Coded data generation or conversion – Analog to or from digital conversion – Digital to analog conversion
Reexamination Certificate
2001-06-13
2002-11-19
Tokar, Michael (Department: 2819)
Coded data generation or conversion
Analog to or from digital conversion
Digital to analog conversion
C341S138000, C341S152000
Reexamination Certificate
active
06483450
ABSTRACT:
BACKGROUND OF THE INVENTION
The invention relates to a method and a device for digital-to-analog conversion of a signal.
Apart from fast analog-to-digital converters, there is also a need for fast digital-to-analog converters for digital signal processing. Such devices or circuit arrangements for digital-to-analog conversion (called D/A conversion in the following) are used for digital signal processing in, for example, television, radio broadcasting or radio receiving technology, as D/A changers, D/A converters or D/A transformers for image signals and sound signals. In that case digital signals are, for processing, converted into analog signals.
The performance capability of digital signal processing has expanded through constantly increasing capacity of memory chips as well as increasing performance of processors at great speed. The performance capability of D/A converters with respect to resolution and bandwidth has increased substantially more slowly by comparison with components of that kind in digital signal processing. In particular, fast D/A converters are needed for direct digital frequency synthesis (abbreviated to DDS), since the performance of the fastest DDS modules currently available is limited by the D/A converter.
SUMMARY OF THE INVENTION
The invention therefore has the object of providing a method and a device for digital-to-analog conversion of a digital signal in which an improved performance capability may be possible with respect to bandwidth and resolution capability.
According to a first aspect of the invention there is provided a method of digital-to-analog conversion of a band-limited digital signal, in which the signal is transformed on the basis of orthogonal functions, wherein coefficients associated with the orthogonal functions and the signal are determined and these are subjected to digital-to-analog conversion and wherein the signal is transformed back in the analog region on the basis of the analog coefficients, which result therefrom, by means of orthogonal functions.
Such a method proceeds from the consideration that, instead of sequential digital-to-analog conversion of individual scanning values of a conventional D/A converter, a whole interval of the time function of the signal is processed. For that purpose, the signal time-limited to the interval is preferably described on the basis of orthogonal functions. The signal is preferably broken down into several intervals. Through limitation of the time function of the signal to the interval with subsequent transformation by means of orthogonal functions, the signal is fully determined in the digital region on the basis of digital coefficients of the orthogonal functions in equidistant or non-equidistant spacing and can be reconstructed from these coefficients. In other words, the digital signal is processed on the basis of orthogonal functions into an equation for its transform, which is then converted from digital to analog and transformed back in the original region, whereby the original function of the signal is determined in the analog region.
Expediently, the signal is limited in the time region to the interval and is represented within the interval by a sum of orthogonal functions with a presettable number of summands, wherein the coefficients, which are associated with the orthogonal functions, for the interval are determined and subjected to digital-to-analog conversion and wherein the signal is represented in the analog region by multiplication of the analog coefficients, which result therefrom, by orthogonal functions. The signal is preferably resolved into several intervals so that the signal can be represented over a large time range. In the case of band limitation of the signal, the scanning theorems are preferably followed. According to the scanning theorems, discrete values of the frequency function or time function suffice for complete description of the signal in the case of limitation of the time function or frequency function. The time function of the signal is preferably represented by development according to a complete system of orthogonal functions. The band-limited signal is fully described by a finite summation.
The achievable quality of the approximation results from the number of summands, which is discontinued in a real system after a finite number. In that case, the minimum value for the number N of the summands (also termed support points) results from the scanning theorems in the time region and frequency region for time-limited and band-limited signals. The number of summands N is preferably determined by the equation:
N
=
T
τ
(
1
)
wherein T=length of the interval in the time region and &tgr;=segment in the time region,
wherein
τ
=
1
2
B
(
Nyquist
criterion
)
(
2
)
wherein B=bandwidth.
The number of summands is in that case preferably selected so that a sufficient resolution is ensured. The systems of orthogonal functions in the digital region (transformation) and in the analog region (inverse transformation) are preferably selected to be the same. Alternatively, the systems of orthogonal functions (also termed basic functions) can also be different.
Expediently, the digital signals are transformed in such a manner that these are multiplied in the digital region by presettable orthogonal functions and the digital coefficients associated with these functions are ascertained. The digital signal is fully described in the digital region on the basis of this transformation. In the example of Walsh functions, the transformation (=determination of the inner product) is described in accordance with the following equations:
x
d
(
t
i
)
=
∑
j
N
a
j
d
·
g
j
d
(
t
)
=
∑
j
N
(
x
d
(
t
)
,
g
j
d
(
t
)
)
·
g
j
d
(
t
)
,
(
3
)
a
d
j
=&Sgr;x
d
(t
i
)·
wal
(
j
&PHgr;)·&tgr; (4)
wherein
Θ
=
t
T
and, for example, wherein g
j
d
(t)=wal (j,&thgr;)=Walsh functions, wherein x
d
(t)=time function of the digital signal, g
j
d
(t)=orthogonal functions in the digital region, a
j
d
=coefficients, in the digital region and N=number of summands (=number of parallel channels or branches or D/A converter).
The equation (3) is the definition of the inner product between x
d
(t
i
) and g
j
d
(t). For brevity, the symbolic term (x(t), g
j
(t)) is used in the following.
In a case where basic functions differ in the digital and the analog, the linking of the coefficients takes place by a linear transformation according to:
x
(
t
)
=
∑
j
N
a
j
d
·
g
j
d
(
t
)
=
∑
j
N
b
j
·
h
j
(
t
)
,
(
5
)
under the precondition that g
j
(t)≈h
j
(t), wherein x(t)=time function of the signal, g
j
d
(t)=orthogonal functions in the digital region, a
j
, b
j
=coefficients in the analog region, h
j
(t)=orthogonal functions in the analog region, a
j
d
=coefficients in the digital region and N=number of the summands.
For determination of the coefficients b
j
in equation (5), the scalar product (inner product) is formed.
∑
j
(
x
,
g
j
)
⏞
a
j
d
g
j
=
∑
j
(
x
,
h
j
)
⏞
b
j
h
j
|
h
i
formation
of
the
inner
product
(
6
)
∑
j
(
x
,
g
j
)
(
g
j
,
h
i
)
=
(
x
,
h
i
)
(
7
)
∑
j
a
j
(
g
j
,
h
i
)
=
b
i
(
8
)
In that case, the coefficients in the digital region are preferably ascertained on the basis of a transformation matrix with matrix elements (g
j
, h
i
)=m
j,i
according to:
(
…
…
b
i
…
)
=
(
…
…
…
…
…
…
…
…
…
…
…
…
…
…
…
(
g
j
,
h
i
)
)
(
…
…
a
j
…
)
(
9
)
In accordance with the respective prescriptions and criteria for the digital signal processing, trigonometric function
Boehm Konrad
Luy Johann-Friedrich
Mueller Thomas
Daimler-Chrysler AG
Davidson Davidson & Kappel LLC
Khai Nguyen
Tokar Michael
LandOfFree
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