LU81648A1 - TIME DOMAIN TRANSVERSE DIGITAL FILTER - Google Patents

Description

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j a — ï AND -DUCHÉ DE LUXEMBOURG

N® patent ............... Q .... | ...... O- * f ^ du ----------- 5 .. .SEP.TEMBKE .... 19.Z9 Minister for the National Economy and the Middle Classes

Title issued: ___________________________________ 3 »· Yrfr

Industrial Property Service

~ ëM LUXEMBOURG

/ fyC. VS? ÀM - J- 0 a Patent Application b, S, Yv I. Request

La -.- Société ... Anonyme ... dit ....: .... nOMPAGNIE ... IM) US! IEIELLE .... DES ....! IÎELEGOMMIMXGATXQNS ........ ..... (1) GIT ~ _ALCATEL, ..... 12., ..... me .... dü..la.J.ay] ie ...-.... Z5. Q0.a..PAEIS. + .... EEÄt; iCE., ..... rep.ri5.enté.e .... by ................ .....

M0DSisi ^ .. JSærPml .... EIPPmïER, ..... Résidenc.e .... YAL..Srffi .... CBQIX, ..... 2-.4 ... Ané.e. ... Lé.QR.QM ......... (2) J ^ ébel..iUXEMB01IRG ^ .... acting ... œ ... quali.té .... de ... representative.-.....................................-....... ...................................

/ λ tnf aépose— ce Ginq .... Sep.tembre ... Mil..l'ieu £ ... Hundred-Sixty-.Tix-Iieuf ............... ..................... (3) at 'Uz ...................... hours , at the Ministry of National Economy and the Middle Classes, in Luxembourg: 1. this request for obtaining a patent for invention concerning: - --------------- ---------------------------------------------------------- --------------------- (4) EXLTRE ... MJMERXQUE ...! TRANSVERSJ ^ .. A ...: ^^ ------ ---------------------------------------------------------- --------------------------------------- declares, assuming responsibility for this declaration, that the inventor (s) is (are):

Michel ... lPZY ...... Engineer, ............. 3.8., Öje ... J.ean ... Za.y ........ .................................................. .................................................. ....... (5) ........................................ .................................................. 913Q0 .... MASSY., .... EEÄNGE ________________________________________________________________________________________________________________ 2. the delegation of power, dated .............. PARIS ............. .......................... on ..24 .... I.LGLIÜT .... 19.Z9 .----- ------ 3. description in language .ErançaîS.e .................................. ............... of the invention in two copies; 4. some ..................... board? ' drawing, in two copies; 5. the receipt of the taxes paid to the Luxembourg Registration Office on ....... C.inq .... S.ep.temhre ... Mil .... Eieui '.... Hundred .... Sixty ... nix ... Ifeuf ...-................................ .................................................. .............

claims for the above patent application the priority of one (s) application (s) of (6) ...... PATENT .................... ............................................... filed (s) ) in (7) ..... ERÂNCE ....................................... ................................-................. ..................

the 8 ... SEP.IEMBHE .... 19.33 .., under ... the ... M ° .... 7.8 ... 25 .... 839 .......... .................................................. ...................... — ........................... ...... (8) "........................................ .................................................. .................................................. .................................................. .................................................. ............................

in the name of -la-demaîade-pesse ......................................... .................................................. ............................-..................... ...............................................

elect domicile for him / her and, if designated, for his / her representative, in Luxembourg ................................ ........

Residence .... VAL .... STE .... CROIX, ..... 2-4-Allée.-Léopol4-Go © bel · ............... .......................................-.......... .......................... d °) requests the issuance of a patent for the subject described and represented in the abovementioned appendices , - mœe-adjournment of this issue at ................... SIX .................. months.

The..................-........ , ..................... ......................................

