Transmission system using time dependent filter banks

In source coding, use can be made of switching filter banks in order to adapt the filter bank to the properties of the signal to be coded. If it is not allowed that the switching introduces transient phenomena in the reconstructed signal, so-called boundary filters have to be used in the system according to the present invention, it is possible to dispose with the transition filters without introducing undesired transient phenomena. In order to obtain said property the new filter coefficients (after switching) have to be a linear combination of the original filter coefficients (before switching).

BACKGROUND OF THE INVENTION 
The invention is related to a transmission system with a transmitter 
comprising a time dependent analysis filter bank for deriving from at 
least one input signal at least two filtered signals, encoding means for 
deriving encoded signals from the filtered signals, and transmitting means 
for transmitting the encoded signals to a receiver via a transmission 
medium, said receiver comprising decoding means for deriving said filtered 
signals from the encoded signals and a time dependent synthesis filter 
bank for reconstructing said at least one input signal from the filtered 
signals. 
The invention is also related to a transmitter, a receiver a coder, a 
decoder and a method for coding and decoding. 
A transmission system according to the preamble is known from the 
conference paper "Exact Reconstruction Analysis/Synthesis Filter Banks 
with Time Varying Filters" by J. L. Arrowood Jr. and M. J. T. Smith as 
published in the conference proceedings of the 1993 IEEE International 
Conference on Acoustics, Speech, and Signal Processing, Volume III, 
Digital Speech Processing, pp. 233-236. 
Such transmission systems can be used for transmitting audio or video 
signals by means of a transmission medium like a radio channel, a coaxial 
cable or a glass fibre. It is also possible to use such transmission 
systems for recording of speech or video signals on a recording medium 
such as a magnetic tape or disc. Applications for such recording are 
automatic answering machined, digital video recorders or video servers for 
video on demand applications. 
Digital transmission or recording of audio and video data involves huge 
amounts of bits to be transmitted or to be stored. To reduce these amounts 
of bits, numerous types of coders have been developed. Some of said coders 
use an analysis filter bank which derives at least two filtered signals 
from an input signal. Each of said filtered signals is converted into an 
encoded signal using a coding method suitable for it. In general, the 
sampling rate of the filtered signals will be reduced before encoding in 
order to keep the total number of samples representing the input signal(s) 
constant. The reduced bandwidth of each of the filtered signals allows 
such sampling rate reduction. The coding of the output signals of the 
filter bank can comprise a quantisation step followed by a lossless coding 
step. 
The encoded signal is transmitted to a receiver which comprises decoding 
means which convert the encoded signals back into at least two signals. 
From these at least two signals a replica of the input signal of the 
transmitter is reconstructed by using a synthesis filter bank. 
This approach allows the coding method used for each of the filtered 
signals to be adapted to the properties of said signals. It has turned out 
that the use of this approach results in an improved ratio between coding 
quality versus bitrate for certain types of signals. 
In the system according to the above mentioned conference paper it is 
proposed to use time varying analysis and synthesis filter banks. The use 
of time varying filter banks has the advantage that the characteristics of 
the filter banks can be adapted to the input signal to be coded, resulting 
into further improved coding properties. By using time varying filter 
banks, transition phenomena can occur when the properties of the filter 
banks are changed in time. To reduce these transient phenomena, in the 
system according to the above mentioned conference paper so- called 
transition filters are used. These transition filters compensate for 
distortion of the signal to be encoded during the change from one bank of 
analysis filters to a different bank of filters. 
Due to the presence of transition filters the number of changes in the 
filter banks per unit of time is limited. This means that for input 
signals having fast changing properties, such like video signals, the 
filter banks can not be adapted fast enough to follow the changing 
properties of the signal to be encoded. 
SUMMARY OF THE INVENTION 
The object of the present invention is to provide a transmission system 
according to the preamble which can be adapted faster to the changing 
properties of the signal to be encoded. 
