Coded data generation or conversion – Analog to or from digital conversion – Analog to digital conversion
Reexamination Certificate
2001-02-22
2003-02-11
JeanPierre, Peggy (Department: 2819)
Coded data generation or conversion
Analog to or from digital conversion
Analog to digital conversion
C341S152000, C341S050000, C382S250000
Reexamination Certificate
active
06518908
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to a method and a device for analog-to-digital conversion of a signal.
RELATED TECHNOLOGY
Analog-to-digital conversion, referred to in the following as A/D conversion, devices or circuitry are used for digital signal processing, e.g., in television, radio or receiver technology, as so-called A/D converters for video and audio signals. In this context, analog signals are converted into digital signals for processing. U.S. Pat. No. 5,568,142, for example, purports to describe a method for analog-to-digital conversion of a band-limited signal, where, on the basis of filters, the signal is partitioned into various signals which, once digitized, are recombined by filters.
The constant rise in memory chip capacity and the increasing power of high-speed processors have resulted in improved performance of digital signal processing. With respect to resolution and bandwidth, the performance of A/D converters is improving at a substantially slower rate than that of comparable components used in digital signal processing. The performance of A/D converters is limited by a constant product of resolution and bandwidth (see R. H. Walden, “Performance Trends for ADC”, IEEE Communication Magazine, February 1999, pp. 96-101). Therefore, to enhance performance, in particular to achieve a highest possible bandwidth, a plurality of conventional A/D converters having time interleaved sampling instants is employed. The disadvantage here is that offset and gain errors resulting from the parallel configuration of the A/D converters cause jump discontinuities to occur at the sampling instants. These jump discontinuities are characterized by discrete disturbance lines, or lines of perturbation, in the useful signal spectrum.
SUMMARY OF THE INVENTION
An object of the present invention is, therefore, to provide a method and a device for the analog-to-digital conversion of an analog signal, which will render possible high performance with respect to bandwidth and resolution.
The present invention provides a method for the analog-to-digital conversion of a band-limited signal (x(t)), wherein the signal (x(t)) is transformed on the basis of orthogonal functions (g
j
(t)), coefficients (a
j
) corresponding to the orthogonal functions (g
j
(t)) and the signal x(t) being defined and digitized, and, on the basis of the digitized coefficients (a
j
d
), the signal (x
d
(t)) being inversely transformed in the digital domain by orthogonal functions (h
j
(t)).
In this context, instead of sequentially digitizing individual sampled values of a conventional A/D converter, the method according to the present invention processes one complete interval of the signal's time function. To this end, the signal that is time-limited to the interval is described on the basis of orthogonal functions. The signal is preferably decomposed into several intervals. By limiting the time function of the signal to the interval, with subsequent transformation with the assistance of orthogonal functions, the signal is substantially fully defined in the digital domain on the basis of discrete coefficients of the orthogonal functions in equidistant or non-equidistant spacing, and can be reconstructed from these coefficients. In other words: on the basis of orthogonal functions, the signal is processed into an equation for its transforms, which is then digitized and inversely transformed into the original domain, with the result that the original function of the signal is defined in the digital domain.
The signal is expediently limited in the time domain to the interval and, within the interval, represented by a sum of orthogonal functions having a predefinable number of summands, or addends, the coefficients corresponding to the orthogonal functions being defined for the interval and digitized, and, through inverse transformation of the digitized coefficients on the basis of orthogonal functions, the signal being represented in the digital domain. The signal is preferably decomposed into several intervals, enabling it to be represented over a large time domain. In band-limiting the signal, it is useful to consider the sampling, or Nyquist, theorems. According to the sampling theorems, when limiting the time or frequency function, discrete values of the frequency function or of the time function suffice for providing a complete description of the signal. The time function of the signal is preferably represented by the development of orthogonal functions in accordance with a complete system. This means that the band-limited signal is fully described by a finite summation. For example, the signal in the analog domain is represented on the basis of the generalized Fourier analysis:
x
(
t
)
=
∑
j
N
a
j
·
g
j
(
t
)
=
∑
j
N
(
x
(
t
)
,
g
j
(
t
)
)
·
g
j
(
t
)
,
(
1
)
a
j
=
(
x
(
t
)
,
g
j
(
t
)
)
=
∫
0
T
x
(
t
)
·
g
j
(
t
)
ⅆ
t
(
2
)
where x(t)=time function of the signal, g
j
(t)=orthogonal functions, a
j
=coefficients, N=number of summands=number of orthogonal functions=number of interpolation nodes in the transformed domain (frequency domain for the special case of the Fourier transform)=number of parallel channels, T=length of the interval in the time domain.
Equation (2) defines the so-called inner product between x(t) and g
j
(t). For the sake of brevity, the symbolic notation (x(t), g
j
(t)) is used in the following text. The closeness of the approximation is determined by the number of summands, which, in a real system, are truncated following a finite number. In this context, the minimal value for the number N of summands, also referred to as interpolation nodes, is derived from the sampling theorems in the time and frequency domain for time-limited and band-limited signals. The number of summands N is preferably determined by the equation:
N
=
T
τ
(
3
)
where T=the length of the interval in the time domain,
&tgr;=the segment in the time domain,
where
τ
=
1
2
B
(
Nyquist
criterion
)
(
4
)
and B=bandwidth.
In this context, the number of summands is preferably selected such that adequate resolution is assured. Preferably, one selects the same systems of orthogonal functions in the analog domain (transform) and in the digital domain (inverse transform). Alternatively, the systems of orthogonal functions, also referred to as basic functions, may also be different.
The digitized coefficients are expediently inversely transformed in such a way that, in the digital domain, the signal is described by multiplying the digitized coefficients by predefinable orthogonal functions, and through subsequent summation. In the case that the basic functions differ in the analog and in the digital domain, then the coefficients are combined by a linear transform, as expressed by:
x
(
t
)
=
∑
j
N
a
j
·
g
j
(
t
)
=
∑
j
N
b
j
d
·
h
j
(
t
)
,
(
5
)
provided that g
j
(t)≠h
j
(t),
respectively
x
(
t
)
=
∑
j
N
a
j
·
g
j
(
t
)
=
∑
j
N
a
j
d
·
h
j
(
t
)
,
(
6
)
provided that g
j
(t)=h
j
(t),
where x(t)=time function of the signal, g
j
(t)=orthogonal functions in the analog domain, a
j
=coefficients in the analog domain, h
j
(t)=orthogonal functions in the digital domain, a
j
d
, b
j
d
=coefficients in the digital domain, N=number of summands.
Depending on the requirements and criteria for the digital signal processing, trigonometric functions, Walsh functions, and/or complex exponential functions are used as orthogonal functions. In the analog domain, trigonometric functions, e.g., sine functions and/or cosine functions, are preferably used. In the digital domain, functions, such as Walsh or Haar functions, which can only assume the values +1 or −1, may be employed.
In an orthonormal system, it hold
Boehm Konrad
Luy Johann-Friedrich
Mueller Thomas
Daimler-Chrysler AG
Davidson Davidson & Kappel LLC
JeanPierre Peggy
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