DE1524317C - Arrangement for successive analog measurement of expansion coefficients of a series expansion of a correlation radio - Google Patents

Description

two time-dependent functions x (t) and y {t) according to orthogonal functions, with a first and a second input of the arrangement for the signal representing the function x (t) or y (i), with one at the first input of the arrangement connected filter set, which can be switched from development coefficient to development coefficient, with an analog multiplier, of which a first input is assigned to the output of the filter set and a second input is assigned to the second input of the arrangement, and with a display device connected to the output of the analog multiplier for displaying the time average of the output signal of the analog multiplier, characterized in that the filter set is a first - known per se - band filter set (3) that a second - known band filter set (4) is connected to the second input (2) of the arrangement, which the phase characteristic of the first band filter set (3) compensates for the fact that both band filter sets (3, 4) each N Have band filters, of which only one is connected to the associated input of the arrangement for each measurement, that the first (3) and the second band filter set (4) are followed by a first (5) and second phase element (6), that both Phase elements (5, 6) can be switched between a first and a second operating state, in which the phase shift of the same frequencies in the entire frequency spectrum of the output signals of the two band filter sets (3, 4) in or

(2i + 1) -y (i = positive or negative integer

or zero) is that the inputs of the analog multiplier (9) are connected to the outputs of the two phase elements (5, .6) and that the following formula applies to the series expansion R _xy (τ):

second operating state of the two phase elements (5, 6),

o) _d "= lower limit frequency of the passband of the η-th band filter,

ω; ,,, = upper limit frequency of the passband of the η-th band filter.

2. Arrangement according to claim 1, characterized in that that the band filter sets (3, 4) are octave or third octave filters.

3. Arrangement according to one of the preceding claims, characterized in that the two Phase members (5,6) are single-stage Görgesglieder known per se.

The invention relates to an arrangement for successively analog measuring expansion coefficients of a series expansion R _xy (τ) of a Korre _T lationsfunktion

+ τ

lim

■ y (t + τ) ■ dt

R _x Jr) = k

sin {a> _hn ■ τ) -

_n τ)

two time-dependent functions x (t) and y (t) according to orthogonal functions, with a first and a second input of the arrangement for the signal representing the function x (t) or y (t) , with one at the first input of the arrangement connected filter set, which can be switched from development coefficient to development coefficient, with an analog multiplier, of which a first input is assigned to the output of the filter set and a second input is assigned to the second input of the arrangement, and with a display device connected to the output of the analog multiplier for displaying the time average of the output signal of the analog multiplier.

Correlation calculation is a branch of mathematical statistics and is used to determine the (causal) relationship between series of values, features and appearances of statistical masses. The degree of this relationship between two statistical masses, which are mathematically represented by time-dependent functions x (t) and y (t) , is determined by forming the correlation function R * _y (r) :

n = 1

(cu _Ä " -

Λ * (τ) - lim

+ r

J-1 J

r) -dt (I)

cos (o) _nn τ) - cos (u) _d "■ τ)

(<"hn - ^ω άη) ^τ '

Constant of arrangement,
Time average of the output signal of the analog multiplier (9) for the «th band filter of both band filter sets (3, 4) in the first operating state of the two phase elements (5, 6),

Time average value of the output signal of the analog multiplier (9) for the «th band filter both band filter sets (3, 4) at

The greater the magnitude of the correlation function, the greater the (direct or indirect) functional dependency there is between the two relevant statistical masses or functions x (t) and y (t). Correlation calculation is used in a wide variety of areas of science, technology and economy, in particular in telecommunications, in acoustics and ultra-acoustics, bionics (a branch of science related to cybernetics, which examines the possibilities of using knowledge of biological processes for technical problems), in control engineering, radar technology,

but also especially in automotive engineering, to z. B. the relationship between noise generation and to determine vibrations in motor vehicles.

In principle, analog computing devices can be used to determine the correlation function according to the above formula (1) who perform the following operations:

a) the signal χ (t) is supplied; ,

b) the signal y (t) is fed into a memory and stored by this (cf. DG Lampard, "A new method of determining correlation functions of stationary time series", Proc IEE 102 [1955], p. 35, 1. Sp., Para. 2 from below);

c) after the time delay τ, the signal y (t + τ) is stored;

d) the signals x (i) and y (t + τ) are fed to a multiplier and multiplied by this;

e) after the multiplication, the mean value of the product is measured long enough to approximately satisfy T - * oo;

f) the processes a) to e) are repeated for a different value τ.

