of loudspeakers together, and shows how signals for one number of loudspeakers may be reproduced via a greater number according to the invention.
• figure 10 only shows up to five-speaker stereo, it is evident that further matrices, e.g. the 6 ⁇ 5 and 7 ⁇ 6 cases, may extend this schematic to any number of loudspeakers. In most practical reproduction matrix decoders, most or all parts of the schematic of figure 10 will not be explicitly implemented, but such a decoder may nevertheless have an overall effect equivalent to that of specific signal paths within figure 10.
• Figure 11 shows the schematic of a general system for encoding n 1 signals (20) from an n 1 -speaker stereo source (1) into m transmission channel signals (60a) by an m ⁇ n 1 transmission matrix encoder means (7) described by an m ⁇ n 1 matrix E mn1 , which are then
• n 2 ⁇ m transmission matrix decoding means 9 described by an n 2 ⁇ m matrix
• the overall encoding/ transmission/decoding signal path (2) constitutes an n 2 ⁇ n 1 reproduction matrix decoding means for the source signals (20).
• figure 12 shows a composite transmission matrix encoder (7) described by an m ⁇ n 1 matrix consisting 3 of the series
• figure 13 shows how a composite transmission matrix decoder (9) in accordance with the invention may be constructed by a series connection of another transmission matrix decoder (9h) with a reproduction matrix decoder (2h) in accordance with the invention.
• An n 1 ⁇ m matrix transmission decoder (9h) described by an n 1 ⁇ m matrix is followed by an
• n 4 is greater than n 2 , and constitutes an n 4 ⁇ m transmission matrix decoder (9) described by the n 4 ⁇ m matrix
• (n+1)-speaker stereo transmission should be such that they constitute the n channels used for transmitting n-speaker stereo plus one additional transmission
• T 4 and T 5 are used to convey additional signals for 4- and 5-speaker stereo respectively.
• E 22 and D 22 is given by the conventional left/right or MS matrix encoding and decoding methods used in the prior art to transmit two-speaker stereo.
• R n+1n for converting n-speaker stereo signals to (n+1)-speaker stereo signals according to the invention
• (n+1) ⁇ (n+1) decoder matrix D n+1n+1 may be devised as follows.
• T 1 to T n form the (n+1) ⁇ n matrix R n+1 n D nn , and the last column is chosen to be any convenient nonzero column vector that is not a linear combination of the first n columns.
• E n+1 n+1 is then computed as the inverse (D n+1 n+1 ) -1 of the decoding matrix.
• i f the matrices all have real f requency-independent entries , as is genera lly
• D nn -1 may conveniently be computed as the transpose of D nn , i.e. the matrix with entries (d ji ) where
• D nn has entries (d ij ).
• the last column of D n+1n+1 can be chosen to meet the requirements of left/right symmetry, by ensuring that T n+1 for odd n is a linear combination of signals only of the form S p in MS form, and that T n+1 for even n is a linear combination of signals only of the form M p or C p in MS form.
• n 2 ⁇ n 1 reproduction matrix decoders falls into two main parts: first imposing an objective requirement that the
• matrix decoder preserves energy if and only if its n 1 columns are of unit length (i.e. the sum of the squares of the absolute values of the matrix coefficients in that column equals one) and the columns are pairwise orthogonal (i.e. the sum of the products of entries of one column with the complex conjugate of the
• n ⁇ n orthogonal matrices The general form of n ⁇ n orthogonal matrices is known to mathematicians, and there is a 1 ⁇ 2(n-1)n - parameter family of such n ⁇ n orthogonal matrices describing rotations in n-dimensional space; all other orthogonal nxn matrices ae obtained from these by reversing the sign of the entries of the last column.
• the product of any two orthogonal matrices is also orthogonal.
• the energy preserving matrices have an especially simple form when expressed in MS form, since sum signals (i.e. those of the form M p or C p ) must be converted into sum signals and difference signals (i.e. those of the form S p ) must be converted into difference
• reproduction decoder matrix must satisfy equations of the form
• figure 17 shows a 4 ⁇ 2
• Two-speaker stereo signals L 2 and R 2 are converted by input MS matrix means (31) into signals M 2 and S 2 ; S 2 may be passed through an optional width gain adjustment means (32); each of M 2 and S 2 is then passed into constant power or sine/cosine gain adjustment means, respectively (33c) and (33d).
• One output from each of these means (33) is passed to a first output MS matrix means (39c) to produce output signals L 4 and R 4
• the other outputs from each of the means (33) is passed to a second output MS matrix means (39d) to produce output signals L 5 and R 5 .
• output signals L 4 , L 5 , R 5 , R 4 may be used to feed a four-speaker stereo loudspeaker arrangement such as that of figure Id, via appropriate gain, equalisation, preamplification and amplification means. If desired, the angle parameters ⁇ 42 and ⁇ D associated with the respective sine/cosine gain
• adjustment means (33c) and (33d) may be made frequency ⁇ -dependent by the methods already discussed in
• FIG. 18 shows a 4 ⁇ 3 reproduction matrix decoding means in accordance with the above equations and the invention.
• Input signals 1,3,03 and R 3 intended for three-speaker stereo reproduction are accepted as inputs;
• L 3 and R 3 are fed to an input MS matrix means (31) to derive signals M 3 and S 3 ;
• S 3 is passed into a constant-power or sine/cosine gain adjustment means (33e) to produce two output difference signals S 4 and S 5 ;
• M 3 and the input C 3 are passed into a 2 ⁇ 2 orthogonal rotation matrix means (33f) producing outputs M 4 and M 5 ;
• M 4 and S 4 are passed through a first output MS matrix means (39e) to produce signals L 4 and R 4 , and
• M 5 and S 5 are passed through a second output MS matrix means (39f) to produce otput signals L 5 and R 5 .
• the signals L 4 , L 5 , R 5 and R 4 are suitable for providing feed signals for a four-speaker stereo arrangement such as that of figure 1d.
