# Method of rounding-off function codes

FIELD: physics.

SUBSTANCE: function codes are rounded-off to the nearest level and the obtained codes are stored. The optimality criterion code is calculated and stored. Starting with a certain initial number L of the function code, the direction of rounding-off this code is changed and the optimality criterion code is calculated. If the optimality criterion code falls, the changed value of the code is stored and a new value of the optimality criterion code is calculated and stored, otherwise the initial L-th function code and the initial optimality criterion code are stored, and calculation is moved on to the next number of the function code L+1, where it is checked whether the optimality criterion code falls in the same way as that when the L-th function code was changed. Further, the process is continued until the optimality criterion code does not fall in a sequence of n function codes, read from the code value in which the last fall in the optimality criterion code took place.

EFFECT: reduced absolute error in the amplitude of the reproduced sinusoidal signal.

The present invention relates to the field of measurement technology and can be used to accurately generate the voltage using a digital-to-analogue converters.

Known the rounding function codes (Ornatsky P.P. - Automatic measurement and instrumentation. - The textbook for high schools. - 4th ed. revised and enlarged extra - Kiev: high school. The head of the publishing house. 1980. - 560 S. - 30502.2402000000. str), which is the analogue of the proposed method. The method is that if the exact value of the function codes in a given point has more bits than necessary, such as m binary digits, rounding code is performed by discarding all binary digits, numbers greater than m. If the code only m binary digits, it means that in the code there are a total of 2^{m}:0, 1, 2...(2^{m}-1) at different levels. Thus, in this way the rounding feature code at a given point is on the negative, that is, nearest the bottom level, which is the true value of the function code.

Also the known method described in the above literature (str), in which the rounding excess, that is nearest the top level, which is the true value of the function code.

However, these methods rounding characterize the Xia methodological errors: in the first method, it is equal to the maximum plus the distance between the levels, in the second way - minus the distance between the levels.

In addition, the known method, which is the prototype (Ornatsky P.P. - Automatic measurement and instrumentation. - The textbook for high schools. - 4th ed. revised and enlarged extra - Kiev: high school. The head of the publishing house. 1980. - 560 S. - 30502.2402000000. str-224) rounding codes specified in n points of a function, namely, that the rounding in each of the n points is carried out to the nearest level, between which is the true value of the function code. In this case, the rounding error is in the range from-1/2 to +1/2 the distance between the levels. Further to generate functions with the help of digital to analog converters rounded values of the codes memorized.

Thus, in the prototype, there is no constant component of rounding error. In addition, rounding to the nearest level provides the best approximation of a function in the metric of the standard deviation, which is the smallest value of the sum of squared errors of rounding is taken over all points.

However, this method of rounding when the specified number of binary bits m and the number of increments n in the period of the function does not give the most accurate reproduction of the sinusoidal signal (the first harmonic), not to minimize the value of K-th harmonic in the spectrum of the generated signal, does not share the most accurate RMS value of the generated signal, etc. Let's call the optimality criterion receive the lowest value of the error of playback of the first harmonic, the lowest value For the harmonic and the lowest error values play the RMS value of the signal.

The task of the invention is to provide a method of rounding feature code that optimizes the chosen optimality criterion, i.e. when the specified number of binary bits m and the number of increments n on the period function minimizes the error of reproduction sinusoidal signal (the first harmonic), or minimizes the value To the harmonics in the spectrum of the reproduced signal, or reproduces with high accuracy the mean value of the generated signal.

This object is achieved in that in the known method, in which the rounding function codes specified in n discrete points, produce to the nearest level, and remember all the codes it receives, in addition, calculate and memorize the optimality criterion, and then, starting from some initial number of L discrete values of the function, change the direction of rounding code and compute the optimality criterion, if the optimality criterion is improved, then the rounded value and retain the appropriate code memorize and calculate and memorize the new value of Crete is theory of optimality, otherwise, remember the previous code value and the criterion of optimality, and make the transition to the next number of discrete values of the function L+1, which tested for improvement (deterioration) of the optimality criterion in the same way, and the process continues until, until you improve the optimality criterion in the sequence of n discrete points, counted from discrete values, in which last improved optimality criterion.

