SU858018A1 - Device for determining m-th moments of pulse transfer function - Google Patents

Description

The invention relates to the field of experimental statistical analysis of stationary ergodic random processes and can be used for operational statistical identification of linear dynamical systems during normal operation by determining the moments of the pulse transition function (IIF).

A device is known that contains multi-link filters, multiplication blocks, averaging blocks, adders, matching blocks (1).

Since in order to determine the moments of IPF at the pace of the experiment, it is necessary to simultaneously obtain a certain set of moments of the autocorrelation and per-correlation functions (ACF and VKF), the use of known devices for these purposes is fraught with large hardware costs and complexity.

Closest to the technical nature of the present invention is a device containing blocks for determining the moments of VKF: the first and second multilink filters, consisting of N + 1 Laguerre cells,

3.

even with a small discrepancy between the real VKF model, it leads to large errors in determining the moments of the VKF. To determine the IPF Moments, it is necessary to use the described device to obtain N + 1 VKF moments, as well as a similar device to obtain N. + 1 ACF moments.

The aim of the invention is to simplify the device for determining the moments of IPF. To do this, as the cells of the first and second multilink filters are used low-pass filters (LPF) with IG) f

Ή (G) - which is much simpler, as well as the introduction of a linear converter (LP) with a variable transmission coefficient.

g

This goal is achieved by the fact that in the device for determining the m-th moments of the pulse transition function, containing (t + 3) groups of multiplication blocks, the first and second multi-link filters, the inputs of which are the first and second inputs of the device, the outputs of the links of the first and second filters connected to the first inputs of the corresponding multiplication blocks of the first and second groups, respectively, the second inputs of the multiplication blocks of the first and second groups are connected respectively to the second and first inputs of the device, the outputs of the blocks A set .----- ¹ ·· · Nia first and second groups are connected respectively to first and second inputs of corresponding adders, yield) of the multi-units of the second filter are connected to first inputs of respective blocks of multiplication of the third group, the second outputs of which are connected to the device pervomuvhodu , the output of each multiplication block of the third group, except the first, is connected to the first input of the corresponding (t – 1) -th multiplication block of each of the groups of multiplication blocks from the 4th. to (t + 3) th, the outputs of which are connected to the corresponding inverting inputs of the corresponding m subtraction blocks, the inverting input of each of which is connected to the output of the corresponding adder, the output of each subtraction block is connected through the corresponding averaging block to the input of the corresponding matching block, the outputs of matching blocks except for the mth, connected to the second inputs of the multiplication blocks of each of the groups from the 4th to (t + 3) th, a linear converter is introduced, the information 'input of which is connected to the output of the first block multiplication of the third group, the control input of the linear converter is connected to the output of the m-th matching unit, and the output of co25

858018 4 is single with an additional inverting input of the m-th subtraction block.

The drawing shows a block diagram of a device.

The device contains the first 1 and second 2 filters, the inputs of which are the inputs of the device, the first group of multiplication blocks 3, the first inputs of which are connected to the first input of the device, and the second inputs to the outputs of the corresponding cells of the filter 2, the second group of 4-multiplication blocks, the first inputs which are connected to the second input of the device, and the second inputs to the corresponding cells of the filter 1, adders 5, the third group of multiplication blocks 6, the first inputs of which are connected to the first input of the device, and the second inputs to the outputs of the corresponding cells filter 1, the outputs of the multiplication blocks 3 and 4 from the first and second groups are connected respectively to the inputs of the adders 5, the multiplication block 7, the output of the m-th adder 5 is connected to the non-inverting input of the subtraction unit 8, the inverter inputs of which the output of the linear converter and the outputs m are connected -th group of multiplication blocks 7, the first input of the m-th multiplication block from this group (k = 0, 1, '2, ..., t-1) is connected to the k-th output of the device, and the second input to the output ( t – k) th block of multiplication from the third group, the output of block 8 of subtraction is connected through averaging block 9 and the mismatch unit 10 to the control input of the linear Converter, the information input of which is connected to the output of the first multiplication unit 6 from the third group.

The device operates as follows.

The signal x (t) goes to the first input of the device, and the signal Y (t) goes to the second input of the device. At the outputs of the third group of multiplication blocks 6 there are signals co ': - © and at the outputs of adders 5 - signals co' co k ”О, N

We will consider the further operation of the device. on the example of one channel to obtain the mth. moment of IPF λ under the assumption that the previous points

Nl: .. ... λζ ..} have already been received. The signals μ * · 'are fed to the second inputs of the multiplication blocks of the m-th group 7, · to the first inputs of which signals

From the OUTPUTs of which ΟΗΓίκΠΒΙ.Ζ ^ -Λ ^ / Ι _ go to the inverting inputs of the subtraction unit 8, to the inverting input of which a signal arrives _; At the same time, the signal μ _{α is} fed to the input of the linear converter, the output of which the signal Ζ = “k ·· jig is fed to the inverting input of the subtraction unit 8, the output of which is sigzed to the input of the averaging unit 9, the output signal M * (Z ] enters through the matching unit to the control input of the linear converter, the transmission coefficient of which changes until the condition M * E Z is met.] ~ О »where M * [Z] is the averaging operator Then in the steady state * ' . M * [Do1 '* ".

those. the magnitude of the PL transfer coefficient is estimated by the m-ro moment of the IPF.