• bandsplitting filter means can be used in association with means (33e) and (33f) to provide frequency-dependent values of the angle
• Figure 19 shows one generic form of an energy-preserving left/right symmetric reproduction matrix decoding means according to the invention, generalising the special cases shown in figures 4, 17 and 18.
• An input MS matrix means (31) converts a first plurality n 1 of loudspeaker feed signals (20) for n 1 -speaker stereo into a number n 1 ' equal to the integer part of 1 ⁇ 2n 1 of difference signals S p (29) and into another
• n 1 " n 1 - n 1 ' of sum signals (28) of the form M p or C p .
• the sum signals (28) are passed into a matrix A means (33g) giving a plurality n 2 " of
• difference signals (49) are passed pairwise through output MS matrix means (39) to provide outputs (40) suitable for providing loudspeaker feed signals for n 2 -speaker
• the matrix A and B means (33g) and (33h) may be
• the 5 ⁇ 4 energy-preserving left/right symmetric equations have matrix A equations that can be parameterised in the form
• ⁇ 5 is an angle parameter. If equal signals are fed to all four speakers of the 4-speaker arrangement, a, b, and c determine the relative energies reproduced via the 5-speaker arrangement.
• listener (4) be the x-axis and the (notional) left direction (6) be the y-axis of rectangular coordinates , and let d irections around the l i stener ( 4 ) be measured as angles measured anticlockwise (i.e. towards
• the quality and direction of sound localisation of the listener is largely determined by the magnitude r E and direction angle ⁇ E of the ratio (e x /E, e y /E) of the sound-intensity gain vector to the energy gain;
• r E sin ⁇ E e y /E , where r E ⁇ 0, by rectangular-to-polar coordinate conversion.
• ⁇ E represents the apparent sound direction when a listener faces the apparent sound source, especially at frequencies between around 700 Hz and 5 kHz, where localisation is largely determined by interaural intensity ratios. This direction is the direction along which the sound intensity gain vector points.
• the quantity r E termed the energy vector magnitude, equals 1 for natural sound sources, but is less than 1 for sounds emerging from more than one loudspeaker, and is useful for describing the stability of the illusory sound image as a listener changes position. It is desirable for stable and natural sound localisation quality that r E be as close to the ideal value 1 as possible.
• the velocity vector magnitude r v should have a value
• the direction ⁇ v is often known as the "Makita localisation” direction, named after an author who introduced this localisation parameter.
• the Makita direction ⁇ V describes the
• the Makita direction ⁇ v should be similar to the energy vector direction ⁇ E for sharp images.
• the imaginary part (Im(v x /P), Im(v y /P)) of the velocity ratio vector, termed the "phasiness vector” mainly affects the subjective quality of an image, rather than its apparent direction, imparting a generally unpleasant quality often termed "phasiness", which also manifests itself in image broadening.
• the magnitude of the phasiness vector should be kept as small as possible, preferably having a length less than 0.2.
• the relative values of matrix coefficients normally depart from real values only by small amount, and such departures are largely confined to transition frequency bands, so that phasiness effects for an ideally situated listener are usually adequately small and may be ignored.
• a computation of the four localisation parameters r v , r E , ⁇ V and ⁇ E can be performed using the above equations for any predetermined loudspeaker arrangement all equidistant from an ideal listening position (4) for any predetermined loudspeaker signal feeds,
• a reproduction matrix decoding means accepting a first plurality n 1 of
• loudspeaker feed signals intended for a first
• n 1 loudspeakers across a sector of directions should give a larger plurality n 2 of output signals intended to feed n 2 loudspeakers in a second stereophonic arrangement across a second sector of directions in such a manner that the four localisation parameters are either substantially
• the values of r V and r E should either be maintained or made closer to 1 by the matrix decoder reproduction, and the values of the reproduced image directions ⁇ V and ⁇ E should be substantially preserved.
• stereophonic recording originally intended to cover a first sector of directions of angular width ⁇ I via a second sector of directions covering a different angular width ⁇ O at the listener.
• a simple proportional widening of the angular dispositions of stereo sound localisation directions is often desired or acceptable.
• the value of l - r E is typically increased by a factor k 2 , and similarly for k less than one.
• Figures 22 to 25 show the localisation parameters when the two-channel stereo signal is fed via a
• reproduction matrix decoder to satisfy from a stereo localisation point of view.
• a decoder of this type will be termed a "preservation decoder", and will also tend to preserve other localisation qualities indicated by r V and r E .
• the ⁇ 50.36° 3 ⁇ 2 decoder is a preservation decoder in this sense, and also preserves all the defects of two-speaker stereo.
• the other, less well defined, aim is to improve the reproduced illusion.
• this may mean using different values of the constants k V and k E of
• decoder matrix parameters to compute the localisatiom parameters of the resulting signals.
• Such a search is not difficult for 3 ⁇ 2 decoders involving only the one free parameter ⁇ , but becomes difficult in more complicated cases, and the search needs to be done again for each possible first and second stereophonic arrangement of loudspeakers.
• ⁇ 2 35°
• ⁇ 3 45°
• ⁇ 4 50°
• ⁇ 6 54°
• ⁇ 7 27°
• ⁇ 5 162 ⁇ 3°.
• the gain coefficients G i of a stereo sound via n 1 loudspeakers form a vector
• Table 1 shows the computed localisation parameters via the 3 ⁇ 2 preservation decoder as compared to the original 2-speaker values for various input signal gains.