__________ i- H. Deposit Report

The above application for a patent for invention has been filed with the Ministry of National Economy and the Middle Classes, Industrial Property Service in Luxembourg, on:

R SEPTEMBER 1 Q7Q

Pr. L & JÆimstre à .......... hours / ^ / of the National Economy kjjes Middle Classes, fi: W ~ rd 'HC-if (| «..4 / jfa A 68007 V% j§ · / [J / - --V: · itt ---: - L-4 -; - / it ιιΤη, Μ awi J8m V "iW ί" n linked. << "iVW'Afcaw ta non ·" oeiceant an mioTit Ha tnendotairo f V \ data Hli ”.. · Λ JB / FG / NV F0 11358 CIT-ALCATEL / T 1 pl.

^. Claiming the Priority of a patent application filed in FRAtîCE,

Cj ^ v * SEPTEMBER 8, 1978, under No. 78 25 839.

- —-——-

PATENT

TIME DOMAIN TRANSVERSE DIGITAL FILTER Invention by Michel LEVY

%

Société Anonyme known as

CIT-ALCATEL INDUSTRIAL TELECOMMUNICATIONS COMPANY

The present invention relates to the technique of filtering electrical signals and more particularly that of transverse digital time domain filters.

, A transverse digital time domain filter is generally constituted by a sampler receiving an input signal x (t), operating at a rate 1 / T and providing samples x (m), and by a calculating member transforming samples x (m) into samples y (m) by the relation 10 y (m) = a (k) x (mk) 2.

k being an integer and a (k) real weighting coefficients.

The calculating element is often assimilated for the non-recursive part to a circuit formed: of a delay line with intermediate taps which is connected to the output of the sampler and in which the samples x (m) progress from one tap to another at the sampling rate 1 / T, of multiplier circuits which are connected to the input, to the intermediate taps and to the output of the delay line and which assign weighting coefficients to the samples available on said inputs, intermediate taps 10 and output, and a summing circuit adding the weighted samples of the input signal available at the output of the multiplier circuits and providing the samples of the output signal.

The object of the present invention is a transverse digital time domain filter using both an input signal and its Hilbert transform.

The digital filter object of the invention comprises two samplers which receive one, a signal x (t), the other a signal x (t) transformed from Hilbert of the signal x (t), which operate in synchronism with the sampling rate 1 / T and which provide one of the samples x (m), the other of the samples x (m) and a calculating element transforming the pairs of samples (x (m), x (m)) in samples y (m) by the relation: y (m) = ΣΓb (k) x (m-2k) + c (k) x (ra-2k) kk being an integer and b (k) and c (k) real weights.

The calculating device can be likened to a circuit comprising: a first delay line with intermediate taps which is connected following the sampler receiving the signal x (t) and in which *.

3.

the samples x (m) progress from one take to the other at a rate 1 / 2T half that of sampling, a sample being stored between each take, a second delay line identical to the first connected following the sampler receiving the signal x (t), 5 of the multiplier circuits which are connected to the inputs, intermediate taps and outputs of the delay lines and which assign weighting coefficients the samples available on said inputs to the intermediate taps and output, and a summing circuit which is connected to the outputs of the multiplier circuits, which adds the weighted samples and which provides the output samples.

Other characteristics and advantages of the invention will emerge from the appended claims and from the description below of an embodiment given by way of example. This description will be made with reference to the drawing in which FIG. 1 represents the diagram of a non-recursive transverse digital time domain digital filter of the prior art and FIG. 2 a non-recursive transverse digital time domain digital filter according to l 'invention.

The non-recursive transverse digital filter with time domain of the prior art represented in FIG. 1 comprises, in a conventional manner, a sample 1 which is connected at the input and which delivers samples x (m) of the at regular intervals T input signal x (t), a delay line 2 with intermediate taps which is connected to the output of the sampler 1 and in which the successive samples ^ x (m), x (m-1), ... x (m-2N) ^ progress from one socket to another at the rate 1 / T, multiplier circuits 3 which are connected to the input, to the intermediate sockets and to the output of the delay line 2 and which deliver to their outputs the samples I * of the input signal affected by weighting coefficients ^ a (o), a (1), .. M a (2N) ^ t a summing circuit 4 which delivers the samples y ( m) the output signal. The samples y (m) correspond to the relation:

2N

5 y (m) = a (k) x (m-k) k o k being an integer and a (k) real weighting coefficients.

