Boots – shoes – and leggings
Patent
1986-09-04
1988-12-06
Harkcom, Gary V.
Boots, shoes, and leggings
364734, G06F 1536
Patent
active
047899530
DESCRIPTION:
BRIEF SUMMARY
FIELD OF THE INVENTION
The invention relates to a circuit arrangement for averaging in the case of a signal consisting of rectangular pulses, on the basis of a time and amplitude-discrete filter.
BACKGROUND ART
Time averaging of signals consisting of rectangular pulses can be effected, e.g., by integration over at least one period of the rectangular signal or by low-pass filtering. Integration can be carried out by means of an up-down counter. A drawback for a processor, however, is then the necessary division by the value of the period, which may be relatively time-consuming.
In the case of low-pass filtering, the definite integral is replaced by an indefinite integral over the range -.infin..ltoreq.t.ltoreq.+.infin.. Accordingly, the transient response of the filter has to be taken into account, as otherwise the results are not exact.
Digital low-pass filters represent periodic networks with alternating pass and stop bands. As a pulse-shaped signal may have spectral components over a very wide frequency range, very accurate tuning of the low pass filter response and clock frequency with respect to the signal is necessary. The essential drawback of the low-pass filter consists in the high stop-band attenuation that has to be implemented. Because of these problems, excessively sophisticated circuitry will have to be implemented in order to achieve acceptable results.
BROAD DESCRIPTION OF THE INVENTION
The object of the present invention is to develop a filter which can be implemented with lower effort than is required for conventional arrangements and which is characterized by a very large ratio of clock frequency to pass bandwith and which enables accurate averaging.
According to the invention, this object is reached by providing means for carrying out moving averaging over specific periods of time which are defined by the variable intervals between the successive pulse edges of the input signal, the amplitude of the pulse sequence being assumed to be constant, and by the fact that the arithmetic mean can then be determined from a specific number of the preceding results of moving averaging. According to the invention, arithmetic averaging is carried out over one cycle duration or over a multiple of the cycle duration. Preferred embodiments for the implementation of moving averaging according to the circuitry and for the subsequent determination of the arithmetic mean are described in subclaims 3 to 5.
The proposed filter according to the invention can be described in its simplest manner by the relation: output value at time t.sub.n, Y.sub.n-1 is the output value at the preceding time t.sub.n-1, and .alpha. is a factor which determines the transient response of the filter.
In the case of a signal consisting of rectangular pulses, it is assumed that the input function assumes only specific values, e.g. X.sub.+ =+1 and X.sub.- =-1 (see FIG. 1). If the input value is X=X.sub.+ at time t.sub.o, we obtain after n steps at time t.sub.n for Y.sub.n ##EQU1## where Y.sub.o is the initial value of Y at time t.sub.o.
This formula can be derived as follows: ##EQU2##
The term ##EQU3## can be mathematically simplified as follows ##EQU4## This relation results from the summation equation for power series ##EQU5## by substitution of q=1-.alpha..
If the number of sample values is just n.sub.1 during the period of time when X assumes the value X.sub.+, Y.sub.n.sbsb.1 is reached after n.sub.1 values. Subsequently, a new cycle starts in which, accordingly, the amplitude value has to be set X=X.sub.-.
The number of sample values now is n=n.sub.2, the value of Y at the end of this cycle then is Y.sub.n.sbsb.2. In the next cycle X=X.sub.+ again. The number of sample values is n=n.sub.3, the value of Y at the end of this cycle is Y.sub.n.sbsb.3.
The relations for Y thus can be described by
Thus, calculation of the output values of the filter is necessary only at the end of each cycle within which X, i.e. the amplitude remains constant.
For an input signal with constant duty cycle, this can be represented as follows:
In th
REFERENCES:
patent: 4193118 (1980-03-01), Nash et al.
patent: 4606009 (1986-08-01), Wiesmann
Holzler, E. et al., Pulstechnik, vol. I, Grundlagen Springer-Verlag, (1982), pp. 277 to 280.
Battelle-Institut e.V.
Harkcom Gary V.
Mai Tan V.
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