• Table 1 shows the computed localisation parameters via the above 4 ⁇ 3 preservation decoder as compared to the original 3-speaker values for various input signal gains. gains 3-speaker parameters 4-speaker parameters L 3 C 3 R 3 r V ⁇ V r E ⁇ E r V ⁇ V r E ⁇ E
• Table 3 shows the computed localisation parameters via the above 5 ⁇ 4 preservation decoder as compared to the original 4-speaker values for various input signal gains. gains 4-speaker parameters 5-speaker parameters
• Table 3 shows the computed localisation parameters via the above 5 ⁇ 3 preservation decoder as compared to the original 3-speaker values for various input signal gains. gains 3-speaker parameters 5-speaker parameters L 3 C 3 R 3 r v ⁇ V r E ⁇ E r V ⁇ V r E ⁇ E
• the decoder angle parameters may vary by up to 6° from the values given, and the direction of the (a,b,c) vector may also vary by 6° without substantial effect.
• (n 1 +1) ⁇ n 1 reproduction preservation decoders can be designed by the above stereo test signal methods for other (n 1 +1)-speaker arrangements.
• Table 5 lists the parameters ⁇ 3 and ⁇ D for 4 ⁇ 3 preservation decoders for various values of the angles ⁇ 4 and ⁇ 5 in figure 1d ⁇ 4 ⁇ 5 ⁇ 3 ⁇ D
• a preservation decoder may, if desired, incorporate means of adjusting decoder parameters according to the angular disposition of the loudspeakers used, or may use fixed typical parameters Improvement Decoders
• the invention may be used to improve the reproduction via more loudspeakers. This may be achieved by altering the decoder parameters from their preservation decoder values computed above.
• n 2 ⁇ 2 improvement decoders may be achieved by forming a composite decoder, as in figure 9, comprising a 3 ⁇ 2 improvement decoder followed by an n 2 ⁇ 3
• a 4 ⁇ 2 improvement decoder may have the angle parameter ⁇ D substantially as shown in table 5 for the 4-speaker arrangement shown in figure 1d, being typically
• angle parameter ⁇ 42 may substantially equal 35° - ⁇ 3 (typically around 25°) at frequencies between around 400 Hz and around 5 kHz, and may substantially equal 55° - ⁇ 3 (typically around 45°) at frequencies above about 5 kHz, where ⁇ 3 is as given in table 5.
• a frequency-dependent 4 ⁇ 2 improvement decoder of this kind may be implemented as in figure 17, but making the ⁇ 42 sine/cosine gain adjustment means (33c) frequency ⁇ -dependent using associated bandsplitting means (34) such as shown in figure 5.
• the ⁇ D sine/cosine means (33d) in figure 17 may similarly be made frequency-dependent if desired. In such decoders, bass energy may be
• loudspeakers L 4 and R 4 preferentially fed to loudspeakers L 4 and R 4 by making ⁇ 42 near 90° and ⁇ D near 0° at low bass frequencies, and to loudspeakers L 5 and R 5 by making ⁇ 42 near 0° and ⁇ D near 90° at low bass frequencies.
• a frequency-dependent 4 ⁇ 2 improvement decoder may also be implemented as in figure 8, substituting for the output matrix means (9) a 4 ⁇ 3 transmission matrix decoder means as described hereafter, with angle parameters ⁇ ' - 45° and ⁇ 3 and ⁇ D substantially as shown in table 5.
• decoders from their preservation decoder values is best determined by a combination of such theoretical computations of localisation parameters and subjective testing on a wide variety of programme material
• Composite improvement decoders can be implemented by cascading two improvement decoders, or by following an improvement decoder by a preservation decoder; such composite decoders may be implemented as a single decoder designed so as to achieve the same result as the cascaded decoders by methods known to those skilled in the art.
• loudspeaker-feed formats such that some matrix
• coefficients have substantially the opposite polarity to other larger predominant matrix coefficients, at least across several octaves which may include the middle frequency region from say 500 Hz to 3 kHz.
• the coefficients that have substantially opposite polarities will have a magnitude of under two-fifths of that of the predominant matrix coefficients.
• the parameters ⁇ and ⁇ 42 preferably lie within 25° and the parameters ⁇ 3 , ⁇ D , ⁇ 4 , ⁇ 5 and the vector (a,b,c) preferably lie within 15° of their preservation decoder values given earlier.
• ⁇ ' 45° for the 3 ⁇ 2 reproduction matrix decoders .
• the transmission signals M, S, T, T 4 and T 5 may be given arbitrary predetermined respective nonzero amplitude gains k 1 ', k 2 ', k 3 ', k 4 ' and k 5 ' in order that the amplitude levels of signals in each
• Such additional amplitude gains may be applied at the encoding matrix stages, and the inverse gains k i ' -1 applied to the respective channel signals at the decoding stage.
• the gains k i ' may be positive or negative, or may have complex values, which may be frequency dependent in the case that equalisation is desired of a transmission channel.
• the transmission channel signals M, S, T, T 4 and T5 are of progressively decreasing average signal energy, so that the magnitudes of the associated channel gains k i ' may be chosen to be progressively of increasing value.
• decoder parameters ⁇ ' , ⁇ 3 , ⁇ D , ⁇ 4 , ⁇ 5 and (a,b,c) are used as in the above numerical equations.
• these equations may not give precisely the optimum preservation or improvement decoder effect, but will still be very close.
• a transmission matrix decoder may be employed based on modified values of the
• modified transmission decoding matrices are orthogonal, such decoders still give overall energy-preserving results.
• the transmission matrix decoder with the same parameters as the encoder can be followed by a reproduction matrix preservation or improvement decoder according to the invention; the transmission matrix decoder and a following reproduction matrix decoder may be
• the frequency-independent m ⁇ m transmission matrix encoder may be fed with the outputs of a
• frequency-dependent m ⁇ n reproduction matrix improvement decoder or equivalent signals may be provided by a frequency-dependent matrix encoding means achieving the effects of such a composite encoder.
• the invention can be used with loudspeaker arrangements for which this equal-distance requirement does not hold, such as the arrangement of figure 1g or
• n -speaker arrangements lying, for example, along a straight line or along a non-circular path or along a circular path whose centre does not lie in the
• a matrix decoder may be provided with or incorporate or be used in association with time delay means for all loudspeakers or for all but those loudspeakers most distant from the preferred listening position, the time delays provided for all loudspeaker feed signals being such as to ensure that the time of arrival at the preferred listening position of an impulse passing through the decoder is substantially identical for all of the loudspeakers.
