Apparatus, Method And Computer Program For Upmixing A Downmix Audio Signal
Abstract:
An apparatus for upmixing a downmix audio signal describing
one or more downmix audio channels into an upmixed audio
signal describing a plurality of upmixed audio channels
comprises an upmixer configured to apply temporally variable
upmixing parameters to upmix the downmix audio signal in order
to obtain the upmixed audio signal. The apparatus also
comprises a parameter interpolator, wherein the parameter
interpolator is configured to obtain one or more temporally
interpolated upmix parameters to be used by the upmixer on the
basis of a first complex-valued upmix parameter and a
subsequent second complex-valued upmix parameter. The
parameter interpolator is configured to separately interpolate
between a magnitude value of the first complex-valued upmix
parameter and a magnitude value of the second complex-valued
upmix parameter, and between a phase value of the first
complex-valued upmix parameter and a phase value of the second
complex-valued upmix parameter, to obtain the one or more
temporally interpolated upmix parameters. A respective method
can be implemented, for example, as a computer program.
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Notices, Deadlines & Correspondence
INNERER KLEINREUTHER WEG 25 A, 90408 NUERNBERG GERMANY
3. JOHANNES HILPERT
HERRNHUETTESTRASSE 46, 90411 NUERNBERG GERMANY
Specification
APPARATUS, METHOD AND COMPUTER PROGRAM FOR UPMIXING A DOWNMIX
AUDIO SIGNAL
Background of the Invention
Embodiments according to the invention are related to an
apparatus, a method, and a computer program for upmixing a
downmix audio signal.
Some embodiments according to the invention are related to a
magnitude-preserving upmix parameter interpolation for
parametric multi-channel audio coding.
In the following, the context of the invention will be
described. Recent development in the area of parametric audio
coding delivers techniques for jointly coding a multi-channel
audio (e.g. 5.1) signal into one (or more) downmix channels
plus a side information stream. These techniques are known as
Binaural Cue Coding, Parametric Stereo, and MPEG Surround etc.
A number of publications describe the so-called "Binaural Cue
Coding" parametric multi-channel coding approach, see for
example references [1][2][3][4] [5] .
"Parametric Stereo" is a related technique for the parametric
coding of a two-channel stereo signal based on a transmitted
mono signal plus parameter side information [6][7].
"MPEG Surround" is an ISO standard for parametric multi-
channel coding [8].
The abovementioned techniques are based on transmitting the
relevant perceptual cues for a human's spatial hearing in a
compact form to the receiver together with the associated mono
or stereo downmix-signal. Typical cues can be inter-channel
level differences (ILD), inter-channel correlation or
coherence (ICC), as well as inter-channel time differences
(ITD) and inter-channel phase differences (IPD).
These parameters are in some cases transmitted in a frequency
and time resolution adapted to the human's auditory
resolution. The update interval in time is determined by the
encoder, depending on the signal characteristics. This means
that not for every sample of the downmix-signal, parameters
are transmitted. In other words, in some cases a transmission
rate (or transmission frequency, or update rate) of parameters
describing the abovementioned cues may be smaller than a
transmission rate (or transmission frequency, or update rate)
of audio samples (or groups of audio samples).
Since the decoder may in some cases have to apply the
parameters continuously over time in a gapless manner, e.g. to
each sample (or audio sample), intermediate parameters may
need to be derived at decoder side, typically by interpolation
between past and current parameter sets.
Some conventional interpolation approaches, however, result in
poor audio quality.
In the following, a generic binaural cue coding scheme will be
described taking reference to Fig. 7. Fig. 7 shows a block
schematic diagram of a binaural cue coding transmission system
800, which comprises a binaural cue coding encoder 810 and a
binaural cue coding decoder 820. The binaural cue coding
encoder 810 may for example receive a plurality of audio
signals 812a, 812b, and 812c. Further, the binaural cue coding
encoder 810 is configured to downmix the audio input signals
812a-812c using a downmixer 814 to obtain a downmix signal
816, which may for example be a sum signal, and which may be
designated with "AS" or "X". Further, the binaural cue coding
encoder 810 is configured to analyze the audio input signals
812a-812c using an analyzer 818 to obtain the side information
signal 819 ("SI") . The sum signal 816 and the side information
signal 819 are transmitted from the binaural cue coding
encoder 810 to the binaural cue coding decoder 820. The
binaural cue coding decoder 820 may be configured to
synthesize a multi-channel audio output signal comprising, for
example, audio channels yl, y2, ... , yN on the basis of the sum
signal 816 and inter-channel cues 824. For this purpose, the
binaural cue coding decoder 820 may comprise a binaural cue
coding synthesizer 822 which receives the sum signal 816 and
the inter-channel cues 824, and provides the audio signals yl,
y2,..., yN.