In fact, in practice, both signals x (t) and y (t) are stored in separate memories so that they can be read therefrom for calculating the correlation function for variable values τ.

It can be seen that such an arrangement for the formation of the correlation function (correlator) especially because of the memory is very expensive.

In contrast, a known arrangement of the type mentioned at the beginning (cf. DG Lampard, loc. Cit., Pp. 35 to 41) manages without such a memory. This arrangement is based on the approximation of the correlation function by a series expansion. To obtain expansion coefficients M _n , the signal x (t) must be sent through all the first η stages of the filter set.
A first disadvantage of this known arrangement is that it requires a set of filters to be specially manufactured, which is also relatively expensive since it has an active component such as electron tubes.
A second, perhaps even more serious, disadvantage is the complicated course of the orthogonal functions φ _η {τ) [cf. above equation (2)], which apart from a weighting factor [ae- ^dT ] ^T (with α, ε and γ as parameters) are so-called Laguerre polynomials L _n (ατ) [cf. there equation (23)

P. 37]:

L _n (ατ) =

R% {t) * R _xy {x) = M ₁ ·
+ M _n ■ φ ,, (τ) +.

.N

Μ _ηΨη (τ)

O ₁ (T) + M ₂ -Cf ₂ (T) + ...

. + M _n - ψ _Ν (τ)

- ^ co). (2)

π = 1

φ _η (τ) φ, _η (τ) άτ = \; ™ Φ „ .

(3)

s! s!

The functions φ ,, (τ) are so-called orthogonal functions, that is, the following applies:

This known arrangement has therefore not found its way into practice.

It is therefore the object of the invention to design the arrangement of the type mentioned at the beginning of the filter set so that conventional filter sets known per se can be used and at the same time the orthogonal ones necessary for the series expansion of the correlation function Functions are designed to be much simpler.

This object is achieved in that the filter set is a first - per se known - band filter set that a second - per se known - band filter set is connected to the second input of the arrangement, which has the phase characteristics of the first band filter set. compensates that both band filter sets each have JV band filters, of which only one is connected to the associated input of the arrangement for each measurement, that the first and second band filter sets are followed by a first or second phase element, that both phase elements between a first and can be switched to a second operating state in which the phase shift of the same frequencies in the entire frequency spectrum of the output signals of the two band filter sets in or (2 i + 1) - ^ - (i = positive or negative

integer or zero) is that the inputs of the analog multiplier are connected to the outputs of the two phase elements and that the following formula applies to the series expansion R _xy {i):

45

50

Such an approximation therefore represents a generalization of the well-known Fourier analysis, where the orthogonal functions are sin 2 πητ and cos 2 πητ .

The known arrangement (see FIG. 1 there on p. 36) has a first input for the function 3c (i) and a second input for the function y (t), of which the second input is directly connected to an input of one Analog multiplier and the first input is connected to the other input of the multiplier via a linear network in the form of a filter set. A low-pass filter and an analog display device are connected to the multiplier. The filter set consists of stages connected in series, each of which consists of at least one KC combination and a buffer in the form of a cathode follower (see FIGS. 3 and 4 there on p. 37). To get the R _xy (r) =

sin

τ) - sin (w _d "· τ)

(w _h "- w _d ") ■ τ

cos (üj ,, "· τ) - cos (a> _d " ■ τ) U "hn - ^a) dn) 'τ

With

k = constant of the arrangement, M _1n = time mean value of the output signal of the analog multiplier for the «th band filter of both band filter sets in the first operating state of the two phase elements, M _2n = time mean value of the output signal of the analog multiplier for the nth band filter of both band filter sets in the second operating mode state of the two phase elements,

_t " _dn = lower limit frequency of the passband of the

«-Th band filter,
o) _hn = upper limit frequency of the pass band of the «th band filter.

Conventional band filter sets can therefore advantageously be used in the arrangement according to the invention be e.g. B. Octave and third octave filters for electroacoustic measurements according to DIN standard 45 651 and 45 652 from January 1964. Band filter sets according to the »Audio-frequency spectrometer are particularly useful type 2112 "from the Danish company Brüel & Kjaer (cf. associated brochure from February 1962, p. 13, 15, 16), whereby a single band filter consists of three resonance circuits coupled to one another, the have no active components.