Therefore the transmission system is characterised in that the transmitter 
comprises transmit switching means for changing the filter coefficients of 
the time dependent analysis filter bank according to a first linear 
transformation, and in that the receiver comprises second switching means 
for changing the filter coefficients of the synthesis filter bank 
according to a second linear transformation being an inverse of the first 
linear transformation. 
By changing the coefficients of the analysis filter bank according to a 
first linear transformation and changing the coefficients of the synthesis 
filter bank according to a second linear transformation being an inverse 
of the first linear transformation, no transition filters are required at 
all. Due to the inverse relationship between the first and the second 
linear transformation it is ensured that the overall transfer function of 
the transmission system is not changed after switching. It is observed 
that it may occur that the second transformation is not completely an 
inverse of the first transformation, but that the second transformation 
acts as an inverse transformation for the relevant data it operates on. 
There exist linear transformations which are an inverse of each other only 
in a limited range of the data they operate on. If said data is limited to 
said range, the second transformation can be regarded as an inverse of the 
first transformation. 
A further embodiment of the invention is characterised in that the first 
switching means are arranged for instantaneously changing the filter 
coefficients of the time dependent analysis filter bank, and in that the 
second switching means arranged for instantaneously changing the impulse 
response of the synthesis filter bank. 
Using these measures it is possible to have a perfect reconstructing 
filterbank even around a switching instant. This property will be showed 
in the detailed description of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In the transmission system according to FIG. 1, a signal to be transmitted 
is applied to a transmitter 2. The input of the transmitter 2 is connected 
to an analysis filter bank 8 and to transmit switching means 16. An output 
of the filter determination circuit provides a switching signal to the 
analysis filter bank 8 and to a first input of a multiplexer 
A first output of the analysis filter bank 8 is connected to an input of a 
coder 10, and a second output of the filter bank 8 is connected to an 
input of a second coder 12. It is observed that the filterbank can have 
more than two outputs and that the transmitter comprises more than two 
coders. It is even possible that the number of outputs of the filter bank 
8 and the number of coders 10 . . . 12 varies in time. The coder 10 and 
the coder 12 constitute the coding means. 
The output of the first coder 10 is connected to a second input of the 
multiplexer 14, and the output of the second coder 12 is connected to a 
third input of the multiplexer 14. 
The output signal of the multiplexer is transmitted via the transmission 
medium 4 to a receiver 6. The input of the receiver 6 is connected to a 
demultiplexer 18. A first output of the demultiplexer 18 is connected to 
receive switching means 26. A second output of the demultiplexer 18 is 
connected to an input of a first decoder 20, and a third output of the 
demultiplexer 18 is connected to an input of a second decoder 22. The 
output of the first decoder is connected to a first input of a synthesis 
filter bank 24, and the output of the second decoder is connected to a 
second input of the synthesis filter bank 24. An output of the receive 
switching means 26 is connected to a switching input of the synthesis 
filter bank 24. At the output of the filter bank 24 the reconstructed 
signal is available. 
In the transmitter 2 the input signal is transformed by the analysis filter 
bank into a plurality N of sub-band signals. In general the sampling 
frequency of each of the sub-band signals is reduced by a factor N with 
respect to the sampling frequency of the input signal. The input signal of 
the analysis filter bank 8 can be represented by an infinite vector u=(. . 
. , u.sub.m-1,u.sub.m,u.sub.m+1, . . . ).sup.T, u.sub.i being subsequent 
samples of the input signal, and (. . . ).sup.T means the transposed 
vector. The output signals of the analysis filter bank 8 can be 
represented by an infinite vector y=(. . , y.sub.1,n-1,y.sub.2,n-1, . . , 
y.sub.N,n-1, . . , y.sub.1,n,y.sub.2,n, . . , y.sub.N, . . 
y.sub.1,n+1,y.sub.2,n+1, . . , y.sub.N,n+1, . . ).sup.T For the relation 
between u and y can be written y=A u, with A= 
##EQU1## 
In (1) h.sub.i,j is the j.sup.th sample of the impulse response of the 
i.sup.th filter in the filter bank 14, M is the length of the impulse 
response of the filters in the filter bank, and N is the number of filters 
in the filter bank. The operator A comprises blocks defining the actual 
filter coefficients, which blocks are repeated periodically. The 
subsequent blocks are shifted over a distance N in horizontal direction 
with respect to each other if the number of samples per unit of time 
representing the complete set of subband signals remains constant. In 
general the horizontal shift is equal to the decimation factor of the 
subband signals. In the above mentioned case the decimation factor of the 
subband signals is equal to the number of subbands. 
