Electricity: measuring and testing – Measuring – testing – or sensing electricity – per se – Frequency of cyclic current or voltage
Reexamination Certificate
1999-10-05
2001-05-15
Metjahic, Safet (Department: 2858)
Electricity: measuring and testing
Measuring, testing, or sensing electricity, per se
Frequency of cyclic current or voltage
C324S532000, C324S533000, C324S1540PB, C324S558000
Reexamination Certificate
active
06232762
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to the field of signal processing, and in particular to apparatus and method for determining the energy of a signal.
An ideal exponentially weighted root mean square (ERNS) detector for determining the energy of an analog signal s(u) is well known from the theory of electrical signal processing. The energy may be determined sequentially by executing three method steps: squaring the signal, integrating the squared signal, and extracting the root of the integrated signal. These method steps are also reflected in the following equation:
y
(
s
(
u
)
,
t
)
=
1
T
∫
-
∞
t
s
2
(
u
)
·
ⅇ
-
(
t
-
u
)
T
ⅆ
u
which describes the functional principle of the ideal analog detector. The detector determines the energy y of the signal s(u) as its RMS value, weighted exponentially with a time constant T, as a function of time t.
The conventional digital ERMS detectors receive a digital signal s
n
at their input in order to deliver a digital energy signal y
n
from the output, with the amplitude values of the energy signal representing the energy of the signal s
n
. They are based on method steps known from theory. To convert these method steps, as a rule as shown in
FIG. 4
a
, they are formed as a series circuit consisting of a squaring element
1
, a low-pass filter
2
, and a root extractor
3
.
FIG. 4
b
shows one possible digital implementation for such a series circuit. Accordingly, squaring element
1
is formed from a first multiplying element
410
that multiplies the digital signal s
n
by itself in order to provide the squared signal s
2
n and its output. The squared signal is then supplied as the input signal to the digital low-pass
2
weighted with a factor tau.
Within the low-pass
2
, the input signal is fed as a first summand to an adding element
420
which delivers at its output the desired energy signal but squared as y
2
n. As the second summand, the output signal y
2
n fed back through a state memory
430
weighted with the factor (1-tau) is supplied to adding element
420
.
Then the squared energy signal y
2
n is subjected by a root extractor
3
. The root extractor
3
comprises a second adding element
440
that receives the squared energy signal y
2
n and outputs the desired energy signal y
n
at its output. To calculate the energy signal y
n
, adding element
440
adds the squared energy signal to two additional signals. These are firstly the energy signal y
n−
1
fed back through a second state memory
450
from its own output and secondly a signal y
2
n−
1
that is obtained by squaring and negating from the fed-back energy signal y
n−
1
.
The conventional calculation of the energy signal y
n
shown here suffers from the following disadvantages:
By squaring the signal s
n
, its dynamic range is sharply increased. It is only possible to store the squared signal in a memory with a very large word width.
The square root routines used in conventional extraction of square roots converge slowly, often as a function of the magnitude of the amplitude of their input signal. They are therefore unsuitable for use in systems that require rapid convergence behavior of the detector, such as compander-expander systems for example.
SUMMARY OF THE INVENTION
An objective of the invention is to improve the methods and devices according to the species for determining the energy of a signal in such fashion that they exhibit faster convergence behavior and reduced computation cost, as well as less storage space.
According to a first embodiment of the method according to the invention, an energy signal y
n
is calculated whose amplitude values represent the energy of signal s
n
, according to the equation
y
n
=
(
tau
*
s
n
2
2
*
y
n
-
1
)
+
(
(
1
-
tau
2
)
*
y
n
-
1
)
(
1
)
with
tau: a specified parameter and
n: the clock pulse, whereby in Equation 1 the method steps of squaring, low-pass filtration, and root extraction are combined.
The parameter tau determines the time constant for the exponential weighting. It bears the following relationship approximately with the time constant T in the analog formula:
tau
=
&LeftBracketingBar;
(
0.5
)
*
(
1
-
ⅇ
(
i
T
*
fs
)
)
(
0.5
-
ⅇ
(
i
T
*
fs
)
)
&RightBracketingBar;
where:
i=sqrt(−1)
fs=sampling frequency of the digital system.
EXAMPLE
with fs=48 kHz and T=20 ms, tau is approximately 0.00104.
The explanations of the parameters tau and n likewise apply to all the following equations in the specification.
In the method performed according to Equation 1, the integrated method step of extracting the root exhibits a quadratic convergence behavior which has a very advantageous effect on the dynamic behavior of the entire process.
In addition, the method step of root extraction in the step of low-pass filtration is integrated, so that the calculation expense is reduced.
To work the method, it is no longer necessary to store the squared signal s
2
n with its large dynamic range; instead, it is sufficient to store the amplitude values found for the energy signal y
n
, which, because of the fact that the root has been extracted, exhibit a value range considerably reduced by comparison with the dynamic range of the squared signal s
2
n. For this reason, in the method according to the invention, a memory with a relatively small word width can be used.
According to one advantageous improvement on the method, the calculation of the first summand in Equation 1 includes the step “multiply signal s
n
by an auxiliary signal tau/2y
n−
1
to obtain a product signal” and “multiply the product signal by the signal s
n
” or alternatively the steps “square the signal s
n
” and “multiply the squared signal s
2
n by the auxiliary signal tau/2y
n−
1
”. Depending on the selected implementation of the method, one alternative or the other can contribute to reducing the computation and storage cost.
The advantages given for the first embodiment of the method according to the invention apply similarly to a corresponding device.
It is advantageous for the corresponding device according to the invention to have an inverter to receive the energy signal y
n
and to output an inverted signal b
n
=tau/2y
n
, designed so that it, by the equation
b
n
=
b
n
-
1
*
2
k
tau
*
(
(
(
1
+
k
)
*
tau
2
k
)
-
(
b
n
-
1
*
y
n
)
)
(
2
)
with
k: a constant preferably between 0.5 and 1, it provides the specified link between the inverted signal b
n
and the energy signal y
n
. The convergence behavior of the inverter can be influenced by the choice of the constant k; in this manner, the quadratic convergence behavior of the entire device can be optimized as well.
The explanation for the constant k likewise applies to all the following equations in the specification.
According to a second embodiment of the method according to the invention, the goal is achieved especially by virtue of the fact that the energy signal y
n
is calculated according to the equation
y
n
=
tau
*
s
n
2
2
*
y
n
-
1
+
(
(
1
-
tau
2
)
*
y
n
-
1
)
(
3
)
with the method steps of squaring, low-pass filtrating, and root extraction being combined in Equation 3.
In the method performed according to Equation 3, the method step of root extraction exhibits a quadratic convergence behavior, which has a highly advantageous effect on the dynamic behavior of the entire method.
In addition, the method step of low-pass filtration is integrated in the step of root extraction, so that calculation cost is reduced.
To work the method, it is no longer necessary to store the squared signal s
2
n with its wide dynamic range; instead, it is sufficient to store the currently determined value for the energy signal y
n
, which, because of the root extraction that has been performed, has a value range that is considerably reduced by comparison with the dynamic range of the squared signal s
2
n. For this reason, in the method according to the invention, a memory with a much reduced word width can be used.
The listed advantages of the sec
Hamdan Wasseem H.
Metjahic Safet
Micronas GmbH
Samuels , Gauthier & Stevens, LLP
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