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Description  |
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BACKGROUND OF THE INVENTION
The present invention relates to a binary transversal filter and, more
specifically, to a binary transversal filter which is principally used in
digital radio-relay systems.
Digital radio-relay systems are dependent upon a complicated transmission
system, such as cosine roll-off filtering or the like, in order to
effectively utilize the frequency and to reduce interference among codes
being transmitted. In the above mentioned transmission system, a binary
transversal filter made up of digital integrated circuits is employed.
Disclosure of a conventional binary transversal filter can be found, for
example, in IEEE Transactions on Communication Technology, Vol. COM-16,
No. 1, February, 1968 pp. 81-93, Herbert B. Voelcker: "Generation of
Digital Signaling Waveforms". According to the binary transversal filter
disclosed in this article, when it is desired to drive a plurality of
stages of shift registers by timing signals to a frequency which is M
times greater than that of the clock pulses of the NRZ
(non-return-to-zero) signals being introduced, the introduced NRZ signals
are converted into RZ (return-to-zero) signals of a pulse width T/M
(wherein T denotes a repetitive period of the input NRZ signals) and are
fed to the shift registers, and the outputs of the shift registers of each
of the stages are synthesized to produce output signals. A tap coefficient
for weighting the outputs of shift registers of each of the stages can be
found based upon a sampling value at a time of an interval T/M of impulse
response of the filter. For example, if it is assumed that M=2, the tap
coefficient can be obtained by
##EQU1##
where a(t) denotes an impulse response of a transfer function H(.omega.)
which is being found.
The tap coefficient given by the above equation (1), however, only holds
true when the signals are introduced in the form of impulses. Actually,
rectangular pulses of a width of T/2 (M=2) are introduced, and, therefore,
the tap coefficient a.sub.n ' is given by
##EQU2##
According to the above-mentioned conventional techniques in which the input
NRZ signals are converted into RZ signals and are fed to the shift
registers, however, the RZ signals thus converted contain frequency
components of the clock pulses giving rise to the occurrence of a spike
carrier corresponding to the frequency spectrum of the clock pulses, and
the frequency components corresponding to this frequency spectrum are
radiated into space as spurious components which fall outside the
transmission band. With the conventional technique, therefore, other
communications circuits relying upon the above-mentioned frequency
components were often disturbed. In addition, a converter for converting
the NRZ signals into RZ signals tends to become more complicated in
construction with an increase in the multiplier M.
SUMMARY OF THE INVENTION
The object of the present invention is to provide a binary transversal
filter which is so constructed as to eliminate the spike carrier which is
caused by the frequency components of clock pulses and to suppress
unnecessary spurious components that fall outside the transmission band.
Another object of the present invention is to provide a binary transversal
filter in which the NRZ signals being introduced are not converted into RZ
signals but are allowed to be directly fed to the shift registers.
In order to achieve the above-mentioned objects, the present invention
deals with a binary transversal filter which has a plurality of stages of
shift registers that are driven by timing signals of a frequency which is
a multiple of that of the clock pulses being introduced, and a weighting
circuit for weighting outputs of shift registers of each of the stages,
where the outputs of the weighting circuit can be synthesized. The NRZ
signals are fed to the shift registers, the shift registers are driven by
timing signals of a frequency which is M times that of the clock pulses of
the NRZ signals, and each tap coefficient a.sub.n of the weighting
circuit, which is connected to the shift registers of each of the stages,
is given by a sampling value of an interval T/M of an inverse Fourier
transformation a(t) of
##EQU3##
where H(.omega.) denotes a transfer function which gives a response being
found, and T denotes a repetitive period of the input NRZ signals.
Further features and advantages of the present invention will become
apparent from the ensuing description, with reference to the accompanying
drawings, to which, however, the scope of the invention is in no way
limited.
BRIEF DESCRIPTION OF THE DRAWING
FIGS. 1A and 1B are respectively a block diagram illustrating a
conventional binary transversal filter, and a timing diagram illustrating
the flow of input signals,
FIG. 2 provides diagrams respectively illustrating output waveforms of the
binary transversal filter of FIG. 1, and the frequency spectrum of the
binary transversal filter;
FIGS. 3A and 3B are respectively a block diagram showing the principle of a
binary transversal filter according to the present invention, and a timing
diagram illustrating the flow of input signals;
FIGS. 4A, 4B, and 4C are respectively a block diagram illustrating a binary
transversal filter according to the present invention, a timing diagram
illustrating the flow of input signals, and a waveform diagram showing
relations among NRZ signals, RZ signals, and clock pulse signals; and
FIG. 5 provides diagrams showing waveforms at each of the portions of the
binary transversal filter of the present invention and their respective
frequency spectra.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 1A is a block diagram showing a conventional binary transversal filter
which consists of: a converter 1, which introduces NRZ signals and
converts them into RZ signals; a shift register 2, of a plurality of
stages 2(-n), 2(-n+1), . . . 2(n-1), 2(n), which receives outputs of the
converter 1; a multiplier circuit 3, which multiplies the frequency of
clock pulses CLK so that the shift register 2 is driven by the multiplied
timing signals; a weighting circuit 4 consisting of resistors r.sub.(-n),
r.sub.(-n+1), . . . r.sub.n-1, r.sub.n, which are connected to output
terminals of each of the stages of the shift register 2; an amplifier
circuit 5, which synthesizes the outputs of the weighting circuit 4 and
amplifies the synthesized output to a predetermined level; and a low-pass
filter (LPF) 6 for removing unnecessary components from the outputs of the
amplifier circuit 5. FIG. 1B shows the state in which an RZ signal
introduced to the shift register 2 at a time t.sub.1 is shifted in the
shift register 2 by the timing outputs of the multiplier circuit at times
t.sub.2, t.sub.3. . .