The binaural cue coding decoder 820 further comprises a side
information processor 826 which is configured to receive the
side information 819 and, optionally, a user input 827. The
side information processor 826 is configured to provide the
inter-channel cues 824 on the basis of the side information
819 and the optional user input 827.
To summarize, the audio input signals are analyzed and
downmixed. The sum signal plus the side information is
transmitted to the decoder. The inter-channel cues are
generated from the side information and local user input. The
binaural cue coding synthesis generates the multi-channel
audio output signal.
For details, reference is made to the articles "Binaural Cue
Coding Part II: Schemes and applications," by C. Faller and F.
Baumgarte (published in: IEEE Transactions on Speech and Audio
Processing, vol. 11, no. 6, Nov. 2003).
However, it has been found that many conventional binaural cue
coding decoders provide multi-channel output audio signals
with degraded quality if the side information is received at a
lower update frequency than the downmix signal.
In view of this problem, there is a need for an improved
concept of upmixing a downmix audio signal into an upmixed
audio signal, which reduces a degradation of the hearing
impression if the update frequency of the side information is
smaller than the update frequency of the downmix audio signal.
Summary of the Invention
An embodiment according to the invention creates an apparatus
for upmixing a downmix audio signal describing one or more
downmix audio channels into an upmixed audio channel
describing a plurality of upmixed audio channels. The
apparatus comprises an upmixer configured to apply temporally
variable upmixing parameters to upmix the downmix audio signal
in order to obtain the upmixed audio signal. The apparatus
further comprises a parameter interpolator, wherein the
parameter interpolator is configured to obtain one or more
temporally interpolated upmix parameters to be used by the
upmixer on the basis of a first complex-valued upmix parameter
and a subsequent second complex-valued upmix parameter. The
parameter interpolator is configured to separately interpolate
between a magnitude value of the first complex-valued upmix
parameter and a magnitude value of the second complex-valued
upmix parameter, and between a phase value of the first
complex-valued upmix parameter and a phase value of the second
complex-valued upmix parameter, to obtain the one or more
temporally interpolated upmix parameters.
Embodiments according to the invention are based on the
finding that a separate temporal interpolation of the
magnitude value of an upmix parameter and of the phase value
of the upmix parameter brings along a good hearing impression
of the upmixed audio signal because a variation of the
magnitude of the interpolated upmix parameter is kept very
small. It has been found that an unnecessarily large variation
of the amplitude of the upmix parameter may result in an
audible and disturbing modulation of the upmixed audio signal.
In contrast, by separately interpolating the amplitude of the
complex-valued upmix parameters from the phase value thereof,
the amplitude variation caused by the interpolation is kept
small (or even minimized) , even in the presence of a large
phase difference between the complex value of the first (or
initial) upmix parameter and the complex value of the second
(or subsequent) upmix parameter. Accordingly, an audible and
disturbing modulation of the upmixed output audio signal is
reduced when compared to some other types of interpolation (or
even completely eliminated).
Thus, a good hearing impression of the upmixed output audio
signal can be obtained, even if the side information is
transferred from a binaural cue coding encoder to a binaural
cue coding decoder less frequently than samples of the downmix
audio signal.
In an embodiment according to the invention, the parameter
interpolator is configured to monotonically time interpolate
between a magnitude value of the first complex-valued upmix
parameter and the magnitude value of the second (subsequent)
complex-valued upmix parameter to obtain magnitude values of
the one or more temporally interpolated upmix parameters.
Furthermore, the parameter interpolator may preferably be
configured to linearly time-interpolate between a phase value
of the first complex-valued upmix parameter and the phase
value of the second complex-valued upmix parameter, to obtain
phase values of the one or more temporally interpolated upmix
parameters. Further, the parameter interpolator may be
configured to combine the one or more magnitude values of the
interpolated upmix parameters with corresponding phase values
of the interpolated upmix parameters in order to obtain the
one or more complex-valued interpolated upmix parameters.
