Non-integral delay circuit

A time-discrete signal is delayed by a selectable fraction (.delta.) of a sampling period of the time-discrete signal. First (F1) and second (F2) differential signals having mutually different phase characteristics are derived from the time-discrete signal and are subsequently combined (MIX) dependent upon the selectable fraction (.delta.) to obtain a phase-adjusted correction signal. The product of the selectable fraction (.delta.) and the correction signal is added to the time-discrete signal to obtain a time-discrete signal which has been delayed by the selectable fraction (.delta.). The second differential signal is obtained by means of a differentiator with asymmetric coefficients in order to optimise the transfer characteristic for .delta.=0.5.

BACKGROUND OF THE INVENTION 
This invention relates to a method of and a device for obtaining a 
non-integral delay, i.e. a delay of a signal by a time interval equal to a 
fraction of a clock period. 
The non-prepublished European Patent Application no. 92.201.894.0, filed on 
Jun. 26, 1993, which corresponds to U.S. Pat. No. 5,349,548, and which 
together with the Applications corresponding thereto is herewith 
incorporated by reference, describes a Variable Phase Delay (VPD) FIR 
filter which can be used to shift a time-discrete signal in time. The 
phase delay can then be any arbitrary traction of a sampling period Ts. 
Such a variable delay is required, for example, to convert the signal to 
another sampling frequency Fs. The transfer function Fvpd of the VPD 
filter is: 
Fvpd=F0+.delta.*[.delta.*F1+(1-.delta.)*sign*F2], where: 
F0=low-pass-filtered (LPF) signal 
F1=Sn-F0=first differential signal 
Sn=nearest sample 
F2=second differential signal 
.delta.=shift relative to the centre of the sampling period, expressed with 
regard to 50% of a sampling period 
sign=sign of the shift relative to Sn 
FIGS. 1 and 2 show two embodiments, i.e. the VPD10 filter (with 10 delay 
sections Z.sup.-1) and the VPD04 filter (with 4delay sections), 
respectively, together with a resulting interpolation characteristic (gain 
G versus frequency in multiples of the sampling frequency Fs) for a delay 
by a .delta.=n/4 for n=-4..3 of a sampling period, which results in an 
interpolation yielding a signal sampled at 8*Fs. The timeshift .delta. is 
related to 50% of the sampling period because, starting from a minimum 
delay of half a sampling period, each delay can be realised by varying 
.delta. and, if necessary, adding a variable number of integer delay 
section. The shadow ranges in the interpolation characteristic are 
situated within bandwidths of 3/8*Fs around multiples of the sampling 
frequency Fs. The impulse response of the VPD10 filter, in the case of 
conversion to a substantially higher sampling frequency (small increment 
of delta), is shown in FIG. 3, together with the control signals 
sign(.delta.) and .delta.. 
If a VPD-filter is to be used for vertical interpolation of TV pictures 
(for example, in standard conversion for matrix display) the problem 
arises that a unit delay consists of a line memory which is substantially 
larger than the required adders and/or multipliers. This means that it is 
then preferable to opt for a short delay network (for example VPD04) and, 
if need be, to use more hardware for further processing. Moreover, a 
vertical prefilter would also require line memories so that it is 
preferred to have an interpolation filter having a "flatter" stop band 
and, consequently, slightly lower peaks around multiples of the transition 
band. Cf. around (N+0.5)*Fs in the characteristic shown in FIG. 2B. 
For use in conjunction with audio signals and composite video signals, a 
smaller ripple would be desirable throughout the characteristic, 
particularly in the pass band and at harmonics thereof (around N*Fs, where 
Fs is the sampling frequency). 
It is one of the objects of the invention to provide a non-integral delay 
circuit which meets at least some of the above-mentioned drawbacks and/or 
requirements. To this end, a first aspect of the invention provides a 
non-integral delay circuit as defined in Claim 1. A second aspect of the 
invention provides for a method as defined in Claim 7. Advantageous 
embodiments are defined in the dependent Claims.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The variable phase delay filter (VPD) described in the non-prepublished 
European Patent Application no. 92.201.894.0, filed on Jun. 26, 1993, 
which together with the Applications corresponding thereto is herewith 
incorporated by reference, exhibits an ideal behaviour for .delta.=0 and 
for .delta.=1 independently of the differentiated signal F2. 
Fvpd(.delta.=0)=F0 and Fvdp(.delta.=1)=Sn. F0 and Sn are "ideal" for they 
both exhibit a linear phase characteristic. Indeed, F0 is the result of 
filtering with symmetric coefficients and Sn is the non-filtered signal. 