• Such delay compensation means may be provided using any available time-delay technology, including
• the intended loudspeaker arrangement is substantially left/right symmetric and the preferred listening position is on the axis of symmetry.
• the delay compensation is not intended to provide
• the ears are less sensitive to localisation at low frequencies below about 200 Hz, and particularly below 100 Hz, than at higher frequencies.
• matrix decoders according to the invention may depart from the strict requirements of the invention at such low frequencies.
• decoders When used with loudspeakers some of which have limited bass reproduction capabilities, decoders according to the invention may incorporate modified matrix decoding parameters such as ⁇ ' or ⁇ , ⁇ 3 , ⁇ D , ⁇ 4 , ⁇ 5 and (a,b,c) at low frequencies in order to redistribute bass energy among the various loudspeakers, in the manner already described for 3 ⁇ 2 reproduction matrix decoders. Such decoders may also incorporate or be used in association with phase compensation means intended to compensate for differences in the bass phase responses of different loudspeakers, so that as much as possible of the remaining low-frequency localisation cues are retained.
• phase compensation means intended to compensate for differences in the bass phase responses of different loudspeakers, so that as much as possible of the remaining low-frequency localisation cues are retained.
• one-piece portable apparatus incorporating signal sources (1) such as cassette tape reproducers, radio reception means and compact disc players, amplification and control means and loudspeakers within a single unit, termed colloquially a "ghetto blaster".
• signal sources (1) such as cassette tape reproducers, radio reception means and compact disc players, amplification and control means and loudspeakers within a single unit, termed colloquially a "ghetto blaster”.
• Apparatus of this kind is sometimes equipped with a pair of
• loudspeaker systems each covering an audio frequency range including the range 400 Hz to 5 kHz, said system being capable of carried as a single unit, responsive to stereophonic source signals and incorporating amatrix decoding means for said source signals and providing feed signals for said loudspeaker systems, whereby at least one of said loudspeaker systems is securely attached to or integrated into the main housing unit of said portable or trasportable system, and whereby two of the additional said loudspeaker systems provided are attachable in close proximity to said mainhousing unit and are also movable or demountable with respect to said main housing unit so as to capable of being used spaced apart from each other and from said main housing unit. It is preferred if the system is so arranged that it may also be used for stereophonic reproduction when said two of the additional said loudspeaker
• said matrix decoder means be in accordance with the invention as described previously.
• Apparatus of this kind preferably incorporates a 3 ⁇ 2 or 4 ⁇ 2 matrix decoding means of the type described earlier, with optional width adjustment means,
• FIG. 27 shows, by way of example, a portable apparatus for multispeaker stereo reproduction of the above kind.
• a main housing unit (81) incorporates a signal source such as a cassette player (li), radio receiver (lj) and/or a compact disc player (lk), control means (82) such as volume, equalisation, width and source selection controls, and a centre loudspeaker (52) preferably placed at the front centre of said housing unit (81), and also incorporates within the main housing unit (81) 3 ⁇ 2 or 3 ⁇ 3 matrix decoder means (2) or (9) (not shown) responsive to stereo signal sources which feeds via amplification means (not shown) incorporated within said main housing unit (81) or within
• a signal source such as a cassette player (li), radio receiver (lj) and/or a compact disc player (lk)
• control means (82) such as volume, equalisation, width and source selection controls
• a centre loudspeaker (52) preferably placed at the front centre of said housing unit (81)
• a centre loudspeaker
• the loudspeaker enclosures (85) for left (51) and right (53) loudspeakers are shown attached to said main housing unit (81), but may be removed and spaced apart (85b) from said main housing unit (81) and each other, while remaining connected by audio signal cables (84) or by other audio signal communications means such as audio infra-red links.
• the left and right loudspeaker enclosures (85) may be attachable to and removable from said main housing unit (81) by means of catches (83), clips, hooks, Velcro or other fastening or attachment means.
• the enclosures (85) may be attached to the main housing unit (81) by means of movable arms or links (not shown) that slide or are otherwise movable (for example by a rotation or pantograph action) that allow the left and right loudspeaker enclosures (85) to be moved away from immediate proximity to said main housing unit (81) while still being physically connected to it by means of said arms or links.
• An advantage of using a movable arm or link means of removing attachable loudspeaker enclosures (85) from immediate proximity to the main housing unit (81) is that this means provides exact control of the relative positions of the loudspeaker units (51-53) to ensure the best stereophonic effect, whereas unskilled users might place entirely removable loudspeaker enclosures (85b) in undesirable locations.
• Moving arms or links also permit the entire unit to be carried by means of a single carrying handle (86) or shoulder strap attached to the main housing unit (81) while the loudspeaker enclosures (85) are removed from immediate proximity to said main housing unit (81).
• four such systems may be provided for use in conjunction with 4X2, 4X3 or 4X4 matrix decoding means, with the outer pair in the movable loudspeaker enclosures (85) and the inner pair enclosed within the main housing unit (81).
• the different loudspeaker systems (51,53) removable from the main housing unit (81) may have different frequency and/or phase response characteristics to those incorporated into the main housing unit (81), and equaliser compensation means may be incorporated into the apparatus for use in connection with said matrix decoding means to compensate for said differences of loudspeaker characteristics.
• said matrix decoder means may use frequency-dependent matrix parameters so as to minimise the bass energy fed to those loudspeaker systems with limited bass capability.
• the centre loudspeaker system (52) may have more bass power output than the movable
• loudspeaker systems (51, 53), and a 3x2 matrix decoder according to the invention may use a decoder parameter ⁇ that decreases to a value near 0° at low bass
• a decoder parameter ⁇ 42 that decreases to a value near 0° at low bass frequencies.