The method is as follows, if the optimality criterion is taken to minimize the uncertainty values play a sinusoidal signal codes which are specified in the n discrete points in his period. If the amplitude of the sinusoidal signal is equal to 2^{m}then you have the following set of codes:

N(i)={2^{m}*sin(2πi/n); i=t, 2, 3...n}

At the first stage produces a rounding to the nearest level n code sequence N(i), and the resulting codes to remember. Then calculate using the Fourier transform of the amplitude value of the first harmonic spectrum of a_{H}sequence N(i), and remember its value. Next, find the absolute error Δ_{H}between amplitudes of the first harmonic spectrum of A_{H}and the ideal sinusoidal signal 2^{m}and also remember it is:

Δ_{H}=2^{m
-AH.}

The absolute error Δ_{H}and the value of amplitude a_{H}characterize the sequence N(i), past the rounding function codes to the nearest level (initial state).

Next choose some function code in the sequence N(i), for example, when i=1, i.e., N(1). Change the direction of rounding code N(1) on the opposite N(1)_{1}. Then perform the Fourier transform of the new sequence N(i)_{1}determine the amplitude of the first harmonic And_{1}and then calculate the error Δ_{1}. If |Δ_{H}|>|Δ_{1}|, rounded code N(1)_{1}save, and save the value As_{1}. If |Δ_{1}|>|Δ_{H}|, code N(1) and a_{1}remember and use in the next step of rounding. In the following denote remember the settings after the j-loop rounding by N(j), Δ_{j}and a_{j}regardless of any changes to these parameters in comparison with the previous j-1 cycle rounding.

Next go to the next code function: N(2), change the direction of rounding, get code N(2)_{1}define And_{2}and Δ_{2}just as it was done to code N(1)_{1}. If |Δ_{1}|>|Δ_{2}|, code N(2)_{1}, Δ_{2}and a_{2}remember. If |Δ_{1}|<|Δ_{2}|, remember the code value N(2), Δ_{1}and a_{1}./p>

This process occurs for N(i) with sequential switching codes. If the following code N(j) (j<n), then again, define And_{j}and Δ_{j}just as in the previous cases. If |Δ_{j-1}|>|Δ_{j}|, rounded code N(j)_{1}and Δ_{j}and a_{j}remember. If |Δ_{j-1}|<|Δ_{j}|, remember code N(j), Δ_{j-1}and A_{j-1}and go to the next code function of the sequence N(i).

If the last time improving optimality criterion (in this case, the decrease of the modulus of the absolute error of the amplitude of the sinusoidal signal sequence codes N(i)) has occurred in the L-th (L<n) a sequence of function codes N(i), and in the next n points reduce the absolute error has not occurred, the process of rounding the ends.

Thus, after implementation of the proposed rounding off function codes according to the optimality criterion that minimizes the module error playback of the first harmonic sequence codes N(i), simulation shows that decreases one order of magnitude compared to the rounding code to the nearest level, the value of the absolute error when the number of binary bits m=(5...12) and the number of dots per period n=(20...100). Similar results were obtained for the suppression of the 2nd or 3rd harmonics in the spectrum of the sequence N(i). Even the best achiev Italy obtained by the criterion of optimality, associated with the exact generating the RMS value of the sinusoidal signal. Under the same conditions on m and n, the gain in accuracy is 50 times compared with the rounding code in the prototype.

The rounding function codes specified in n discrete points, which consists in rounding to the nearest level and memorizing the received codes, characterized in that compute and remember the code optimality criterion, and then, starting from some initial numbers L function code, change the direction of rounding this code and calculate code optimality criterion, if the code optimality criterion decreases, then the modified value code memorize and calculate and memorize the new code value of the optimality criterion, otherwise remember the original L-th function code and the source code of the optimality criterion, and make the transition to the next code number the function L+1, which checks to reduce code optimality criterion in the same way that when you change the L-th feature code, and the process continues until, until you reduce the code optimality criterion in the sequence of n code function, counted from the value of the code in which the last time there was a decrease of code optimality criterion.

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