In an embodiment according to the invention, the parameter
interpolator is configured to linearly time-interpolate
between the magnitude value of the first complex-valued upmix
parameter and the magnitude value of the second, subsequent
complex-valued upmix parameter, to obtain magnitude values of
the one or more temporally interpolated upmix parameters.
By performing a monotonic or even linear time interpolation
between magnitude values of the subsequent complex-valued
upmix parameters, a disturbing amplitude modulation of the
upmixed audio signal (which would be caused by other
interpolation schemes) can be avoided. Regarding this issue,
it has been found that the human auditory system is
particularly sensitive to amplitude modulation of audio
signals. It has also been found that the auditory impression
(or hearing impression) is significantly degraded by such a
parasitic amplitude modulation. Accordingly, obtaining a
smooth and non-modulated variation of the upmix parameters,
which results in a smooth and non-modulated temporal evolution
of the audio signal amplitude, is an important contribution to
the improvement of the hearing impression of an upmix signal
in the presence of an interpolation of the upmix parameters.
In an embodiment of the invention, the upmixer is configured
to perform a linear scaled superposition of complex-valued
subband parameters of a plurality of upmixer audio input
signals in dependence on the complex-valued interpolated
upmixing parameters to obtain the upmixed audio signal. In
this case, the upmixer may be configured to process sequences
of subband parameters representing subsequent audio samples of
the upmixer audio input signals. The parameter interpolator
may be configured to receive subsequent complex-valued upmix
parameters, which are temporally spaced by more than the
duration of one of the subband audio samples, and to update
the interpolated upmixing parameters more frequently (e.g.
once per subband audio sample).
Thus, the upmixer may be configured to receive updated samples
of the upmixer audio input signals at an upmixer update rate,
and the parameter interpolator may be configured to update the
interpolated upmix parameters at the upmixer update rate. In
this way, the update rate of the upmix parameters may be
adapted to be the update rate of the upmixer audio input
signals. Accordingly, particularly smooth transitions between
two subsequent sets of upmix-parameters received by the
apparatus (e.g. at an update rate smaller than the upmixer
update rate) may be obtained.
In a preferred embodiment of the invention, the upmixer may be
configured to perform a matrix-vector multiplication using a
matrix comprising the interpolated upmix parameters and a
vector comprising one or more subband parameters of the
upmixer audio input signals, to obtain as a result a vector
comprising complex-valued subband samples of the upmixed audio
signals. By using a matrix-vector multiplication, a
particularly efficient circuit implementation can be obtained.
The matrix-vector multiplication defines, in an efficient-to-
implement form, the upmix-parameter-dependent linear
superposition of the audio input signals. A matrix-vector-
multiplication can be efficiently implemented in a signal
processor (or in other appropriate hardware or software units)
if the entries of the matrix are represented split-up into a
real part and an imaginary part. Handling of complex values
split-up into a real part and an imaginary part can be
performed with relatively little effort, as the real-
part/imaginar-part splitting is well-suited both for a
multiplication of complex numbers and, particularly, for an
addition of the results of the multiplication. Thus, while
other number representations bring along severe difficulties
either with respect to a multiplication or with respect to an
addition (which operations are both needed in a matrix-vector-
multiplication) , the usage of a real-part/imaginary-part
number representation provides for an efficient solution.
In an embodiment of the invention, the apparatus is configured
to receive spatial cues describing the upmix parameters. In
this case, the parameter interpolator may be configured to
determine the magnitude values of the upmix parameters in
dependence on inter-channel level difference parameters, or in
dependence on inter-channel correlation (or coherence)
parameters, or in dependence on inter-channel level difference
parameters and inter-channel correlation (or coherence)
parameters. Further, the parameter interpolator may be
configured to determine the phase values of the upmix
parameters in dependence on inter-channel phase difference
parameters. Accordingly, it can be seen that in some cases it
is possible, in a very efficient manner, to obtain the
magnitude values and the phase values of the upmix parameters
separately. Thus, the input information required for the
separate interpolation can be efficiently obtained even
without any additional magnitude-value/phase values separation
unit if the abovementioned parameters (ILD, ICC, IPD, and/or
ITD) or comparable parameters are used as input quantities to
the parameter interpolator.
