GB2030410A

GB2030410A - A Digital Time Domain Transversal Filter

Info

Publication number: GB2030410A
Application number: GB7928969A
Authority: GB
Original assignee: Alcatel CIT SA; Compagnie Industrielle de Telecommunication CIT Alcatel SA
Current assignee: Alcatel CIT SA
Priority date: 1978-09-08
Filing date: 1979-08-20
Publication date: 1980-04-02
Also published as: LU81648A1; IT1119359B; FR2435858B1; NL7906619A; DE2933003A1; BE878383A; FR2435858A1; IT7968785A0

Abstract

The filter comprises two samplers (5 and 6), the first of which receives an input signal x(t) and the second of which receives the Hilbert transform signal @(t) of the input signal x(t), the samplers operating synchronously at the rate 1/T and respectively providing samples x(m) of the input signal x(t) and @(m) of the signal @(t), together with a calculator unit for transforming the sample pairs (x(m), @(m)) into output samples y(m) of an output signal, according to the relationship: <IMAGE> where m and k are integers and b(2k) and c(2k) are real weighting coefficients. It is convenient to use Hilbert transform when filtering single sideband signals, and the present filter makes use of both the input signal and its Hilbert transform, but without doubling the number of samples on which calculations are performed during any one sampling period. <IMAGE>

Description

SPECIFICATION A Digital Time Domain Transversal Filter The present invention relates to a digital time domain transversal filter for filtering electrical signals.

A digital time domain transversal filter is, in generai, constituted by a coupler receiving an input signal x(t), and providing signal samples x(m) at a rate 1/T, and by a calculator unit for transforming the samples x(m) into samples y(m) according to the relationship:

where k is an integer and a(k) are real weighting coefficients.

The non-recursive part of the calculator unit is often considered to be in the form of a circuit comprising: 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 the next at the sampling rate 1/T; multiplier circuits which are connected to the input, to the intermediate taps and to the output of the delay line and which weight the samples available at the said input, intermediate taps and outputs with the weighting coefficients; and a summing circuit adding the weighted samples of the input signal available at the outputs of the multiplier circuits and providing samples of the output signal.

The present invention provides a digital time domain transversal filter which makes use both an input signal and of its Hilbert transform.

The present invention provides a digital filter comprising two samplers, the first of which receives an input signal x(t) and the second of which receives the Hilbert transform signal x(t) of the input signal x(t), the samplers operating synchronously at the rate 1/T and respectively providing samples x(m) of the input signal x(t) and x(m) of the signal x(t), together with a calculator unit for transforming the sample pairs (x(m), x(m)) into output samples y(m) of an output signal, according to the relationship:

where m and k are integers and b(2k) and c(2k) are real weighting coefficients.

The calculator unit may be considered to be a circuit comprising: a first delay line with intermediate taps which is connected in series with the sampler receiving the signal x(t) and in which the samples x(m) progress from one tap to the next at a rate 1/2T (i.e. half the sampling rate) with a sample stored between each tap, a second delay line identical to the first connected in series with the sampler receiving the signal Q(t), multiplier circuits connected to the inputs, the intermediate taps and the outputs of the delay lines to weight the samples available at the said inputs, intermediate taps and output using the weighting coefficients; and a summing circuit which is connected to the outputs of the multiplier circuits to sum the weighted samples and provides the output samples.

An embodiment of the invention is described by way of example with reference to the accompanying drawing, in which: Figure 1 is a circuit diagram of a non-recursive digital time domain transversal filter according to the prior art; and Figure 2 is a non-recursive digital time domain transversal filter in accordance with the invention.

The non-recursive digital time domain transversal filter of the prior art shown in Figure 1 comprises, as is conventional, a sampler 1 which is connected at its input and which delivers samples x(m) of an input signal x(t) at regular intervals T, a delay line 2 with intermediate taps 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 tap to the next at the rate 11T, multiplier circuits 3 which are connected to the input, to the intermediate taps and to the output of the delay line 2 and which deliver at their outputs samples of the input signal which have been weighted with weighting coefficients (a(O), a(l),... a(2N)), and a summing circuit 4 which delivers the samples y(m) of the output signal.The samples y(m) obey the relationship:

where k is an integer and a(k) are real weighting coefficients.

When the filter is considered to be of infinite length, this relationship may be written in the form:

As is well known, this relationship shows that a time domain transversal filter of infinite length provides a correlation between the samples of x(m) of the function of x(t) and sample a(m) of the impulse response of the function. The filter is defined by the coefficients a(m) which may be used to define a function a(t) of limited spectrum [-1/2T, 1/2T]:

which is used below and which is called herein the analog impulse response of the filter. Its samples a(kT) define the filter coefficients.

Figure 2 is the circuit diagram of a non-recursive digital time domain transversal filter in accordance with the invention. This filter comprises: two samplers 5 and 6, the first of which 5 receives an input signal x(t) and the second of which 6 receives the Hilbert transform Q(t) of the input signal x(t), the samplers operate in synchronism at the rate 1/T and the first sampler 5 provides samples x(m) and the second sampler 6 provides samples Q(m); a first delay line 7 with intermediate taps connected to the output of the first sampler 5 and in which the samples x(m) progress from one tap to the next at a rate 1/2T (i.e. half the sampling rate) with a sample x(m) being stored between each pair of adjacent taps;; a second delay line 8 identical to the first and connected to the output of the sampler 6 and in which the samples Q(m) progress from one tap to the next at a rate 1/2T (i.e. half the sampling rate) with a sample Q(m) being stored between each pair of adjacent taps;; first multiplier circuits 9 connected respectively to the input, intermediate taps and the output of the first delay line 7, and second multiplier circuits 10 are similarly connected to the second delay line 8, the first multipliers 9 delivering samples of the input signal x(t) weighted by respective weighting coefficients (b(O), b(2), b(4),... b(2N)), the second multiplier circuits 10 delivering samples of the Hilbert transform signal Q(t) of the input signal x(t) weighted by respective weighting coefficients (c(O), c(2), c(4), . . . c(2N)); and a summing circuit 11 connected to the output of the multiplier circuits to sum the output signals of the multiplier circuits 9 and 10 and deliver samples y(m) of the output signal.