• reproduction with associated visual images where it is required to match the directions of sounds with those of associated visual images for listeners across a broad listening and viewing area. While applicable to situations where the visual image is that of physically present objects, such as in theatrical or live music performances, the invention is particularly applicable to reproduced images derived, for example, from
• a visual reproduction means such as a display screen or projection means in a main housing unit, said housing unit also incorporating or being securely attached to at least one loudspeaker system covering at least a primary audio frequency range of 400 Hz to 5 kHz, and used with at least two loudspeaker systems each covering at least said primary frequency range capable of being moved so as to be spaced apart from and disposed to the two sides of said main housing unit, and a matrix decoding means according to earlier descriptions of the invention responsive to stereophonic source signals associated with the visual image and providing signals intended for reproduction via said loudspeaker systems.
• Said movable loudspeakers may, if desired be attachable to and removable from said main housing unit by
• attachment or fastening means may be connected physically to said main housing unit by means of arm or link means, which may by sliding, rotation,
• pantograph or other action allow movement of said movable loudspeaker systems such that they may be used either in close proximity to said main housing unit or spaced apart and disposed to either side of said main housing unit.
• Figures 28 and 29 show two examples of audiovisual apparatus according to this aspect of the invention.
• a main housing unit (81) incorporates a display
• main housing unit (81) is used with two loudspeaker enclosures (85), one placed to either side of the main housing (81) and spaced apart from it, each containing loudspeaker means covering at least said primary frequency range, said main housing unit (81) also containing one or two loudspeaker systems (52) covering at least said primary frequency range.
• the main housing unit (81) is used with two loudspeaker enclosures (85), one placed to either side of the main housing (81) and spaced apart from it, each containing loudspeaker means covering at least said primary frequency range, said main housing unit (81) also containing one or two loudspeaker systems (52) covering at least said primary frequency range.
• matrix decoding means (not shown) responsive to stereo signals and providing signals suitable, after such processing and amplification means as may be neccessary or
• Figure 28 shows the case where a
• single centre loudspeaker (52) is used, in association with a 3X2 or 3x3 matrix decoder means (not shown);
• said loudspeaker is preferably placed centrally below or above said display screen (87) or display means in order to ensure correct localisation of central sound images with respect to the visual image.
• Figure 29 shows the case where two loudspeaker systems (52) are incorporated into or immediately attached to said main housing unit (81) to either side of said display screen (87), for use with a 4 ⁇ 2, 4 ⁇ 3 or 4 ⁇ 4 matrix decoder means (not shown).
• the quality of stereophonic images is largely independent of the ratio of the spacing between the outer loudspeaker systems (85) to the spacing between the inner loudspeaker systems (52), over a range of values of said ratio between about 2 and 5.
• a wider or narrower spacing of the outer loudspeaker enclosures (85) has little effect on the acceptability of stereophonic imaging over a wide range of placements.
• the matrix decoder means may, if desired, incorporate electronic width adjustment means in order to provide a desired width of stereophonic sound stage with any given
• the audiovisual apparatus may incorporate equa l i sa t ion means for compensating for any differences in frequency or phase response between inner (52) and outer (85) loudspeaker systems, and said matrix decoder means may additionally or instead have modified decoding matrix parameters at low frequencies so as to
• the invention is also well suited for use with high quality high-fidelity sound reproduction systems used for example for music reproduction not necessarily associated with visual images.
• loudspeaker units will generally be
• preamplifier control means which may incorporate matrix decoder means according to the invention or which may be used in association with physically separate matrix decoder means apparatus.
• a preamplifier control means apparatus responsive to stereo source signals (1) incorporating matrix decoder means as earlier described according to the invention, said apparatus providing output signals intended, after subsequent amplification means (92) which may, if desired, be integrated with said apparatus for feeding to a stereophonic loudspeaker arrangement (50)
• said preamplifier control means apparatus (91) also incorporates visual signal control means for receiving, selecting and/or modifying associated visual images intended to match reproduced sound images in direction.
• FIG 31 another form of the invention provides a matrix decoder means apparatus (2)
• arrangement (50) comprising at least three loudspeaker systems or units disposed across a sector (3) of directions in front of a preferred listening position (4).
• PA apparatus intended to provide stereophonic reproduction with improved image stability for an audience of larger size than normally encountered in domestic applications.
• PA apparatus may be used in cinema or film auditoria, for live amplified music, and in audiovisual and theatrical applications, among other applications.
• loudspeakers in a given cluster may handle different frequency ranges. Where the cluster of loudspeakers is- mounted vertically on top of one another, such clusters are often termed "stacks" of loudspeakers.
• Conventional stereophonic live music and theatrical PA apparatus usually uses a pair of stacks or clusters to either side of a stage or performance area, and occasionally a third central cluster is used placed over or behind the centre of the performance area.
• Such clusters or stacks are fed by amplification
• prerecorded sounds sounds from various performers or their instruments picked up by microphones or electrical means, and sounds derived from effects devices such as synthetic echo or reverberation units.
• stereophonic mixing apparatus (1) may incorporate or may feed a matrix decoding means (2) according to previous descriptions of the invention, and said matrix decoding means (2) may feed, via amplification means (92) three or more loudspeaker systems, clusters or stacks (50) in a stereophonic arrangement across,
• Figure 32 illustrates an example in which two
• loudspeaker stacks (51) and (53) are disposed at the respective left and right sides of a performance area (87) and a central loudspeaker system or cluster (52) is suspended over the front of said performance area (87) in order to avoid visual obstruction of the
• input and output sockets or connection means should meet professional standards for heavy-duty use, for example by the use of XLR-type or quarter-inch (6.3mm) jack connectors, and that adjustment means be provided to cope with typical operational problems.