Indeed, substituting (1) and (2) in PrL ^ ODM, yes (b) jav (3) eO

Since t

K Cs) lip (t- sMs-- 1 _ _r -t / T_ _w

A-sh * * * * ⁴ . ^c is chosen value T>> τ _κχ, where τ _κχ - random process correlation interval x (t), from (4) to obtain .pish *, _(g) 'Mo - point CCF * o "= - moment of ACF

On the other hand, VKF and ACF are related by the Wiener-Hopf equation.

Κ_ (τ> * ρί (υ) κ _χ (τ-υ) <η, (8) У А О where h (U) is the IPF of the studied object

TO-4 (6U ⁵⁰

R)

Substituting formula (8) into the dispersion in (6), we obtain ™ K-0 *** oo where λ _κ = Г'С'Ч (T) dt о -

1Ye (9) we get

-K '' ° Do’zh-1 * after pre (9) moment of IPF, m-O, N (.40)

Comparing (5) and (10) we get that if there is a block. multiplications from the mth group of 7 to choose with the transmission coefficient C *, then the resulting estimate λ £ is the mth moment of the IPF. Along the way, we note that by switching the averaging block to the corresponding output of the adders 5 or multiplication blocks from the third group 6, it is possible to obtain the necessary moments of VKF or ACF at the output of the averaging block 9.

When determining the zero moment of the IAP, as follows from (5) and (10) with m = 0,; The mth group of the block® multiplication is missing.

The introduction of a linear converter and the use of aperiodic links in multi-link filters allows us to simplify the device.

Claims (2)