The output signals of the filter bank are reduced in sample rate and coded 
by the coders 10 . . . 12, in order to reduce the bit rate for 
transmission. The coders 10 . . . 12 are arranged for quantising the 
decimated output signals of the filter bank to obtain a first bit rate 
reduction. The quantised signal are encoded using a loss less coding 
scheme to obtain a further bit rate reduction. Such combination of 
quantising and loss less coding is disclosed in U.S. Pat. No. 4,901,075, 
which is incorporated by reference herein. 
The encoded signals, together with the output signal of the transmit 
switching means are multiplexed by the multiplex to a bit stream, and are 
transmitted to the receiver 6. In the receiver 6 the bit stream is 
demultiplexed, in order to obtain the coded signals and the switching 
signal. The decoded signals at the output of the demultiplexer 18 are 
decoded by the decoders 20 . . . 22. The output signals of the decoders 20 
. . . 22, are synthesized to an output signal under control of the 
switching signal at the output of the demultiplexer 18. The switching 
signal indicated the instants at which the synthesis filter bank 24 has to 
be switched. The switching signal can carry all new filter parameters, but 
it is more likely that the switching signal carries an index of a set from 
a plurality of sets of predetermined filter coefficients. 
The output signals of the decoders 20 . . . 22 are represented by the 
infinite vector y as defined above. It is observed that the output signals 
of the decoders 20 . . 22 will differ slightly from the output signals of 
the analysis filter 8 due to quantisation. This difference however is 
neglected in describing the system. 
The output signal of the synthesis filter bank 24 can be represented by an 
infinite vector z=(. . . , z.sub.k-1,z.sub.k,z.sub.k+1, . . . ).sup.T. 
z.sub.i constituting subsequent samples of the output signal of the 
synthesis filter bank 24. For z can be written z=Sy, with S being the 
synthesis matrix describing the synthesis filter bank 24. For S can be 
written: 
##EQU2## 
In (2) g.sub.i,j is the j.sup.th sample of the impulse response of the 
i.sup.th filter in the synthesis filter bank 24. 
For a perfect reconstructing system the operation of the synthesis 
filterbank 24 must be inverse to the operation of the analysis filter bank 
14. This can be expressed by S.multidot.A=I. 
According to the invention it is foreseen to alter the analysis filter bank 
8 and the synthesis filterbank 24 in time in dependence on the properties 
of the signals received. Consequently a criterion has to be available to 
judge whether a switch of the filter parameters is necessary. A 
possibility is to perform a complete analysis, coding, decoding and 
synthesis operation with a limited number of set of different filter bank 
parameters, and to select that set of filter bank parameters leading to 
the best coding performance for a particular part of the input signal. 
If the set of filter bank coefficients is changed, the operator A changes 
into: 
##EQU3## 
In (3) P is the number of analysis filter after the change of the filter 
bank, Q is the length of the impulse response of the filters after the 
change of the filter bank, and f.sub.i,j are the coefficients of the 
changed filter bank. The operator S changes into 
##EQU4## 
In (4) l.sub.i,j are the coefficients of the new synthesis filter bank. 