• the matrix decoder means should preferably incorporate or be used in association with delay
• compensation means to compensate for the positioning in distance of central or inner loudspeaker systems or clusters. Also, in general, suspended central
• loudspeaker systems or clusters may have more limited bass capability than the outer stacks or clusters, since large bass units are too heavy or large for suspension without visual obstruction of the
• the matrix decoder means (2) should thus preferably incorporate means of adjusting the low-frequency decoder matrix parameters so as to minimise the bass fed to such central loudspeakers, for example by putting ⁇ or ⁇ 42 close to 90° at low frequencies.
• the bass transition frequency at which such parameter modifications take effect should be adjustable to match different bass deficiencies.
• Such a matrix decoder may also provide user preset
• n 2 of loudspeaker systems or clusters may be used for each frequency range for which distinct loudspeaker types are provided, with a separate decoder provided for each plurality n 2 used.
• n 2 5 for treble loudspeaker systems
• n 2 3 or 4 for mid-frequency loudspeaker units
• the inputs of said separate decoders may be derived using electronic cross-over filter networks of the kind normally used to provide feed signals for PA loudspeaker units covering a partial frequency range.
• the invention provides a solution to particular
• drivers are generally positioned to one side and towards the front of the listening area, and stereo loudspeakers have generally to be
• third central loudspeaker (52) is provided supplementing the typical left and right loudspeakers (51) and (53) conventionally provided, said centre loudspeaker
• the left (51) and right (53) loudspeakers may be mounted at the two sides of the dashboard or in the respective front doors of the vehicle.
• the invention may also be used with two or three
• Equalisation means associated with each of the
• loudspeaker systems may be incorporated or added to compensate both for different frequency responses of different loudspeaker systems and for typical
• the invention may be used with any combination of items listed above. Generally, the invention may be used with any combination of items listed above. Generally, the invention may be used with any combination of items listed above.
• front seating area of the vehicle responsive to two or more stereo source signals, and delay compensation means may also be used in association with each or some of the loudspeaker feed signals for said
• a second stereophonic arrangement disposed either to the front or the rear of a rear seating area, may also or additionally be provided according to the invention to serve listeners in said rear seating area. Because of the proximity of listeners to the loudspeaker arrangement in an in-car system, some empirical
• any matrix means described may have component means rearranged, combined, split apart and recombined; gains and polarity inversions may be inserted and addition means replaced by
• Means responsive to signals in left/right form may be made responsive to signals in MS form by the addition or deletion, as appropriate, of MS matrix means, and conversely for means responsive to signals in MS form.
• means producing signals in one of left/right or MS forms may produce signals in the other form by the addition or deletion, as
• MS matrix means Any means satisfying known matrix equations may be replaced by any other means producing results satisfying the same matrix equations designed by methods known to those skilled in the art.
• any matrix means comprising two cascaded matrix means may be replaced by a single matrix means described by the matrix coefficients of the product of the matrices describing the input/output behaviour of the component matrix means.
• loudspeakers or loudspeaker systems are referred to, clusters of loudspeaker units or systems placed relatively close to one another so as substantially to act as a single loudspeaker may equally be used.
• different pluralities of loudspeakers may be used for reproduction of each component frequency range fed by an appropriate decoder according to the invention for that frequency range.
• the invention may equally be applied to stereophonic loudspeakers covering other sectors of directions, such as for example, a sector behind a listener, to one side of a listener or above or below a listener, or to a vertical sector.
• the invention may also be applied to a stereophonic arrangement of loudspeakers covering a sector of directions used in conj ucti on with other loudspeakers in other directions, such as rear loudspeakers
• any additional loudspeakers or additional signals from other sources fed to the loudspeakers do not affect the scope of the invention.
• additional "surround" signals may be transmitted and reproduced to supplement the front-stage stereo effect produced by the invention.
• Transmission channel signals may be transmitted and received in either left/right or MS form; this may also include the possible use of a left/right form of transmission signals T 2n-1 and T 2n of the form
• the invention is also applicable to stereophonic
• the permissible degree of departure that substantially retains the psychoacoustic advantages of the invention is such that, at any frequency, the gain of any two stereophonic signal components passing through a reproduction decoder according to the invention differs by not more than 3 dB, and preferably by less than 2 dB, and highly preferably by less than 1 dB, and such that, expressed in terms of the effect
• some matrix coefficients of said decoder are, across several octaves of the audio frequency range, substantially of opposite polarity to and of magnitude less than two fifths of the dominant or largest matrix coefficients.
• Such small departures from exact energy preservation to within a constant of proportionality may typically be implemented by small departures from exact energy preservation of the matrix A means (33g) and the matrix B means (33h) of figure 19.
• the matrix A means (33g) and the matrix B means (33h) of figure 19.
• the matrix B means may be adjustable, for example for the purposes of electronic width control or other desired effects, such that, at each frequency, different signal components of the signals (28) or (29) passing through matrix A means (33g) or matrix B means (33h) to produce signals (48) or (49) have a difference in relative total energy gain of not more than 3 dB, and preferably less than 2 dB, and highly preferably less than 1 dB.
• the matrix A means (33g) may be energy preserving and the matrix B means (33h) may be energy preserving with an added overall gain of between -3 dB and + 3 dB , or the s i gna ls ( 28 ) and ( 29 ) may be gi ven possibly differing gains within 3 dB of one another, or the signals (48) and (49) may be given possibly differing gains within 3 dB of one another when matrix A mean: (33g) and matrix B means (33h) are energy preserving, providing that these gain modifications are such as to retain the substantially opposite polarity of some matrix coefficients relative to the dominant matrix coefficients of the overall matrix reproduction decoder of figure 19, and that said substantially opposite polarity coefficients have a magnitude of less than two-fifths of said dominant matrix coefficients.
• the decoder will remain according to the invention.
• the present invention can also be applied to the provision of, e.g., a 3-speaker stereo feed from an ambisonically encoded signal.