Since F2 has no influence for .delta.=0 and .delta.=1, it is better to 
optimise F2 for another value of .delta.. For this, the transfer 
characteristics of the VPD filter in the case of ideal sub-filters are 
considered, as is shown in FIGS. 4A and 4B. An error reduction can be 
obtained if the characteristics are not only made zero for .delta.=0 and 
.delta.=1 but are also minimised for .delta.=0.5. This can be achieved by 
designing the differentiator D for supplying the second differential 
signal F2 for .delta.=0.5 rather than for .delta.=0. 
Step 1: This requires a differentiator with asymmetric instead of 
anti-symmetric coefficients. 
Since the phase error for a shift of -0.5 is opposed to the error for a 
shift of +0.5, the asymmetry should be reversed for negative shifts. 
Step 2: The sequence of the differentiator coefficients should be reversed 
with the sign of the shift .delta.. 
A block diagram for such a VPD10 filter in accordance with the invention is 
shown in FIG. 5, together with the impulse response of the differentiator 
D for a positive and a negative sign of the shift .delta.. 
Further improvement is possible by: 
Step 3: Adding additional differentiators with other control functions. For 
this the operation of the VPD filter is considered in the time domain with 
reference to FIG. 6. Columns 1..3 of FIG. 6 give the signals of the 
sampling periods n+4..n+6 of FIG. 3 together with the functions 
M1=.delta.*.delta. and M2=sign*.delta.*(1-.delta.) by which F1 and F2 are 
multiplied, respectively. The factor .delta.*(1-.delta.)is a periodic 
parabola which after multiplication by the sign bears a close resemblance 
to a sinewave having a frequency equal to the sampling frequency, which is 
eventually modulated with F2. Column 4 shows that a more elaborate 
modulation of the F2 factor M2=sign*.delta.*(1-.delta.) is possible if 
other coefficients are chosen when the sign changes. Since the F2 factor 
M2 is zero for .delta.=0 and .delta.=1, the response can be optimised for 
.delta.=0.5 and sign=.+-.1 with the aid of F2 without the result for 
.delta.=0 and .delta.=1 being influenced. Obviously, this is not essential 
but it facilitates the design. In order to improve the response for other 
values of .delta., a differentiator may be added whose result (F3) is 
multiplied by a function M3 which is non-zero for these other values of 
.delta.. It would be convenient if this function were zero for the values 
of the delay .delta. already discussed. It is possible, for example, to 
take the square of the absolute value of .delta.-0.5, which yields a 
parabola of twice the frequency with zero points for .delta.=N/2. However, 
it is simpler to start from the F2 factor and to multiply this factor by 
(.delta.-0.5). This F3 factor M3 and the result of modulation by this 
factor is indicated in column 5 of FIG. 6. 
A further improvement can be obtained by adding another differentiator (F4) 
whose result is multiplied by the absolute value of (.delta.-0.5), which 
is subsequently added to F2 and is then also multiplied by the F2 factor. 
Thus, the differential signal F4 is multiplied by 
M4=sign*.delta.*(1-.delta.)*abs(.delta.-0.5). Column 6 of FIG. 6 gives an 
example of the contribution of F4, and column 7 shows that with the 
combination of F3 and F4 the response can be selected independently for 
four additional shift values. 
Step 3b: Take the control functions (.delta.-0.5) and abs(.delta.-0.5), 
respectively, for the two following differentiators, and add the result to 
F2 for further processing in the mixer. 
FIG. 7 shows the resulting block diagram. This diagram shows only one 
differentiator having an output Fx. Each differentiator is of the same 
construction but has other coefficients C1..CB, where B is the number of 
taps of the delay network. The parts to be added or removed in order to 
change the length of the VPD filter in accordance with the invention are 
shown in broken lines. 
FIG. 8 shows that the result with the simple F3 and F4 factors is even 
better than with purely quadratic control functions. The error is zero for 
multiples of 1/8 of the sampling period Ts. To optimise the control 
functions, but also if only a few values of delta are used, it may be 
advantageous not to compute the control functions but to select them from 
a number of fixed values with the aid of a multiplexer or ROM. For 
example, if a VPD filter is used for 4*upsampling, only 4 values of delta 
are required: 0, .+-.1/2 and 1. Complete parametrisation and mixing of the 
functions is then reduced to some multiplexed adders. 
Step 4: For optimisation the control function can be implemented by 
selection from a number of fixed possibilities by means of a table (ROM) 
or multiplexer, with the shift as a parameter. 
Obviously, further improvement is possible with even more differentiators 
in conjunction with higher-order control functions, but the said functions 
F2..F4 with the associated control functions already prove to be adequate 
in order to provide reductions of the distortion of better than -60 dB. In 
principle, the sub-filters can also be given odd lengths with .delta. 
adjusted etc. However, this leads to less simple versions. 