even with a small discrepancy between the model of the real ICF, it leads to large errors in the determined moments of the ICF. To determine the same IFP moments, it is necessary to use an omica-effloro device for obtaining N + 1 ICF moments / and also a similar device for obtaining N. 1 moments of ACF. the present invention is a simplification of the device for determining the moments of the IFP. For this, in the first and second multi-link filter cells, a filter {I.1 frequency bursts (LPF) with IG1f ir vle-- is used. which is significant, as well as the introduction of a linear converter (LP) with a regedy ratio, transmissions. The goal is achieved by the fact that the device for determining the mth moments of the impulse transition function containing (t + 3) multiplication unit groups, the first and The second multi-tier filters, the inputs of which are respectively the first and second inputs of the device, the outputs of the links of the first and second filters are connected to the first .NQI inputs of the corresponding units of a multiple of 1 and 2, respectively, of the first and second groups. the second multiplication units of the first and group are connected respectively to the second and first inputs of the device, the outputs of the first and second groups are connected respectively to the first and second inputs of the corresponding adders, the outputs of the links of the second multi-stage filter are connected to the first inputs of the corresponding blocks of the third group, the outputs which are connected to the first input of the device, the output of each multiplication unit of the third group, except for the first one, is connected to the first input of the corresponding (t − 1) -th blis of your life Each of the blues multiplied by the 4th. Before (t + 3) -th, the outputs of which are connected to the corresponding inverter inputs by the input of the corresponding m subtraction blocks and the inversion input of each of which is connected to the output of the corresponding sum of the torus, the output to the ukrugo b ckg you can connect through the system to the system and the system will be connected to the system of the torus matching, outputs (sop1as (jas1, except for t-th, are connected with the second part and multiplication units of each of the groups from the 4th to (t + 3) -th), a linear converter is introduced, the input of which is connected to the output of the first b okmiozhsn The third link controlling the “stroke” of the linear converter is connected to the output of the t-th matching block, and the output is connected to an additional and curved input of the th-th subtraction block. In the drawing, the device has the first 1 and second 2 filters, the input of which are the inputs of the device.The first root of blocks 3 of the multiplication, the first inputs of which are connected to the first input of the device, and the second inputs - to the outputs (of the corresponding peek 2, the second group of block 4. multiplication, the first inputs are connected to the second input and the second inputs to the corresponding cells of the filter | a 1, adders 5, the third rpjmny multiplication blocks 6, the first inputs of which are connected to the first input of the device, and the second INPUT - to the outputs of the corresponding fishtrap cells, the outputs of the 3 and 4 multiplications from the first and the second troupe are connected respectively to the inputs of adders S, block 7 multiply1-1, output t-th: umm lor 5 is connected to non-goverted} fused input of block 8 subtraction, to the inverting inputs of which plug the output of the fox P5yu generator and outputs of the th group of block 7 multiplication , the first input is t b The multiplication curve from this group (kO, I, 2, ..., t-1) is assigned to the k-th output of the device, and the second input to the output (mk) -ro of the multiplication unit from the third group, the output of the subtraction unit 8 is connected through the averaging block 9 and the block 10, expanding linearly to the control input of the linear input, which is connected to the output of the first multiplication unit b from the third tinder. The device works as follows. Sipol x (t) goes to the Yurv input of the mouth} x S1Ga, and Oagnal Y (t - to the second input of the Uptp ciBa. At the outputs of the third group of b blocks, umuhkuvzl have a message / 4 K (t) IU (t X {tD dr / U) -:: - O., .... a on eummat f f 5 s gnaly)) Shgg; ar G 1) Gi.igg o (&amp;) k о, N iMbae &amp; iiyia work yetpt etbu asmagr m , on the ni tMepe one} channel dl. IAP X | on the assumption that the previous moments L x X I l o Ni-- ni- «} have already been received. Oppals / itV will dry m the second consists of yMROxoetaie m-o group 7, the first inputs of which are received respectively SIGISH1 k A rvw-V h -2 - J from the outputs of which signals.Z. U - 0; vn-1). Arrive at the inverting inputs of the subtraction unit 8, the inverting input of which receives the signal 0; At the same time, from the TTP My arrives at the input of the linear transducer, from the output of which Zlc is Z - k- / jj, arrives at the inverting input of the block 8, the output from which is sig-Z p -K /. is fed to the input of averaging unit 9, from the output of the latter, the signal goes through the matching unit to the control input of the linear converter, the transfer coefficient of which. change (until the condition ME 1.1 O is fulfilled, where M1Z is the Totd averaging operator in the steady state ... ... l. ". with -.1 mA. T. BejoraiHa of the transfer factor of the LP transfer is The moment iTt-ro is ISH. # Deistasno, Substituting (1) and (2) into (3, hell, () Kx (Duck as Jt) "ffi o (s) ytr-s) i ,, - jth ,. -, ls) io (T-sMs - l pt: fr w. To choose BeiaswHy T t ,, where KX, rubbed the correlation of the random x (t) from (4) we get 1 1st K u sh W: -1M ) at Iev rK (t) at:., .l | o K W-KДд. l4. CC) dt: - the moment of the CCF L () 3f moyunnt ACF With another oraL, VKF and ACF are related by the Wiener-Hopf equation K .... (- D) Jti (U) Kx (TU) clt, (8) where) is the IAP of the object being investigated. Substituting formula (8) into (6) after transforming, we get ... (-oat where Lz is the moment of JPF. we get Ye () h. Lo., Nl oC vn n / JtM-K. , W-0, N Xu) o Seravsva (5) and (10) we get, if the k-th block. If ukshsheni from t-th group 7 to choose with the transfer coefficient C, then we get the ff at-mc with the m-th moment of the IFP. . It is worth noting that by switching the averaging block to the corresponding output of adders 5 or bds of multiplication from the third group b, it is possible to get the necessary moments of the CCF or ACF during the averaging of the block 9, When determining the 1st moment of the IPF, as follows: C (5) and (10) with m O, the plN group does not have a block multiplication group. The introduction of a linear converter and the use of aperiodic links in multi-link filters simplifies the device. The invention of the device for determining the th moments of the pulse transition function 1n, containing m + 3 groups of multiplication blocks, the first and second multi-link filters, whose inputs are respectively the left and second inputs of the device, the outputs of the links of the first and second filters are connected to the first inputs corresponding multiplexing, respectively, of the first n of the second group, the second inputs of the multiplication blocks of the first n of the second group, are connected respectively to the second and first inputs of the device, the outputs of the multiplying blocks are first orszh group are connected respectively to first and second inputs of corresponding adders, the outputs misngozvennogo filter units are connected to first inputs of respective blokoa umnozheyush third grugty, echo output cat "fyh connected to the first input ustrshstva, yield kdzhdo O; the third multiplication block, besides the first, is connected to the first input of its corresponding (ml) -ro block multiplying each of the groups of multiplication blocks Pt 4th to (tf 3) -th, the outputs of which are connected with the corresponding immu- rity of the corresponding m blocks The output, each wiring input of each of the corresponding outputs of the corresponding summer, the output of each unit is connected, 785801 Chersel corresponding bl (averaging input, coherence, B), the outputs of the matching unit, except for the second, are connected to the second inputs of the blocks. None of the groups from the 4th to the (t h-3) th, about the t h and h aa s so that, for the purpose of simplification, a linear converter is inserted into the device, the information input of the cathoho is connected to the output the first unit is the multiply unit of the third group, the control input of the linear converter, the ip caller is connected to the output of the t-th clipping unit, and the output is connected to the additional inverting input m-ro of the subtraction unit. Sources of information that are taken into account in case of ekayurtne 1. USSR Copyright Certificate No. 619931, cl. From € G to 7/48, 1975. / ... 2. USSR author's certificate in application 2406332 / 18-24, cl. G 08 G 7/48, 1976 (prog. 1 LL J8,