SU432546A1 - DEVICE FOR INTERPOLATION FUNCTIONS - Google Patents

Description

one

The device for the interpretation of functions belongs to the field of automata and computational ones. It can find a location for the internation of arbitrary functions specified in the nodes by the values of ordinates and the values of the derivatives of the functionalized function. The interpolation results are presented in analog form.

There is a famous digital-analogue itori torus that implements a linear imitation of the functions given by a discrete set of the ordinates b {and the first derivative of a, in the nodes of the interpolation.

Oii contains a digital-to-analog polynom block calculator, the first input of which is connected to the device's therv.m input, three digital-to-analog converters, the output of the first of which is connected via a scale resistor to the device output and the first digital-to-digital output. tax unit for calculating polynomials; The first input is connected to the second input of the device, and the second is connected to the second output of the digital-analog unit, the first input of the third digital-to-analog converter and through the delay unit to the first input of the second digital-analog converter, the second input which is connected to the third meter input device.

A significant disadvantage of this interpolator is the complexity of the constructions; is low

fidelity and; 1 sterilizable fu, nktsii, which is associated with the use of the method of linearization and termination.

For the purpose of termination of the device, the output of the second and; a phy-piao convertible transducer connection: ph: 1 with the second input of the digital-analog block, the second output — with the output of the third digital-analog audio socket.1 and the third input of the n-analog analog block and output — with the second input of the third digital -An awesome ireob: ralovatsl.

The drawing shows a block diagram of a device proposed for interpolation of functions, consisting of, -: 1 semi-analog block / calculating a polynomial of the form / (a). Ah- + Bx. qi (pp () - analogue conversions 2 - f, delay unit 5 and scale resistor 5. The numbers 7, 8, 9, 10 denote respectively: the input code of the node functions, the input code of the values of the wrist interpolation function at the nodes of interpolation, code input: Identify the argument Lee for the device that produces the result of interiolation; in the form of an analogue 10, eg / csn 1. Numbers 1} and 12 obosiachsng-: inputs and tones, respectively, and 1. proportional to the coefficients .4 and B iteriol cnomngo polyHOiia.

C fro-a; alo; -a bls

pre-lasiachia

for poimea tech; the whole value of the argument given by the sequence of pulses of the unitary code that goes to the input I for calculating polynomials of the form f (x) Ax + Bx, taking into account the coefficients A and B, which enter its inputs // and 12 in the form of (PIP, as well as for generating the cipher of the end of the next interpolation interval and transmitting this signal to the input terminal of the digital-analog converter 4 and the input of the delay unit 5.

The input // of the coefficient L is connected with the inverse output of the digital-analog converter 4 and the output of the digital-analog converter 3. The input 12 of the coefficient B St for the digital output of the digital-analog converter 3. The output 10 of the block / is connected via a scale resistor 6s OTOM of a diff-ro-analog converter 2 and an output W of the device. The output signal of the end of the next interpolation interval is associated with the setup inputs of the digital-to-analog converters 4 and 2 and through the delay block 5 - with the installation input of the digital-analog converter 3. The digital input of the block / is connected to the input 9.

The digital-to-analog converter 2 is designed to receive the code of the next node {; howl ordinates of the interchangeable function and convert it to a voltage proportional to Coefficient C.

Input of digital-to-analog converter 2 connect to input 7.

A digital-to-analog converter is designed to receive the code of the next node value of the first derivative of the interpolation function converting this code into proportional ground and inverse voltages to analog outputs, as well as to transfer this code to digital-analog converter 4 at the moments of pulse arrival from the output delay block 5.

The digital-to-analog converter is connected to input 8 of the device, and the digital output is connected to the corresponding input of digital-to-analog converter 4.

The digital-to-analog converter 4 is designed to receive a code from the output of the digital-to-analog converter 3, and convert it to voltage.

The delay unit 5 is designed to delay the signal of the end of the next interpolation interval by the time determined by the transition processes in the digital-analog converter 4 when the latter is set to the zero state.

The internal resistances of digital-to-analog converters 2-4 and block 1 are taken equal to each other.

The device works as follows:; m way.

In the initial state, in the subtracting counter of the digital-analog block / the maximum number / U is set, „2 - 1, and in the registers of digital-analog converters 2, 3

and 4, respectively, the code of the 1st order of the interpolated function and the codes of the derivatives of yi and yi-iIn idle mode (when the output outputs of digital-to-analog converters 2-4 are disconnected), the voltage Ui is present on the output of digital-analogue converter 2 the outputs of digital-to-analog converter 3 are voltage Ul, and

at the inverse output of the digital-to-analog converter 4 is the inverse voltage (-i-i) corresponding to the codes indicated above.

In operating mode, the effect of the indicated voltages at the input of the // unit / is voltage:

,, fy., --- 2

input 12 is the voltage

and at the output 10 of the device (with) the value of the scale resistor 6 we have;

U: -.

and.

iN, n

four

: As the counter of the digital-to-analog block 1 is filled with pulses of the current value of the argument, the number in it (Lm, - .x) decreases and finally, when N, n becomes slave zero. In this case, the voltage at the output 10 varies in a stepwise parabolic manner to a magnitude:

// // one

L BLIXIO

where D Uvyhl is the block quantization level. With the arrival at input 9 of the next pulse of the current value of the argument, the considered interpolation interval ends. The end of interval signal, which is generated in this case in block 1, sets up the digital-to-analog converters 2 and 4, and after some time, determined by the block parameters for; 1, buckle 5, sets the digital-to-analog converter 3. Derivative code ui of the function to be interpolated

this time is transmitted to the register of the digital-to-analog converter 3. Then the codes of the next () -th node ordinate and the derivative r, // -., are fed to the device inputs 7 and 8.

At the end of the transient processes and as soon as the next pulses of the current value of the argument are considered, the device under consideration interpolates at an interval limited by the / -and (-1) -th nodal ordinates. The interpolation result for the t-ro inter face can be analytically determined by the formula: 4 - ((.) (4 IL 2-2 .-) -i-U,. Thus, the proposed device interpolates arbitrary functions defined by nodal codes. the ordinates and the values of the first derivative in the interpolation nodes. At the same time, it is simpler than the known devices of this type and has twice the utilization factor for the first time. Object of the Invention A device for interpolating functions containing a digital-analog block whose first input with the first input three digital-to-analog converters, the output of the first of which is connected via a scale resistor to the device output and the first output of the digital-analog polynomial calculator; the first input of the first digital-analog converter is connected to the second input of the device, and its second input is connected to the second output digital-analog block, the first input of the third digital-analog converter and through the delay unit - with the first input of the second digital-analog converter, the second input of which is connected to the third input devices, characterized in that, in order to simplify the device, the first output of the second digital-to-analog converter is connected to the second input of the digital-analog block, the second output to the third digital-to-analog converter and the third input of the digital-analog block and the third output the second input of the third digital-to-analog converter.