Optimising differentiators for .delta.=0.5 etc., which requires multiplexed 
taps of the delay sections, and adding further differentiators with 
separate control signals are two separate steps, which may each provide 
improvement. This will be demonstrated by means of FIG. 9. 
The embodiments are based on the diagram shown in FIG. 7. Only the 
coefficients will be given with interpolation characteristics. In the 
lists of coefficients Fxcdiv (x=0..4) is the number by which the 
coefficients Fxc are to be divided. In the examples, Fxcdiv is a power of 
2 and the coefficients are given as integers. This means that the 
coefficients in the examples have been quantised, which renders the 
examples suitable for direct digital implementation. 
FIG. 9 shows the interpolation characteristics of a VPD04 filter in 
accordance with the invention (without multiplexer) for a delay .delta. of 
1/8. The coefficients of the low-pass filter LPF are F0cdiv=64, 
F0c=(37,-5). The coefficients of the differentiators are F2cdiv=64, 
F2c=(49,49,-8,-8), F3cdiv=32, F3c=(5,5,-3,-3). Comparison with FIG. 2 
shows a substantial improvement, particularly for harmonics of the 
transition band. In this VPD filter, only the function F3 has been added. 
Indeed, the coefficients of the differentiators are identical in pairs so 
that the multiplexer shown in FIG. 5 is not required. Nevertheless, the 
approximation to the desired response is very satisfactory, as will be 
apparent from FIG. 10 which shows the interpolation characteristic for 
obtaining an interpolated signal sampled at 32*Fs. 
FIG. 11 shows the interpolation characteristic for obtaining an 
interpolated signal sampled at 8*Fs, of a VPD filter in accordance with 
the invention with 12 delay sections and the following coefficients. The 
coefficients of the low-pass filter LPF are F0cdiv=256, F0c=(161, -48, 23, 
-11, 5, -2). The coefficients of the differentiators are F2cdiv=256, 
F2c=(180, 185, -25, -33, 8, 15, -5, -7, 3, 4, 0, -3), F3cdiv=128, F3c=(13, 
18, -3, -12, -1, 8, 1, -3, 0, 1, -1, 1). The coefficients of the 
sub-filters have been derived from an interpolation filter for obtaining 
an interpolated signal which is sampled of 8*Fs, designed with a Kaiser 
window with beta =4.5. The impulse response error is given in FIG. 12, in 
which the sync function waveform is the transfer characteristic of a 
Kaiser window with beta =4.5 and the waveform E represents an error 
magnified 100 times. The largest errors occur at .delta.=0, 1/4, 1/2 and 
1/4. These are errors purely caused by quantisation of the coefficients. 
Although the coefficients of F4 are zero the attenuation is still 
substantially 60 dB. If the filter would be used only for 4*upsampling, F3 
may also be dispensed with. The remainder, i.e. 11 delay sections and 17 
8-bit coefficients plus some adders for the mixers, is substantially less 
complex than the filter in the IC SAA7220 (upsampling filter for CD audio) 
and, moreover, the attenuation is almost 10 dB better. 
Summary: In order to improve the phase and frequency characteristics of the 
VPD filter the following steps are taken: 
1. The differentiator is modified to obtain non-linear phase 
characteristics. 
2. The sequence of the coefficients is reversed depending on the sign of 
the delay. 
3. If required, additional differentiators with other control functions are 
added. 
4. If desired, the control functions can be selected from a table. 
In essence, in a method of delaying a time-discrete signal by a selectable 
fraction (.delta.) of a sampling period of the time-discrete signal, first 
(F1) and second (F2) differential signals having mutually different phase 
characteristics are derived from the discrete signal and are subsequently 
combined (MIX) in dependence on the selectable fraction (.delta.) to 
obtain a phase-adjusted correction signal. The product of the selectable 
fraction (.delta.) and the correction signal is added to the time-discrete 
signal to obtain a time-discrete signal which has been delayed by the 
selectable fraction (.delta.). The second differential signal (F2) is 
obtained by means of a differentiator with asymmetric coefficients in 
order to optimise the transfer characteristic for .delta.=0.5. 
In general, the VPD filter can be used for interpolation, sampling 
frequency conversion and as a variable delay for time-discrete signals. 
Specific examples are: 
standard conversion for TV (aspect ratio conversion between 16/9 and 4/3 in 
plus, LCD and plasma displays); 
line-locked colour decoder operating on single crystal clock; 
ghost correction in TV; 
conversion of DVB audio (various audio standards in Digital Video 
Broadcast) to one sampling frequency. 
It is to be noted that the embodiments described above illustrate rather 
than limit the invention, and that those skilled in the art will be able 
to design many alternative embodiments, without departing from the scope 
of the appended Claims. For example, the time-discrete signal may either 
be amplitude-discrete, in which case it is a digital signal within the 
narrow meaning of that expression, or have a continuous amplitude.