• Ambisonic techniques are described and claimed in patents GB2073556,GB1550627, GB1494752, GB1494751 all assigned to NRDC and in the present inventor's paper "Ambisonics in Multichannel Broadcasting and Video” pp 859-871, J. Audio Eng. soc. Vol 33 no. 11 (1985 Nov.). This aspect is not limited to B format but may also apply to other ambisonic formats.
• T M 2 sin( ⁇ - 45°) (21) for a parameter ⁇ that equals about 35.26° below 5kHz and 54.70° above 5 kHz, where the 3 speaker feeds are given by the equations:
• the matrixing of equ. (21) is energy preserving as ⁇ varies, and the matrixing of equ. (22) shown as (9) in figure 8 is orthogonal, and so also preserves total energy.
• T dec ' 0.41421[(W-X)cos( ⁇ -45°) + (W+X)sin( ⁇ -45°)], (24) where, as before, ⁇ typically varies from about 35° below 5 kHz to about 55° above 5 kHz; the precise variation of ⁇ with frequency may be chosen by subjective tests on imaging quality.
• the decoder algorithm shown in the Figure may be replaced by any frequency-dependent matrix algorithm whose matrix coefficients equal those given by the Figure.
• the decoder described above for 3-speaker stereo can be generalised to an n-speaker decoder, as shown in Figure 34b.
• the final matrix D n,3 is an n ⁇ 3 transmission decoding matrix of the form also described above.
• signals emerging from the input matrix (equ. 23) are called M dec , S dec , T dec and signals entering the output matrix are denoted M, S, T.
• the matrix may be implemented by bandsplitting in a manner analoguous to Figure 5.
• the rotation matrix is implemented in a fashion analogous to that described with respect to Figure 8 above.
• the matrix is shown in Figure 34c.
• the function of the filter means 38 and all pass 38a and gain 38b is the same as in Figure 8, and the element referenced 38 is identical to 38e, 38c is identical to 38a and 38d is identical to 38b. It can be shown that this is a close approximation to the ideal rotation matrix for values of phi near 45 °, e.g. 35 or 55°.
• this aspect can also be used with any signals incorporating directionally encoded 360° surround sound signals that are linear combinations of an omnidirectional signal W, a signal X with gain proportional to cosine of direction and a signal Y with gain proportional to sine of direction.
• those elements may have been transformed by, e.g., a forward dominance transformation.
• Lorentz transformation termed by the inventor the "forward dominance" transformation, and defined in detail below, has the effect of increasing front sound gain by a factor ⁇ while altering the rear sound gain by an inverse factor 1/ ⁇ .
• Figure 16 shows a design process for a transmission hierarchy.
• the last column of D m can be chosen at will subject to linear independence of the other columns and this choice then determines the corresponding coefficients of the encoding matrix.
• the encoder values may vary moment by moment provided that the choice is transmitted to the decoder as a side chain signal so that decoder can perform the inverse of the encoding function at any given moment.
• Error noise artefacts such as those introduced by data compression can be subjectively minimised by adaptively modifying the encoding equation to match the instantaneous distribution of signal energies among the speaker feed signals, and using an inverse equation for the decoder.
• a preferred strategy adjusts the coefficients so the transmission channels more nearly diagonalise the signal correlation matrix than would a fixed encoding function.
• the appendix below lists a cascadable hierarchy of conversion matrices between any numbers n 1 and n 2 speaker feed signals between 1 and 5 for multi-speaker stereo based on the results of encoding from n 1 speakers and decoding into n 2 speakers using the orthogonal transmission systems designed using the flow diagram of figure 16 with the earlier highly preferred values of ⁇ ', ⁇ 3 , ⁇ D , ⁇ 4 , ⁇ 5 and the vector (a,b,c) parameters, whose transmission encoding and decoding matrices were given earlier.
• the conversion matrices from a smaller to a larger number of loudspeakers in the hierarchy listed in the appendix are preferred matrix reproduction decoders as described earlier, and that the conversion matrices from a larger number of loudspeakers to a smaller number of loudspeakers have matrices that are the matrix transposes of the matrices from the smaller to the larger number with any frequency-dependent all-pass component deleted.
• the following pages describe how a more general hierarchy may be constructed for conversion between formats having different numbers n of channels.
• a cascadable hierarchy transmission system constructed following the method of Figure 16 when the input to a given conversion stage has a smaller number of channels than the output from the stage then an upconversion matrix as previously described for n-speaker stereo is used. Where a smaller number of channels are output then a downconversion matrix is used.
• the transmission decoding and encoding matrices D m and E m in the construction of fig. 16 are orthogonal it can be shown that the downconversion matrices are the matrix transpose of the upconversion matrices.
• R ji an "upconversion" matrix, and write A i ⁇ A j , if and only if R ji takes linearly independent signals in the system A i into linearly independent signals in the system A j (which requires that n i ⁇ n j ).
• R ii is the n i ⁇ n i identity matrix I ii , i.e. conversion of a system to itself leaves signals unchanged.
• R ki R kj R ji .
• R ki R kj R ji .
• upconversion matrices but to any three systems such that the middle system is an upconversion of the "maximum" system of which the two outer systems are upconversions. All of the conditions (1) to (5) hold for earlier described systems of upconversion and down-conversion between n-speaker stereophonic signals, but apply to other cases.
• Cascadable hierarchies are desirable because not only do they allow sounds encoded for any one system A i to be converted by a matrix means R ji for reproduction from any other system A j in the hierarchy with
• cascadable hierarchy of systems means that any user can convert a directionally encoded sound , no matter what i ts h i story and or i gins earlier in the sound chain, into any other directional sound encoding mode in the hierarchy, knowing that the results will not degrade excessively by doing so. While the desirability of having a cascadable hierarchy is evident, it has not in the prior art been obvious how to design it. In general, one only knows the upconversion matrices that substantially preserve the originally intended directional effect via a more
• the design method is based on encoding, for every i from 1 to n, the n i encoding system signals A i into a collection Z i of n i transmission signals via an
• n i columns of the transmission decoding matrix D jj corresponding to transmission signals present in Z i has the form of the n j ⁇ n i matrix R ji D ii .
