Fractional delay digital filter

Details Fractional delay digital filter Fractional delay digital filter

1999-12-06

2003-10-28

Corrielus, Jean B. (Department: 2631)

Pulse or digital communications

Systems using alternating or pulsating current

Antinoise or distortion

C375S296000, C375S349000, C375S350000, C708S300000

Reexamination Certificate

active

06639948

ABSTRACT:

This application claims priority under 35 U.S.C. §365(a) from International Application No. PCT/FR98/00615, filed Mar. 26, 1998, and published under PCT Article 21(2), on Oct. 8, 1998, in French, which is hereby incorporated by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention concerns digital signal processing devices which perform fractional delay operations in a linear processing context.
The theory of such devices is well known. Conventionally, and as shown in
FIG. 1
, these devices comprise on the input side a row of finite impulse response interpolation filters each of which performs a fractional delay operation specific to each input signal.
Each finite impulse response interpolation filter is an approximation of an ideal fractional delay filter. The coefficients of the finite impulse response interpolation filters are calculated using either conventional methods which minimize the mean square error or the Lagrange method.
The delayed signals are then each subjected to specific linear processing, after which they are added. There are also similar devices using an arrangement which is the opposite of that just mentioned. In this case, the same input signal is duplicated to provide a plurality of signals identical to it, which signals are then subject to specific linear processing and a specific fractional delay operation. Such devices are used in voice coders employing fractional pitch resolution, for example.
2. Description of Related Art
FIGS. 1
to
3
show a prior art digital device in which M input signals u
1
, u
2
, . . . , u
M
are delayed before they are subjected to linear processing by a filter T
1
through T
M
and added by an adder S. This type of device is used in conventional applications, for example antenna processing, in which case the delays are chosen as a function of the antenna pointing angle.
The required delay r
k
is rarely an integer multiple of the sampling period. The delay r
k
therefore comprises an integer number of sampling periods to which a non-zero fraction &tgr; of a period is added. Delays which are a multiple of the sampling period are not considered hereinafter because they are particularly simple to implement. The delays to be obtained are considered to consist of this additional fraction of a sampling period.
The device shown in
FIGS. 1
to
3
is fed with M input signals u
k
where k varies in the range from 1 to M. As shown in
FIG. 1
, each of the M input signals u
k
is delayed by a fractional delay r
k
specific to it.
A finite number of fractional delays r
k
is therefore required. A highest common factor r
o
of the fractional delays r
k
can be found. In practice an interpolation filter is implemented for each multiple of r
o
in the range from zero and the value of the sampling period T
e
. As shown in
FIG. 2
, D interpolation filters h
i
, denoted R
0
, R
1
, . . . , R
D−1
are obtained in this way, producing delays of value
i
D
×
T
e
,
where i varies in the range from 0 to (D−1).
Because the same number L of coefficients is chosen for each filter, D filters h
i
(n) are obtained, where i varies in the range from 0 to (D−1) and n varies in the range from 0 to (L−1).
As shown in
FIG. 3
, each input signal u
k
, where k varies in the range from 1 to M, is submitted to an interpolation filter h
&tgr;k
(n), denoted RF
k
, which is one of the D filters h
i
(n) denoted R
i
in
FIG. 2
, i being in the range from 0 to (D−1).
The equations and the criteria used to calculate the coefficients h
i(n)
of the D interpolations R
0
to R
D−1
will now be summarized.
Let &tgr;
k
denote the normalized fractional delay value, that is to say
τ
k
=
r
k
T
e
where r
k
is the required fractional delay for the signal and T
e
is the sampling period.
Let u
k
(n) be the input signal obtained by sampling an analog u
k
0
(t). Assuming that the sampling was done correctly, it is theoretically possible to obtain the delayed digital signal, defined as the samples of the analog signals delayed by u
k
(n), from u
k
0
(t−&tgr;
k
T
e
). The skilled person knows that from the signal u
k
(n), all samples of which are known, the corresponding analog signal u
k
0
(t) can be found using the interpolation equation
u
k
0
⁡
(
t
)
=
∑
m
=
-
∞
∞
⁢
u
k
⁡
(
m
)
⁢
sin
⁡
(
π
⁡
(
1
T
-
m
)
)
(
1
T
e
-
m
)
=
∑
m
=
-
∞
∞
⁢
u
k
⁡
(
m
)
⁢
sinc
⁡
(
1
T
e
-
m
)
in which case the delayed analog signal r
k
is
u
k
0
⁡
(
t
-
r
k
)
=
∑
m
=
-
∞
∞
⁢
u
k
⁡
(
m
)
⁢
sinc
⁡
(
t
-
r
k
T
e
-
m
)
=
∑
m
=
-
∞
∞
⁢
u
k
⁡
(
m
)
⁢
sinc
⁡
(
t
T
e
-
τ
k
-
m
)
The delayed digital signal u
k
ret
(n) is then obtained from:
u
k
ret
(
n
)=
u
k
0
(
nT
e
−r
k
)
that is:
u
k
rct
⁡
(
n
)
=
∑
m
=
-
∞
∞
⁢
u
k
⁡
(
m
)
⁢
sinc
⁡
(
n
-
τ
k
-
m
)
=
h
ideal
,
τ
⁢
 