This means that, if necessary, the arrangement according to the invention can be assembled from devices that are already available for other purposes, in particular band filter sets, and can be dismantled again after use. The orthogonal functions, ie the factors of the _{expansion coefficients} M 1n and M _2n dependent on τ, can be calculated very easily and therefore very quickly for different values of τ and summarized in tables, while in the known arrangement a complicated calculation using the Laguerre -Polynomials takes place. Despite the simplicity of the orthogonal function in the arrangement according to the invention, good accuracy is achieved with the series expansion of the correlation function with a relatively low JV, ie the series expansion converges very quickly.

_{Once the expansion coefficients} M 1n and M _{2n are available} , they only need to be multiplied and added with the associated values for the orthogonal functions from the previously prepared table in order to obtain the value of the correlation function as a good approximation for a certain value of τ. The correlation function R _X y (r) can then be determined for a different value of r on the basis of the table and the previously measured development _{coefficients M 1n} and M _2n .

Single-stage Görges members known per se (cf. Franckel, "Theory of Alternating Currents", Springer-Verlag, Berlin 1930, p. 56) highlighted. The Görgesglieder ensure particularly precisely that the desired phase shift in the entire passband of the individual band filters of the band filter sets occurs. The Görgesglieder exist in principle from bridge circuits of passive components such as coils and ohmic resistors.

The invention is explained in more detail with reference to the drawing, in the single figure of which an exemplary embodiment of the arrangement according to the invention is shown is.

A signal corresponding to the function x (t) is fed into a first input 1 of the arrangement, which is connected to the input of a band filter set 3 of switchable band filters. Similarly, a signal corresponding to the function y (t) is fed to an input 2 of the arrangement which is connected to the input of a second band filter set 4 made up of switchable band filters. The individual band filters of each band filter set 3 or 4 can lie parallel to one another, with one of the band filters being connected to the associated input 1 or by means of a rotary switch. 2 of the arrangement is connected. By the second band filter set 4, the phase characteristic of the first band filter set 3 is compensated so that the output signals at outputs 12 and 13 of the band filter sets 3 - or. 4 µm in phase, where i can be a positive or negative integer or zero.

A first and a second phase element 5 and 6 are connected to the outputs 12 and 13, respectively. The phase elements 5 and 6 shift the phase of the output signals of the band filter sets 3 and 4 so that the Outputs 7 and 8 of the phase elements 5 and 6, two different phase relationships can be obtained. When the phase elements 5 and 6 are in an operating state, their output signals are in phase or in Opposite phase, while in the other

stood out of phase by (2 i + 1) -y-, where

i can be a positive or negative integer or zero. For the first operating state of the phase elements 5 and 6, it is therefore sufficient in the simplest case to simply bypass them.
The two inputs of an analog multiplier 9 are connected to the outputs 7 and 8, the output 10 of which is connected to a display device 11 which displays the time average value of the output signal of the analog multiplier 9.
The desired _{expansion coefficients M 1n}

and M _2n are obtained one after the other by first connecting the respective corresponding individual bandpass filters of the bandpass filter sets 3 and 4 to the input 1 and 2, respectively, for one operating state of the phase elements 5 and 6.

The same processes are then carried out for the other operating states of the phase elements 5 and 6 repeated.

Use a successfully tested embodiment of the arrangement shown in the drawing:. {, dete for the belt filter sets 3 and 4 the analyzer type 2112 from the Danish company Brüel & Kjaer, for the Phase members 5 and 6 single-stage Görgesglieder known per se (see above), which were dimensioned so that the phase difference for the second operational feed

stood -j- was, while the Görgesglieder were bridged for the first operating condition. Although any devices known per se can be used as analog multiplier 9 and display device 11, in the present case a display of random signals from the Danish company Disa, type number 55 A 06, was used. With such an arrangement, the development coefficients of autocorrelation (x (i) = y (t)) and cross-correlation functions (x (t) = f y (t)) of noise and vibrations in motor vehicles were measured. .

1 sheet of drawings

Claims (1)

Patent claims: 1. Arrangement for successive analog measurement of expansion coefficients of a series expansion R _X y {r) of a correlation function + τ 1 Γ lim Il +
Γ J
- T x {t) ■ y (t + τ) · dt