In an embodiment of the invention, the parameter interpolator
is configured to determine a direction of the interpolation
between the phase values of subsequent complex-valued upmix
parameters such that an angle range passed in the
interpolation between a phase value of the first complex-
valued upmix parameter and a phase value of the (subsequent)
second complex-valued upmix parameter is smaller than, or
equal to, 180°. In other words, in some embodiments it is
ensured that a phase variation caused by the interpolation is
kept sufficiently small (or even minimized). Even though the
human auditory perception is not particularly sensitive to
phase changes, it may be advantageous to limit the phase
variation. For example, fast phase variation of the upmix
parameters might result in difficult-to-predict distortions
such as frequency shifts or frequency modulation. Such
distortions can be limited or eliminated by carefully deciding
how to interpolate the phase values of the upmix parameters.
Another embodiment according to the invention creates a method
for upmixing a downmix audio signal.
Yet another embodiment according to the invention creates a
computer program for upmixing a downmix audio signal.
Brief Description of the Figures
Embodiments according to the invention will subsequently be
described taking reference to the enclosed figures, in which:
Fig. 1 shows a block schematic diagram of an
apparatus for upmixing a downmix audio signal,
according to an embodiment of the invention;
Fig. 2a and 2b show a block schematic diagram of an apparatus
for upmixing a downmix audio signal, according
to another embodiment of the invention;
Fig. 3 shows a schematic representation of a timing
relationship between samples of the downmix
audio signal and a decoder input side
information;
Fig. 4 shows a schematic representation of a timing
relationship between the decoder input side
information and temporally interpolated upmix
parameters based thereon;
Fig. 5 shows a graphical representation of an
interpolation path;
Fig. 6 shows a flow chart of a method for upmixing a
downmix audio signal, according to an
embodiment of the invention; and
Fig. 7 shows a block schematic diagram representing a
generic binaural cue coding scheme.
Detailed Description of the Embodiments
Embodiment according to Fig. 1
Fig. 1 shows a block schematic diagram of an apparatus 100 for
upmixing a downmix audio signal, according to an embodiment of
the invention. The apparatus 100 is configured to receive a
downmix audio signal 110 describing one or more downmix audio
channels, and to provide an upmixed audio signal 120
describing a plurality of upmixed audio channels. The
apparatus 100 comprises an upmixer 130 configured to apply
temporally variable upmixing parameters to upmix the downmix
audio signal 110 in order to obtain the upmixed audio signal
120. The apparatus 100 also comprises a parameter interpolator
140 configured to receive a sequence of complex-valued upmix
parameters, for example a first complex-valued upmix parameter
142 and a subsequent second complex-valued upmix parameter
144. The parameter interpolator 140 is configured to obtain
one or more temporally interpolated upmix parameters 150 to be
used by the upmixer 130 on the basis of the first (or initial)
complex-valued upmix parameter 142 and the second, subsequent
complex-valued upmix parameter 144. The parameter interpolator
140 is configured to separately interpolate between a
magnitude value of the first complex-valued upmix parameter
142 and a magnitude value of the second complex-valued upmix
parameter 144 (which magnitude value interpolation is
represented at reference numeral 160), and between a phase
value of the first complex-valued upmix parameter 142 and a
phase value of the second complex-valued upmix parameter 14 4
(which phase value interpolation is represented at reference
numeral 162). The parameter interpolator 140 is configured to
obtain the one or more temporally interpolated upmix
parameters 150 on the basis of the interpolated magnitude
values (also designated as amplitude values, or gain
values)(which is represented with reference numeral 160) and
on the basis of the interpolated phase values (also designated
as angle values)(which is shown at reference numeral 164).
In the following, some details regarding the functionality of
the apparatus 100 will be described. The downmix audio signal
110 may be input into the upmixer 130, for example in the form
of a sequence of sets of complex values representing the
downmix audio signal in the time-frequency domain (describing
overlapping or non-overlapping frequency bands or frequency
subbands at an update rate determined by the encoder not shown
here). The upmixer 130 is configured to linearly combine
multiple channels of the downmix audio signal 110 in
dependence on the temporally interpolated upmix parameters
150, or to linearly combine a channel of the downmix audio
signal 110 with an auxiliary signal (e.g. de-correlated
signal) (wherein the auxiliary signal may be derived from the
same audio channel of the downmix audio signal 110, from one
or more other audio channels of the downmix audio signal 110
or from a combination of audio channels of the downmix audio
signal 110) . Thus, the temporally interpolated upmix
parameters 150 may be used by the upmixer 130 to decide upon
the amplitude scaling and a phase rotation (or time delay)
used in the generation of the upmixed audio signal 120 (or a
channel thereof) on the basis of the downmix audio signal 110.