When we assume that the filter is of infinite length, we can write this relation in the form 10 y (m) = *> _ a (k) x (m-k) k

This relation shows, as is well known, that a transverse filter with a time domain of infinite length performs a correlation between the samples x (m) of the function x (t) and those a (m) of its impulse response. The filter is determined from the coeffi cients a (m) which can be used to define a function a (t) with bounded spectrum ["-1 / 2T, 1 / 2T: a (t) -ΣΖ. A <" )? ln (t-mî ^ m ('f'VTKt-mT) which will be used later and which is called here analog impulse response of the filter. Its samples a (kT) determine the 20 coefficients of the filter.

FIG. 2 represents the diagram of a non-recursive transverse digital filter with time domain according to the invention. This filter includes: J * 5.

- two samplers 5 and 6 which receive one 5 an input signal x (t) and the other 6 the Hilbert transform x (t) of the input signal x (t), which operate in synchronism with the rate 1 / T and which deliver one 5 of the samples x (m) the other 6 of the samples 5 Ions x (m), - a first delay line 7 with intermediate taps, which is connected to the output of 1 'sampler 5 and in which the samples x (m) progress from one take to the other at the rate 1 / 2T half that of sampling, a sample x (m) being stored 10 between each take, - a second delay line 8 identical to the first, which is connected to the output of the sampler 6 and in which the samples x (m) progress from one take to the other at the rate 1 / 2T half that of sampling , a sample x (m) being stored between each tap, - multiplier circuits 9, 10 which are connected to the input, to the intermediate taps and to the output, each of the first line delay 7 and the others 10 of the second delay line 8 and which each deliver 9 the samples of the input signal x (t) 20 assigned weighting coefficients ^ b (o), b (2), b ( 4), ...., b (2N) ^ the other 10 samples of signal x (t), Hilbert transform of signal x (t), assigned weights ^ c (o), c (2) , ..., c (2N) j - and a summing circuit 11 which is connected to the outputs 25 of the multiplier circuits, which adds the output signals of the multiplier circuits 9 and 10 and which delivers the samples y (m) of the signal of exit.

1. ’· 6.

The samples y (m) of the output signal are defined from the samples x (m) of the input signal x (t) and x (m) of the signal x (t), Hilbert transform of the signal x (t) , by the relation:

NOT

y (m) = b (2k) x (m-2k) + c (2k) x (m-2k) k o 5 k being an integer and b (2k), c (2k) real weighting coefficients.

The delay lines 7 and 8 can be constituted by delay lines identical to that 2 of the filter shown in FIG. 1 of which only one out of two taps is used.

The coefficients of the filter according to the invention can, in a manner analogous to those of the filter shown in FIG. 1, be determined from the analog impulse response previously defined. To demonstrate this, it suffices to note that the two filters, that shown in FIG. 1 and that shown in FIG. 2, being assumed to be of infinite length, can give the same output signal if certain relationships are verified between their weighting coefficients.

The relation defining the output samples of the filter represented in figure 1 supposed of infinite length: + oo 20 y (m) = a (k) x (mk) k - "a * can be written by separating the even and odd indices y (m) = _ a (2p + 1) x (m-2p-1) + a (2p) x (m-2p) P - oo »J 1 λ 7.

According to the sampling theorem, the samples x (m) unambiguously define the real signal x '(t) with limited spectrum £ / 2T, 1 / 2tJ corresponding to the relation:

x. (t) = 2Z siaJÆlKksrJ

m C ^ Ht-mT) 5 Similarly, the samples x (m) unambiguously define the real signal x ’(t) with limited spectrum jj-1 / 2T, 1 / 2t], Hilbert transform. of the signal x ’(t), responding to the relation: a" (t) = m (1l7T) (t-mT)

Now we show that the analytical signal X '(t) corresponding to the real signal with bounded spectrum x' (t): X '(t) = x' (t) + j x '(t) whose spectrum is limited to the interval [θ, 1 / 2τ | is perfectly defined by the pairs of samples (x '(2KT), x (2KT)) which are none other than (x (2m), x (2m)) and only the samples x (m) and x (m) are 15 linked by the relations: (2) x (m) --1 TZ iisttsül and î (a) .J è 2 <2i2i ± Ü ** i -9 · 2i + 1 wi - 2i + 1

For the demonstration of these properties one can refer to the article by J.OSWALD entitled "the signals with limited spectrum and * 1 8.

their transformations "appeared in the review" Cables and transmission "4th year July 1950.

