SU1658178A1 - Interpolator - Google Patents

Abstract

This invention relates to analog computing. The purpose of the invention is to improve the accuracy by implementing the Hermite cubic interpolation polynomial. The interpolator contains seven sample-hold blocks and six integrators. 2 Il.

Description

The invention relates to analog computing and can be used in devices for processing discrete measurements.

The purpose of the invention is to improve accuracy.

FIG. 1 shows a diagram of the device; in fig. 2 - diagrams of voltages forming a pulse transient function.

The interpolator contains blocks 1-7 sampling-storage, integrator, input 14, output 15.

The interpolator works as follows.

Input 14 is supplied with a period T pulses, the amplitudes of which are proportional to the values of the interpolated function. In blocks 1-7, the storage samples are stored respectively in discrete values xi, xi, xi-2. xi-s interpolated signal. All sampling-storage units are controlled by pulses of a clock frequency (not shown). In block 1, the value of xi is remembered, and in blocks 2. 3 and 7, the inverted

the values of the signals arriving at their inputs. The time constants of the integrators 8, 9, and 10 are equal to the sampling step T. The output signals of blocks 1–7 of the sample-storage are integrated in pairs by the integrators 8–10, at the outputs of which the signals reconstructed by linear interpolation are formed

The algebraic sum of the signals arriving from the outputs of the first and second linear interpolators is integrated by integrator 11, covered by negative-chain sampling-storage unit 4; feedback.

The magnitudes of the transfer coefficients of the sample-storage block 4 have the following values (top to bottom): "41 0.5; “42 -0.5; "43 -1. The integral times of signal integration for each input of the integrator 11 are equal to the sampling step T.

The algebraic sum of the signals from the outputs of the second and third linear interpolators is integrated by integrator 12. covered by block 5

Yo

ate

00

00

sampling-storage by a negative feedback circuit.

The magnitudes of the transmission coefficients of the sample-storage block 5 have the following meanings: "51 0.5; Kb2-0.5; Kaz -1. The integration times of the signals over each input of the integrator 12 are equal to the sampling step T.

The algebraic sum of the signals from the outputs of the first and third interpolators, from the outputs of the integrators 11 and 12, are integrated by the integrator 13, covered by the block 6 by the negative feedback circuit, and the transmission coefficients of the iloc 6 have the following values: and the transmission coefficients over the inputs of the integrator 13 are calculated as follows: Ki3.i - 1 / T; Code Ki3; 4 3 / T;

Kl3; 3 Kl3; 5-1 / T.

At the output of each of the 4-6 sample-storage blocks, a step voltage is formed (with fine tuning of the transfer coefficients and no drift, the zero blocks have a step amplitude equal to zero), the amplitude of which is proportional to the integration error in the corresponding integrator, which due to various random factors ( The zero drift of the interat (interference) may not be equal to zero. An error signal is fed through a negative feedback circuit to the input of the corresponding integrator. with the integration error correction.

The principle of operation of the proposed Inverpol Tore is based on the use of Hermite interpolation polynomial:

L. (t. -: - ri) - h, 2 (r, / T) 3 - 3 (n / T f + 1 + + X | (1) t (n / 1) 3-2 (n / T ) + + (TiA) + xY-1 3 (r, / T f - 2 (n / T) 31

+ xil + 1, t (p / t / -O / t) 2,

where, xo-co-rises, the zone-none 1nni of the interpolated function and its first derivative in the interpolation node; T is the discretization step of the function and its first derivative b — Tit / T; t / T - is whole, c be from t / T; Tr t - ti.

Expressing the discrete values of the first loss; one function through the corresponding values of the interpolated function

Х | (1) - (хи1-хи) / 2т; XKI (I) - (xi + 2 - xi) / 2T,

and laying down T 1 for release 1 for I -2 for simplicity;

X O ol the remaining values of I,

we obtain the formula for the impulse transition function of the interpolator

,;

| - s + 1 p. 1 K (t) -

 | t3 - 2 t + 1.

- 3 + in -

3 t 4;

0 5

0

5 0 5

50

0

five

Ot 4

Blocks 1, 2 and 8 form the scheme of the first linear interpolator, and groups of blocks 2, 3, 9 and 3, 7, 10 form, respectively, the schemes of the second and third linear interpolator.

For the known interpolator, the error estimate for the parabolic interpolation of the harmonic signal is

D, T.

The interpolation error of the harmonic signal in the proposed device is calculated by the formula

-shys AE efficiency of the proposed device is characterized by the attitude

D. / Dz 0.44N

where N is the number of counters per one harmonic period.

For example, with N 10, the proposed device has a more than fourfold gain in accuracy compared to the known one.

Claims (1)

Claims of Invention An interpolator comprising a first sampling-storage unit whose input is an interpolator input, and an output connected to the first input of the first integrator, the second input of which is connected to the output of the second sampling-storage unit, and the output to the first input of the second integrator, the output of which is the output of the interpolator, the third sampling-storage unit, the output of which is connected to the pepper input of the third integrator, the output of which is connected to the input of the third knockout-storage unit, with the aim of increasing precision, which introduced the fourth, fifth, sixth and seventh sampling-storage units, the fourth, fifth and sixth integrators, while the output of the first integrator is connected to the input of the second sampling-storage location and to the first inputs of the third integrator and the fourth unit sampling-storage output The third integrator is connected to the second inputs of the fourth integrator and the fourth sampling-storage unit and the first inputs of the fifth and sixth sampling-storage units and the fifth integrator, the output of the second sampling-storage unit is connected to the second input of the third integrator, the output of the third sampling-storage unit with the first input of the sixth integrator, the second input of which is connected to the output of the seventh sampling-storage unit, the output of the sixth integrator is connected to the input of the seventh high output unit Borki-storage, the second inputs of the fifth block of the sample-storage, the fifth and second integrators, the outputs of the fourth and fifth blocks of the sample-storage are connected to the third inputs of the fourth and fifth integrators, respectively, the outputs of which are connected to the third inputs of the fourth and fifth respectively sampling-storage units, as well as with the third and fourth inputs of the second integrator, the output of which is connected to its fifth input through the sixth sampling-storage unit. well Fzg.1