⁢
k
⁡
(
n
)
*
u
k
⁡
(
n
)
where the symbol * symbolizes the convolution operation and where h
ideal,&tgr;k
(n)=sinc (n−
&tgr;k
).
The transfer function in the frequency domain of the filter h
ideal,&tgr;k
is
h
ideal
,
τ
⁢
 
⁢
k
⁢
(
f
)
=
ⅇ
-
j
⁢
 
⁢
2
⁢
π
⁢
 
⁢
f
f
e
⁢
τ
k
.
In theory, there is therefore an ideal filter h
ideal,&tgr;k
enabling the delayed sampled signal to be obtained from the sampled signal u
k
.
A filter of this kind cannot be implemented in practice because:
the summation is infinite, and
the filter is non-causal, i.e. it would be necessary to know the future samples to calculate the result.
The non-causal aspect means that it is only possible to approximate a version having an additional constant delay &tgr;
0
denoted h
ideal,&tgr;+&tgr;0
(n).
In practice, and as shown in
FIG. 3
, a known process is used to obtain a filter h
&tgr;
, having a finite number L of coefficients and constituting a good approximation of the filter h
ideal,&tgr;+&tgr;0
.
Finite impulse response filters are used in the most widespread applications. It is more difficult to design infinite impulse response filters and they require greater computation accuracy because the data is looped and computation errors can accumulate. Moreover, in a non-static environment, such as antenna processing, the long memory of the filters can be a problem: for example, it is difficult to change the pointing direction of an antenna suddenly.
All-pass filters, a subset of infinite impulse response filters, have the beneficial property of a constant modulus. The absence of amplitude error is unfortunately accompanied by an increased phase error compared to finite impulse response filters of the same complexity. To avoid these problems only finite impulse response filters are used.
Various methods are available for calculating the coefficients h
&tgr;
(n) of a finite impulse response filter h
&tgr;
approximating h
ideal,&tgr;+&tgr;0
.
When a finite number L of coefficients of the FIR filter has been chosen, a first method entails choosing a set of coefficients h
&tgr;
(n) with n varying in the range from 0 to (L−1) which minimizes the mean square error ∫|E
&tgr;
(f)|
2
df, where
E
τ
⁢
(
f
)
=
∑
n
=
0
L
-
1
⁢
h
τ
⁢
(
n
)
⁢
ⅇ
-
j
⁢
 
⁢
2
⁢
π
⁢
 
⁢
f
f
e
⁢
τ
-
H
ideal
,
τ
+
τ
0
⁢
(
f
)
f
e
being the sampling frequency and the integration being formed over a wanted frequency band.
E
&tgr;
(f) is often used to define cost functions used to assess the quality of a filter. This method is referred to as method M1. Its result is a truncated and delayed version of the ideal filter h
M1,&tgr;
(n)=sinc(n−&tgr;
0
−&tgr;).
A second method entails first calculating the coefficients h
&tgr;
(n) using the previous method and then multiplying them by an apodization window w(n). This method is referred to as method M2. Its effect is to smooth the frequency response of the filter.
If h
M1,&tgr;
(n) are t

Affiliated with

Also associated with

Rating

Fractional delay digital filter does not yet have a rating. At this time, there are no reviews or comments for this patent.

If you have personal experience with Fractional delay digital filter, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fractional delay digital filter will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFUS-PAI-O-3143384