The relations (2) make it possible to express the samples x (m-2p-1) as a function of the samples x (m): 5 x (m-2p-1) «| ζίΓ S (m-2P-U2l4,1) 1 * i -o- 2i + 1

The relation (1) then becomes (3) y (m) = 7 - ia (2p + 1) + VZ, a (2p) x (m-2p) p - »> \ i -oo 1Γ 2i + 1 / p - <«

Bn changing in the first part of the relation (3) the index p by the index u defined by the relation: 10 u = pi we get J \ (4) y (m) = 2 ^ jâ ~ a. (. ^ + 2, è + 1) £ (m-2u)} + a <2P) x (m "2P) u *. Oa ^ i -τβ 2i + 1 J p - ç> a * Considering the a (m) like the samples at regular intervals T of the function a (t) with bounded spectrum one can define coefficients â (m) as being the samples at regular intervals T of the function â (t) Hilbert transform of the function a (t) and we have by application of relations (2):

â (2u) = -J, Y * a (2u ± dd ± U

"i - <** 2i + 1 9.

’·. * *

The relation (4) then becomes + v »y (m) = 7 * a (2p) x (m-2p) - 7 ^, - 7 â (2u) x (m-2u)

P - - U --SO

We find the expression of the filter output signal of figure 2 assumed of infinite length by posing: 5 \ b (2p) = a (2p) (c (2p) = -â (2p) = L · lÈî · & -2ρ + 21 + 1 '* i 2i + 1 "

These relationships show that the coefficients b (2p) can be considered as the samples a (2pT) of the analog impulse response a (t) while the coefficients c (2pT) can be considered as the opposites of the samples â (2pT) of the Hilbert transform of the function a (t). They also give a simple method for determining the weighting coefficients of the filter shown in FIG. 2 from those of the filter shown in FIG. 1.

The filter which has just been described in relation to FIG. 2 has a structure which is better suited than that of the filter of the prior art * represented in FIG. 1 in cases where common information has to be drawn from a signal x (t) and its Hilbert transform, for example in single-sideband amplitude modulation transmission systems.

It is possible, without departing from the scope of the invention, to modify certain provisions or to replace certain means by equivalent means.

. One can in particular supplement the transverse filter according to the invention with a conventional recursive part.

Claims (1)

2. Filter according to claim 1 characterized in that the calculating member comprises: - a first delay line (7) with intermediate taps which is connected to the output of the first sampler (5) and in which the samples x (m ) progress from one take to another at a rate 1 / 2T half that of sampling, a sample x (m) being stored between each take, - a second delay line (8) identical to the first (7 ), which is connected to the output of the second sampler (6) and in which the samples x (m) progress from one take to the other at a rate 1 / 2T half that of sampling, a sample x (m ) 'Being stored between each socket, 11.' · · * * * * - multiplier circuits (9,10) which are connected first (9) to the input, to the intermediate sockets and to the output of the first * delay line (7) and the second (10) at the entry, at the intermediate taps and at the exit of the second delay line (8) which deliver the first (9) samples of the input signal x (t) assigned weighting coefficients (b (o), b (2), b (4), .... b (2N)) and the second (10) samples of the Hilbert transformed signal x (t) of the input signal x (t) assigned weighting coefficients (c (o}, c (2), c (4), ...., c (2N)), c - and a summing circuit (11) which is connected to the outputs of the multiplier circuit and which delivers the samples y (m) of the output signal. F. ^ eqewM