If the system during the switching operation still has to be perfect 
reconstructing, the filter coefficients f.sub.i,j and l.sub.i,j can not be 
chosen at will. According to the inventive concept the coefficients 
f.sub.i,j and l.sub.i,j have to be derived by a linear transformation from 
the coefficients h and g respectively. This linear transformation will be 
discussed below. The transformation is performed by selecting one or more 
blocks of rows from the A operator comprising h coefficients, and 
multiplying the "partial matrix" B obtained by an invertible 
transformation matrix T. The result of said transformation is a partial 
matrix C which contains one or more blocks of rows of the A matrix 
comprising f coefficients. 
The number of blocks to be selected from the A matrix for calculating the 
transform depends on the number of filters in the filter bank 14 before 
and after switching. The size of the partial matrix must be such that 
after transformation, it contains an integer number of blocks comprising f 
coefficients. This means that the number of rows of the partial matrix 
must be an integer number times the least common multiple (lcm) of N and 
P. 
A similar operation has to be performed on the synthesis matrix S. The 
transformation is performed by selecting one or more blocks of columns 
from the A operator S comprising g coefficients, and multiplying the 
"partial matrix" U obtained by the inverse of the transformation matrix T. 
The result of said transformation is a partial matrix V which contains one 
or more blocks of columns of the A matrix comprising l coefficients. 
In the following an example of such transformations is given. The 
transformation of a filterbank with two filters to a filter bank with four 
filters is considered. The A matrix of the example filter before switching 
is equal to: 
##EQU5## 
The S matrix corresponding to the example filter is equal to: 
##EQU6## 
If a switch has to be made from the filter bank with two filters (N=2) to 
a filter bank with four filters (P=4), the blocks to be selected from the 
operator A have to comprise lcm(2,4) =4 rows. In the same way is found 
that the blocks to be selected from the operator S comprises 4 columns. 
For the partial matrix B we have now 
##EQU7## 
Using a transform matrix T= 
##EQU8## 
in the transformation T.multidot.B results in a partial matrix C= 
##EQU9## 
Consequently for the operator A describing the switching operation can be 
written: 
##EQU10## 
For the partial matrix U can be written: 
##EQU11## 
With the inverse transform matrix T.sup.-1 = 
##EQU12## 
in the transformation U.multidot.T.sup.-1 for the partial matrix V is 
found: 
##EQU13## 
For the operator S describing the switching operation is finally found: 
##EQU14## 
If the operators S and A according to (10) and (14) respectively are 
multiplied, a matrix substantially equal to an infinite identity matrix is 
found. When actually calculating S.multidot.A, some deviation from the 
unity matrix may be found. This deviation is due to the limited accuracy 
of the representation of the filter coefficients. However this deviation 
can be reduced at will by increasing the accuracy of the representation of 
the filter coefficients. 
It is observed that the transformation matrices T and T.sup.-1 need not to 
be square. If the product of sample rate per filtered signal and the 
number of filters is not constant, it is possible to have non-square 
matrices T and T.sup.-1. 
In the FIR filter according to FIG. 2 an input is connected to an input of 
a delay element 40 and to an input of a multiplier 32. An output of the 
delay element 40 is connected to an input of a delay element 42 and to an 
input of a multiplier 34. An output of the delay element 42 is connected 
to an input of a delay element 44 and to an input of a multiplier 36. The 
output of the delay element 44 is connected to an input of a multiplier 
38. The outputs of the multipliers 32, 43, 36 and 38 are connected to a 
corresponding input of an adder 30. The output of the adder 30 constitutes 
the output of the filter. 
FIG. 2 shows an implementation of a switch of the analysis filter bank 
using FIR filters. It is assumed that the length of the impulse response 
remains the same for ease of explanation, but it is clear that the length 
of the impulse response may change at a switch of filter parameters. 
At the instant t=-1, the switch is not performed yet, and the coefficients 
of the i.sup.th filter are h.sub.i,0, h.sub.i,1,h.sub.i,2 and h.sub.i,3. 