The samples y(m) of the output signal are defined on the basis of the samples x(m) of the input signal x(t) and Q(m) of the signal Q(t), i.e. the Hilbert transform of the signal x(t), by relationship:

where k is an integer and b(2k), c(2k) are real weighting coefficients.

The delay lines 7 and 8 may be constituted by delay lines identical to the delay lines 2 of the filter shown in Figure 1 with only every other tap being used.

The coefficients of a filter in accordance with the invention may, in a manner analogous to that of the filter shown in Figure 1, be determined from the analog impulse response as defined above. To show this it is sufficient to observe for both filters, i.e. that shown in Figure 1 and that shown in Figure 2, and supposing then to be of infinite lengths will give the same output signal provided certain relationships hold between their weighting coefficients.

The relationship defining the output samples of the filter shown in Figure 1 , supposed to be of infinite length, is:

and may be written with the odd and even indices separated:

According to the sampling theorem, samples x(m) defining a real signal x' (t) of limited spectrum [--1/2T, 1/2T] unambiguously obey the relationship:

Likewise, samples Q(m) defining a real signal x'(t) of limited spectrum [--1/2T, 1/2To unambiguously, representative of the Hilbert transform of the signal x'(t), obey the relationship:

Now it can be shown that the analytic signal X'(t) corresponding to the real frequency limited signal x'(t) where: : X' (t)=x' (t) +job' (t) whose spectrum is limited to the range [0, 1/2T] is completely defined by the pairs of samples (x' (2KT), Q'(2KT)) which are none other than (x(2m), Q(2m)) and the samples x(m) and Q(m) are linked by the relationships:

To demonstrate these properties reference can be made to an article by J. Oswald entitiled "les signaux à spectre limited et leurs transformations" (Spectrum limited signals and their transformations) which appeared in the journal "Cables et transmission" year 4 July 1 950.

The relationships 2 make it possible to express the samples x(m-2p-1) as a function of the samples Q(m) as follows:

Relationship 1 then becomes:

By changing the index p in the first part of relationship 3 for an index u defined by the relationship: u=p-i the following relationship is obtained:

Considering, as before, the coefficients a(m) as samples at regular intervals T of the limited spectrum function a(t), it is possible to define coefficients â(m) as being the samples at regular intervals T of the function â(t) (the Hilbert transform of the function a(t)) and by applying the relationships (2), the following relationship is obtained::

The relationship (4) then becomes

The expression for the output signal of the filter of Figure 2, supposing it to be of infinite length, can then be found by putting:

These relationships show that the coefficients b(2p) may be considered to be samples a(2pT) of the analog impulse response a(t) while the coefficients c(2pT) may be considered as negative versions 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 Figure 2 from those of the filter shown in Figure 1.

The filter which has just been described with reference to Figure 2 is better adapted than the prior art filter shown in Figure 1 for cases where common information is to be drawn from a signal x(t) and its Hilbert transform, e.g. in single sideband amplitude modulation transmission systems.

Without going beyond the scope of the invention, it is possible to modify various arrangements or to replace various means by other equivalent means. In particular, the transversal filter in accordance with the invention may be used in conjunction with a conventional recursive portion.

Claims

1. A digital time domain transversal filter comprising two samplers, the first of which receives an input signal x(t) and the second of which receives the Hilbert transform signal Q(t) of the input signal x(t), the samplers operating synchronously at the rate 1/T and respectively providing samples x(m) of the input signal x(t) and Q(m) of the signal Q(t), together with a calculator unit for transforming the sample pairs (x(m), x(m)) into output samples y(m) of an output signal, according to the relationship:

where m and k are integers and b(2k) and c(2k) are real weighting coefficients.

2. A filter according to claim 1, wherein the calculator unit comprises: a first delay line with intermediate taps which is connected to the output of the first sampler and in which the samples x(m) progress from one tap to the next at a rate 1/2T (i.e. half the sampling rate) with a sample x(m) being stored in between each pair of adjacent taps; a second delay line identical to the first, connected to the output of the second sampler and in which the samples Q(m) progress from one tap to the next at the rate 1/2T (i.e. half the sampling rate) with a sample Q(m) being stored in between each pair of adjacent taps:: first multiplier circuits connected respectively to the input, the intermediate taps and the output of the first delay line, and second multiplier circuits connected respectively to the input, the intermediate taps and the output of the second delay line, the first multiplier circuits delivering samples of the input signal x(t) weighted by respective weighting coefficients (b(O), b(2), b(4),... b(2N)) and the second multiplier circuits delivering samples of the Hilbert transform signal Q(t) of the input signal x(t) weighted by respective weighting coefficients (c(O), c(2), c(4),... c(2N)); and a summing circuit connected to the outputs of the multiplier circuits and delivery samples y(m) of the output signal.

3. A digital time domain transversal filter substantially as herein described with reference to Figure 2 of the accompanying drawings.