The parameter interpolator 140 is typically configured to
provide temporally interpolated upmix parameters 150 at an
update rate which is higher than the update rate of the side
information described by the upmix parameters 142, 144. For
this purpose, subsequent complex-valued upmix parameter are
obtained (e.g. received or computed) by the parameter
interpolator 140. A magnitude value and a phase value of the
complex-valued upmix parameters 142, 144 are separately (or
even independently) processed using a magnitude value
interpolation 160 and a phase value interpolation 162. Thus,
temporally interpolated magnitude values of the upmix
parameters and temporally interpolated phase values of the
upmix parameters are available separately, and may either be
fed separately to the upmixer 140, or may be fed to the
upmixer 130 in a combined form (combined - after separate
interpolation - into a complex-valued number). The separate
interpolation brings along the advantage that an amplitude of
the temporally interpolated upmix parameter typically
comprises a smooth and monotonic temporal evolution between
subsequent instances in time at which the updated side
information is received by the apparatus 100. Audible and
disturbing artifacts, such as an amplitude modulation of one
or more subbands, which are caused by other types of
interpolation, are avoided. Accordingly, the quality of the
updated audio signals 120 is superior to the quality of an
upmix signal which would be obtained using conventional types
of upmix parameter interpolation.
Embodiment according to Fig. 2
Further details regarding the structure and operation of an
apparatus for upmixing an audio signal will be described
taking reference to Figs. 2a and 2b. Figs. 2a and 2b show a
detailed block schematic diagram of an apparatus 200 for
upmixing a downmix audio signal, according to another
embodiment of the invention. The apparatus 200 can be
considered as a decoder for generating a multi-channel (e.g.
5.1) audio signal on the basis of a downmix audio signal and a
side information SI. The apparatus 200 implements the
functionalities which have been described with respect to the
apparatus 100. The apparatus 200 may, for example, serve to
decode a multi-channel audio signal encoded according to a so-
called "binaural cue coding", a so-called "parametric stereo",
or a so-called "MPEG Surround". Naturally, the apparatus 200
may similarly be used to upmix multi-channel audio signals
encoded according to other systems using spatial cues.
For simplicity, the apparatus 200 is described which performs
an upmix of a single channel downmix audio signal into a two-
channel signal. However, the concept described here can be
easily extended to cases in which the downmix audio signal
comprises more than one channel, and also to cases in which
the upmixed audio signal comprises more than two channels.
Input signals and input timing
The apparatus 200 is configured to receive the downmix audio
signal 210 and the side information 212. Further, the
apparatus 200 is configured to provide an upmixed audio signal
214 comprising, for example, multiple channels.
The downmix audio signal 210 may, for example, be a sum signal
generated by an encoder (e.g. by the BCC encoder 810 shown in
Fig. 7) . The downmix audio signal 210 may, for instance, be
represented in a time-frequency domain, for example in the
form of a complex-valued frequency decomposition. For
instance, audio contents of a plurality of frequency subbands
(which may be overlapping or non-overlapping) of the audio
signal may be represented by corresponding complex values. For
a given frequency band, the downmix audio signal may be
represented by a sequence of complex values describing the
audio content in the frequency subband under consideration for
subsequent (overlapping or non-overlapping) time intervals.
The subsequent complex values for subsequent time intervals
may be obtained, for example, using a filterbank (e.g. QMF
Filterbank) , a Fast Fourier Transform, or the like, in the
apparatus 100 (which may be part of a multi-channel audio
signal decoder), or in an additional device coupled to the
apparatus 100. However, the representation of the downmix
audio signal described here is typically not identical to the
representation of the downmix signal used for a transmission
of the downmix audio signal from a multi-channel audio signal
encoder to a multi-channel audio signal decoder, or to the
apparatus 100. Accordingly, the downmix audio signal 210 may
be represented by a stream of sets or vectors of complex
values.