The output sample y.sub.i,-1 is equal to 
EQU y.sub.i,-1 =h.sub.i,0 .multidot.u.sub.-1 +h.sub.i,1 .multidot.u.sub.-2 
+h.sub.i,2 .multidot.u.sub.-3 +h.sub.i,3 .multidot.u.sub.-4 (15) 
At instant t=0 the switch is performed, and all filter coefficients are 
simultaneously changed. The output signal y.sub.i,0 is consequently equal 
to: 
EQU y.sub.i,0 =f.sub.i,0 .multidot.u.sub.0 +f.sub.i,1 .multidot.u.sub.-1 
+f.sub.i,2 .multidot.u.sub.-2 +f.sub.i,3 .multidot.u.sub.-3 (16) 
At t=1 no change takes place in the filter coefficients any more. The 
output signal y.sub.i,1 is equal to: 
EQU y.sub.i,1 =f.sub.i,0 .multidot.u.sub.1 +f.sub.i,1 .multidot.u.sub.0 
+f.sub.i,2 .multidot.u.sub.-1 +f.sub.i,3 .multidot.u.sub.-2 (17) 
In the FIR filter according to FIG. 3 an input is connected to an input of 
a delay element 60 and to an input of a multiplier 52. An output of the 
delay element 60 is connected to an input of a delay element 62 and to an 
input of a multiplier 54. An output of the delay element 62 is connected 
to an input of a delay element 64 and to an input of a multiplier 56. The 
output of the delay element 64 is connected to an input of a multiplier 
58. The outputs of the multipliers 52, 54, 56 and 58 are connected to a 
corresponding input of an adder 50. The output of the adder 50 constitutes 
the output of the filter. 
FIG. 3 shows an implementation of a switch of the synthesis filter bank 
using FIR filters. Again it is assumed that the length of the impulse 
response remains the same. At t=-1 the switch is not performed yet, and 
the output signal z.sub.-i,-1 is equal to: 
EQU z.sub.i,-1 =g.sub.i,0 .multidot.y.sub.i,-1 +g.sub.i,1 .multidot.y.sub.i,-2 
+g.sub.i,2 .multidot.u.sub.1,-3 +g.sub.i,3 .multidot.u.sub.i,-4 (18) 
At the switching instant t=0, now not all filter coefficient values are 
modified, but only the first one. z.sub.0,i is not equal to: From (19) it 
can be seen that the coefficients of the filters in the synthesis filter 
bank are 
EQU z.sub.i,0 =l.sub.i,0 .multidot.y.sub.i,0 +g.sub.i,1 .multidot.y.sub.i,-1 
+g.sub.i,2 .multidot.y.sub.i,-2 +g.sub.i,3 .multidot.y.sub.i,-3 (19) 
changed piecemeal. For the output signals z.sub.i,1, z.sub.i,2 and 
z.sub.i,3 can now be written: 
EQU z.sub.i,1 =l.sub.i,0 .multidot.y.sub.i,1 +l.sub.i,1 .multidot.y.sub.i,0 
+g.sub.i,2 .multidot.y.sub.i,-1 +g.sub.i,3 .multidot.y.sub.i,-2 (20) 
EQU z.sub.i,2 =l.sub.i,0 .multidot.y.sub.i,2 +l.sub.i,1 .multidot.y.sub.i,1 
+l.sub.i,2 .multidot.y.sub.i,0 +g.sub.i,3 .multidot.y.sub.i,-1 (21) 
EQU z.sub.i,3 =l.sub.i,0 .multidot.y.sub.i,3 +l.sub.i,1 .multidot.y.sub.i,2 
+l.sub.i,2 .multidot.y.sub.i,0 +l.sub.i,3 .multidot.y.sub.i,1 (22) 
The switching operation according to (18)-(21) results in an instantaneous 
change of the impulse response of the filter without any transient 
phenomena. 
FIG. 4 shows the amplitude transfer function of the filter bank according 
to (5). It can be seen that the input signal is split up in two sub-band 
signals. 
FIG. 5 shows the amplitude transfer function of the four filters of the 
analysis filter bank according to the right block of (14). It can be seen 
now that the input signal is split up in four subband signals.