• D jj must be linearly independent of each other and of the columns of R ji D ii in order that D jj be invertible.
• the transmission decoding matrix D jj for a system A j should chosen such that for all systems A i ⁇ A j , the n i columns of D jj
• a j 's equipped with all such conversion matrices R ji can be shown to form a cascadable hierarchy.
• FIG. 16 the construction associated with figure 16 provided such a cascadable hierarchy in the special case of frontal stage stereo signals, where A i may be the signals intended to feed i-speaker stereo speakers.
• a i may be the signals intended to feed i-speaker stereo speakers.
• other kinds of sound reproduction system may be added to the above frontal stage stereo hierarchies to form a more flexible cascadable hierarchy also allowing various forms of surround-sound and ambisonic sound reproduction, while allowing flexible conversion between all reproduction or directional encoding modes.
• 3-speaker stereo conveying signals L 3 , C 3 and R 3 , all as described earlier for a frontal stage, and in addition,
• B-format ambisonic coding conveying three signals W, X and Y conveying 360° horizontal azimuthal sounds, encoding sounds from an azimuthal directional angle ⁇ with respective gains 1, 2 1 ⁇ 2 cos ⁇ and 2 1 ⁇ 2 sin ⁇ .
• BEF-format enhanced ambisonic coding conveying five signals W, X, Y, E, F conveying 360° horizontal
• azimuthal sounds encoding sounds from an azimuthal directional angle ⁇ with respective gains:
• ⁇ S is a predetermined frontal encoding stage half width typically between 60° and 70°
• ⁇ B is a predetermined frontal encoding stage half width typically between 60° and 70°
• k G is a fixed gain chosen from a range of values between 3 and 31 ⁇ 2 ( a prefered value is 3.25), and the gains k E , k F and k B may be chosen by the user to be greater than or equal to zero, and less than or equal to one, such that typically k E may equal one for azimuth 0° sounds and typically k B and k F may have roughly equal values around one half.
• BE-format ambisonic which uses the four signals W, X, Y, E defined above for BEF-format.
• BF-format ambisonic which uses the four signals W, X, Y, F defined above for BEF-format.
• the BEF-format signals provide additional information permitting sound reproduction with improved frontal-stage image stability and improved front/rear stage separation as compared to reproduction from B-format.
• the BE-format signals provide only improved frontal image stability, and the BF-format signals provide only improved
• BEF-format (A 10 ).
• a cascadable hierarchy may be formed from the ten directional encoding systems just described using five transmission channels M T , S T ., T T , B T , F T giving satisfactory subjective results when one encoding is reproduced via reproduction from any other, when a transmission system using encoding matrices E i i with matrix coefficients similar to those indicated below is constructed: mono E 11
• frontal stereo stage signals for 2:1, 3:1 and 3:2 stereo are also encoded into the M T , S T and T T transmission channels in the same way as frontal-only stereo signals, but that rear-stage stereo signals are encoded into these three transmission channels at a reduced gain, because it has been found that frontal stereo reproduction of "surround sound" material sounds best if the rear stage sounds are reproduced around 3 to 6 dB down.
• the B T transmission channel is intended to convey predominantly rear stage material, and F T corresponds to the difference signal across a frontal stage minus a difference signal across a rear stage.
• the decoding matrices On of this transmission hierarchy are simply given by the matrix inverse E ii -1 of ⁇ i i , which may be computed from the above matrices using any matrix inverse program on a computer or calculator.
• R j i is an upconversion matrix whenever the transmission signals of A i are also transmission signals for A j , which can be determined by inspection of figure X3.
• Such conversion can be achieved by using intermediate transmission channel signals via encoding and decoding matrices, which may be, but need not be, of the form of the signals M T , S T , T T , B T and F T described above.
• the transmission signals may be encoded with an additional nonzero gain, and decoded with the inverse of said gain, said gain possibly being different for each transmission signal, or desired independent linear combinations of M T , S T , B T , T T and F T may be used as intermediate transmission signals.
• (E ii ) old is tne encoding matrix given above and (E ii ) new is the encoding matrix used with the modified A i .
• depleted BEF-format to consist of the signals
• Depleted BE-format is similarly described as comprising the four signals W, X', Y and E from depleted
• BEF-format In recording or mixing applications, it may be desired to position monophonically recorded sounds to an azimuth ⁇ in BE-, BF-, BEF-, depleted BE- or depleted BEF-format, and this may be done by subjecting the monophonic signal to an arrangement of four or five gains respectively equal to: 1 for W, 2 1 ⁇ 2 cos ⁇ for X, 2 1 ⁇ 2 sin ⁇ for Y,
• half-stage widths ⁇ S and ⁇ B and k G are as before and where k E , k F and k B are optionally
• BE-, BEF- BF-, depleted BE- and depleted BEF-format signals from B-format ambisonic signals W O , X O and Y O containing significant signals only across a limited sound stage by matrixing. For example, if sounds in B-format
• any output signals may be subjected to predetermined nonzero gains, including possibly polarity inversion, so as to achieve output signals having levels and/or polarities suitable for use with available signal channels or recording or transmission channels.
• Some of the prior art surround sound systems for directional encoding of 360° azimuthal sound including all systems in the prior art UMX hierarchy and the B-format encoding, have mathematical rotational symmetry in the sense that, for every angle of rotation of the whole 360° sound stage, there exists a corresponding n ⁇ n matrix on the n channel signals of the directional encoding such that the application of this matrix to the original encoded signals produces signals encoded for the same encoding system, but with all encoded sound source positions rotated by said angle of rotation within the 360° stage.
• the following upconversion matrices are subjectively exceptionally good performers, giving substantially optimal preservation of the originally intended stereo effect via a larger number of speakers.

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• 1991
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