SU1328828A1 - Device for solving equations in operative form - Google Patents

Abstract

The invention relates to computing and can be applied in the field of instrumentation. The aim of the invention is to improve the accuracy of the solution. The goal is achieved by introducing into the device functional converters and normalization units of the spectral characteristic of noise. The device provides steady, signal recovery at any is. seeming operator and any noise with a known correlation operator. 1 il. E x 30

Description

one

The invention relates to analog computing, in particular, machine-based signal processing, and can be applied to restore the shape of an electrical signal, and is encoded by a linear transformation with a known transfer function and an impaired noise with a known spectral distribution.

The purpose of the invention is to improve the accuracy of solving the equation in an operator form.

The drawing shows a device for solving equations in an operator form.

The device contains the first node 1 of the normalization of the spectral characteristics of noise, summatr 2, the inverter 3, the scaling unit 4, the second node 5 of the normalization of the spectral characteristics of noise, the second functional transducer 6, the third functional transducer 7, the first function

national converter 8, the third node 9 of the normalization of the spectral characteristics of noise. The node for normalizing the spectral characteristic of the noise contains a differential amplifier 10, a low-pass filter 11, and a square root extractor 12.

The device works as follows. .

The signal from the device input passes through node 1 normalized: neither the spectral characteristic of the noise and the post. It goes to the first input of the adder 2. From the last output, the signal enters block 4 and then passes through block A, node 5, functional converters 6 and 8, node 9 and inverter 3. From the output of inverter 3, the signal goes to the second input of adder 2. From output 6, the signal passes through the converter 7 and is fed to the output of the device.

In the node the normalization of the spectral characteristics of the noise signal enters

35

The first functional converter implements the transfer function h (p) of operator A. The second functional converter implements the transfer function of operator h (p) associated with operator A (the same as that of operator A, but replacing the argument with a complex conjugate value). The third functional converter realizes the transfer function 40 (2) of the operator U, which correlates the output waveform. If operators A and U are integral, then the first and third functional transducers are implemented with inertial amplifiers, and the second functional transducer as inertial amplifiers with an impedance inverter.

As an example of the operator A

45

On the non-inverting input differential-5o, you can bring the integrator RC-chain. Such a chain has a transmitted amplifier 10. From the output of the latter, the signal passes through blocks 11 and 12 and is fed to the inverting input of amplifier 10. From the output of block 12, the signal goes to the output of the node that normalizes the spectral characteristic of the noise.

The scaling unit changes the signal's amplitude with a ratio of

exact function hCp)

one

КС „+ I

Re55

the datch function of the conjugate operator hCp) -

1 - RC,

performed

R

in the form of an impedance inverter with a resistor R on the input and a capacitor C on

portionality

Options

Formula y (t)

Determines the amount of noise in the resulting signal and the magnitude of the reconstruction error (s). The magnitude of noise and restraint is related to conservation law. For a given maximum permissible noise level, one can calculate the variance of the coefficient and the value of the coefficient k. Likewise, the noise level and the corresponding U value are calculated for a given constraint.

The noise spectral response node transforms the signal so that the random component has the character of white noise (i.e., the noise spectrum becomes uniform). At. whitening the signal is converted by

 / h x (t)

Formula y (t)

where - the noise correlation operator / integral operator having the transfer function (L (p), the core of which is the correlation function of the random process (t).

The first functional converter implements the transfer function h (p) of operator A. The second functional converter implements the transfer function of operator h (p) associated with operator A (the same as that of operator A, but replacing the argument with a complex conjugate value). The third functional converter implements the transfer function 2 (p) of the operator U, which correlates the output waveform. If operators A and U are integral, then the first and third functional transducers are in the form of inertial amplifiers, and the second functional transducer in the form of an inertial amplifier with an impedance inverter.

As an example of the operator A

exact function hCp)

one

КС „+ I

Re

conjugated opera

RC,

performed

R

in the form of an impedance inverter with a resistor R at the input and a capacitor C at

output In this case, the integrator RC circuit with a smaller time constant is chosen as the operator U in this case.

The proposed device synthesizes the signal

4 (t) R (a)) f (t),

: where R (W)

U () I) synthesized operator;

| S (t) Af (t) +) (t) - output signal

distorted by operator A and hit by noise (t); f (t) is an undistorted signal; H (t) - output signal

devices; S - correlating noise operator; And - the operator, sopr - female A;

and - operator, control of the output signal form.

The value of t) is calculated from the equation

tg R (W) 2 R (w)

p1 is assumed to be zero if the left side of the equation is always smaller. Here, is the predetermined boundary value of the noise energy. In this case, R is the solution of the variational problem

HRA - and I

EliR g.

New g (synthesis error) is equal to

45

gHIR (Qg) A - and 11 (wpA - and .. ..

Thus, the uncertainty is minimal with a given limit on noise. The device is thus synthesized (the signal is restored) as accurately as possible.

To clarify the form of the output signal generated by the proposed device, suppose that the signal in front of the scaling link is 4 (t). Then the second term of the summed signal is

 "

(t) --1

AA

 f (t),

and since the first term has

, -, Sh ..

the form of this device solves the equation {

) Sr 4 (t) + H- (t) His solution can be written in the form

4 (t) (I - Я) 5I f (t)

.and the output signal looks like 1 „. .

Y (t)

- (t)

 and (+ and 1)

S § (t)

 R | (t),

20

.

45

thirty

35

40

,

as noted.

The proposed device provides a synthesis of;; ignition, which is closest to the recoverable under a given restriction on the noise level and for a given type of possible distortion. The synthesis problem and the noise level are bound by the law of conservation. The device provides stable signal recovery at any distorting operator A and at any noise with a known correlation operator.

Claims (1)

Claims. A device for solving equations ib of operator form, containing an adder, a scaling unit, a first functional converter and an inverter, the output of the adder being connected to the input of the scaling unit, the output of the inverter connected to the first input of the adder, with the aim of increasing the accuracy The second and third functional transducers and three nodes for the normalization of the spectral noise characteristic are introduced, each of which contains a differential amplifier, a low-pass filter and a quad extraction unit. A differential root, the output of the differential amplifier through a chain of series-connected low-pass filters and a square root extraction unit is connected to the investment input of a differential amplifier input,: the non-inverting input of the differential amplifier of the first noise spectral characterization node is the input of the device node of the normalization of the spectral characteristics of the noise hearth: connected to the second input of the adder, the output of the scaling unit with a non-inverting input of the differential amplifier of the second node for spectral noise equalizing, the output of the square root extraction unit of which is under connected to the input of the second functional converter, the output of which is connected to the inputs of the third and first functional converters, the output of the first functional converter is connected to the non-inverting input of the differential amplifier of the third noise spectral normalization node, the output of the square root extractor, the output of the third functional converter is the output of the device. Editor M.Blanar Sos Avitel V. Likhatsky Tehred I.Popovich Proofreader L.Pilipenko Order 2489/51 Circulation 672 Subscription VNIIPI USSR State Committee for inventions and. Discoveries 113035, Moscow, Zh-35, Raushsk nab., 4/5 Production and printing company, Uzhgorod, Projecto st., 4