In the following, it will be assumed that subsequent time
intervals of the downmix audio signal 210 are designated with
an integer-valued index k. It will also be assumed that the
apparatus 200 receives one set or vector of complex values per
interval k and per channel of the downmix audio signal 210.
Thus, one sample (set or vector of complex values) is received
for every audio sample update interval described by time index
k.
To facilitate the understanding, Fig. 3 shows a graphical
representation of a timing relationship between samples of the
downmix audio signal 210 ("x") and the corresponding decoder
side information 212 ("SI"). Audio samples ("AS") of the
downmixed audio signal 210 received by the apparatus 200 over
time are shown at reference numeral 310. As can be seen from
the graphical representation 310, a single audio sample AS is
associated with each audio sample update interval k, as
described above.
The apparatus 200 further receives a side information 212
describing the upmix parameters. For instance, the side
information 212 may describe one or more of the following
upmix parameters: inter-channel level difference (ILD), inter-
channel correlation (or coherence) (ICC) , inter-channel time
difference (ITD), and inter-channel phase difference (IPD).
Typically, the side information 212 comprises the ILD
parameters and at least one out of the parameters ICC, ITD,
IPD. However, in order to save bandwidth, the side information
212 is typically only transmitted towards, or received by, the
apparatus 200 once per multiple of the audio sample update
intervals k of the downmix audio signal 210 (or the
transmission of a single set of side information may be
temporally spread over a plurality of audio sample update
intervals k) . Thus, there is typically only one set of side
information parameters for a plurality of audio sample update
intervals k.
This timing relationship is shown in Fig. 3. For example, side
information is transmitted to (or received by) the apparatus
200 at the audio sample update intervals k=4, k=8, and k=16,
as can be seen at reference numeral 320. In contrast no side
information 212 is transmitted to (or received by) the
apparatus 200 between said audio sample update intervals.
As can be seen from Fig. 3, the update intervals of the side
information 212 may vary over time, as the encoder may for
example decide to provide a side information update only when
required (e.g. when the decoder recognizes that the side
information is changed by more than a predetermined value) .
For example, the side information received by the apparatus
200 for the audio sample update interval k=4 may be associated
with the audio sample update intervals k=3,4,5. Similarly, the
side information received by the apparatus 200 for the audio
sample update interval k=8 may be associated with the audio
sample update intervals k=6,7,8,9,10, and so on. However, a
different association is naturally possible, and the update
intervals for the side information may naturally also be
larger or smaller than shown in Fig. 3.
Output signals and output timing
However, the apparatus 200 serves to provide upmixed audio
signals in a complex-valued frequency composition. For
example, the apparatus 200 may be configured to provide the
upmixed audio signals 214 such that the upmixed audio signals
comprise the same audio sample update interval or audio signal
update rate as the downmix audio signal 210. In other words,
for each sample (or audio sample update interval k) of the
downmix audio signal 210, a sample of the upmixed audio signal
214 is generated.
Upmix
In the following, it will be described in detail how an update
of the upmix parameters, which are used for upmixing the
downmix audio signal, can be obtained for each audio sample
update interval k, even though the decoder input side
information is updated only in larger update intervals (as
shown in Fig. 3). In the following the processing for a single
subband will be described, but the concept can naturally be
extended to multiple subbands.
The apparatus 200 comprises, as a key component, an upmixer
which is configured to operate as a complex-valued linear
combiner. The upmixer 230 is configured to receive a sample
x(k) of the downmix audio signal 210 (e.g. representing a
certain frequency band) associated with the audio sample
update interval k. The signal x(k) is sometimes also
designated as "dry signal". Also, the upmixer is configured to
receive samples representing a decorrelated version of the
downmix audio signal.
Further, the apparatus 200 comprises a decorrelator (e.g. a
delayer or reverberator) 240, which is configured to receive
samples x(k) of the downmix audio signal and to provide, on
the basis thereof, samples q(k) of a de-correlated version of
the downmix audio signal (represented by x(k)). The de-
correlated version (samples q(k)) of the downmix audio signal
(samples x(k)) may be designated as "wet signal".
The upmixer 230 comprises, for example, a matrix-vector
multiplier 232 which is configured to perform a complex-valued
linear combination of the "dry signal" (x(k)) and the "wet
signal" (q(k)) to obtain a first upmixed channel signal
(represented by samples yi(k)) and a second upmixed channel
signal (represented by samples y2