FIG. 2 shows one example of output waveforms of the binary transversal
filter of FIG. 1A, and its frequency spectrum. The diagram (a) of FIG. 2
shows an output waveform that is to be found, and the diagram (b) shows a
frequency spectrum of the waveform shown in diagram (a). In the diagram
(b), the abscissa represents angular frequency and the ordinate represents
spectrum density. With reference to the diagram (b), the frequency
spectrum of the output that is to be found becomes zero at a frequency
1/T. If the waveform of diagram (a) is sampled with impulses of an
interval T/2 as shown in the diagram (c), the frequency spectrum of the
impulses becomes as shown in the diagram (d). In the practical hardware,
rectangular pulses of a width T/2 are introduced as shown in the diagram
(e). The frequency spectrum, therefore, becomes as shown in the diagram
(f).
According to the conventional filter as mentioned above, since the RZ
signals contain large amounts of clock pulse components, a spike carrier
having frequency components of the clock pulses appears at frequencies
1/T, 2/T, . . . and causes unnecessary spurious components that fall
outside the transmission band.
The principal object of the present invention is to eliminate unnecessary
spurious components. The fundamental principle of the present invention is
illustrated in FIG. 3A. With reference to FIG. 3, the present invention
consists of a modification of the circuit of FIG. 1A, wherein an RZ signal
which is delayed by a time T/2 by a delay circuit 11, i.e., an RZ signal
which is out of phase with respect to the output of the converter 1 is fed
to a shift register 12, and outputs of each of the stages of the shift
register 12 are taken out via a weighting circuit 14 and are synthesized,
to obtain the sum of the thus synthesized output of the weighting circuit
14 and the resultant output of the weighting circuit 4. With reference to
the RZ signal components, therefore, the resultant output of the weighting
circuit 4 and the resultant output of the weighting circuit 14 are added
together, but spike carrier components of clock pulses acquire the
opposite phase and are removed. In this case, tap coefficients of the
weighting circuits 4 and 14 must be selected to be suitable values that
are different from those of the conventional filters.
FIG. 3B is a time chart illustrating the flow of RZ signals.
According to the circuit illustrated in FIG. 3A, the RZ signals A and the
RZ signals B which lag by T/2 behind the RZ signals A are introduced into
the shift register 2 and into the weighting circuit 14, and are processed.
However, since the RZ signals A and the RZ signals B which are synthesized
together are equivalent to the original NRZ signals, the present invention
feeds the NRZ signals directly to a shift register to process them as
illustrated in FIG. 4A.
With reference to FIG. 4A, an input terminal IN introduces the NRZ signal,
which is directly applied to an input stage 21.sub.(-n) of a shift
register 21 consisting of a plurality of stages 21.sub.(-n),
21.sub.(-n+1), . . . 21.sub.(n-1), 21.sub.(n). On the other hand, the
frequency of the clock pulses CLK is doubled by a multiplier circuit 22,
whereby the shift register 21 is driven by timing signals of the doubled
frequency. The outputs of each of the stages of the shift register 21 are
fed to an operational amplifier 24 via weighting resistors R.sub.(-n),
R.sub.(-n+1), . . . R.sub.(n-1), R.sub.(n) of a weighting circuit 23, and
the output of the operational amplifier 24 is produced via a low-pass
filter 25, which removes frequency components greater than 2/T. FIG. 4B
shows the state in which the NRZ signal fed to the input terminal of the
shift register 21 at a time t.sub.1 is shifted in the shift register 21 by
the timing signals of the multiplier circuit 22 after the lapse of times
t.sub.2, t.sub.3, . . . FIG. 4C shows a relation between the NRZ signals
and the clock pulses in the circuit of FIG. 4A, in which the diagram (a)
shows NRZ signals, the diagram (b) shows clock pulses and the diagram (c)
shows outputs of the multiplier circuit.
The weighting circuit 23 in the circuit of FIG. 4A is described below in
detail with reference to FIG. 5.
With reference to the diagram (a) of FIG. 5, when M=2, the input NRZ signal
can be considered to be composed of pulses A and B, each having a pulse
width T/2. By using impulses .delta..sub.a (t-T/4) and .delta..sub.b
(t+T/4) instead of the above-mentioned pulses A and B, let it be assumed
that the impulse response at t=0 of the binary transversal filter is given
by a(t) and the spectrum of the impulse response, is as given by
A(.omega.) of the diagram (b) of FIG. 5. Then, the synthetic waves of the
two impulse responses, and the spectrum thereof, are given by
##EQU4##
This is because, when a(t).revreaction.A(.omega.), we obtain
a(t-t.sub.0).revreaction.A(.omega.)e.sup.j.omega.t o. Here, the symbol
.revreaction.indicates that the Fourier transform of the left side is the
right side, and the inverse Fourier transform of the right side is the
left side.
The synthetic wave should serve as an impulse response for the transfer
characteristics H(.omega.) of a filter that is to be materialized.
Therefore, if the transfer characteristics H(.omega.) are given, there is
obtained from the equation (3)
##EQU5##
Therefore, the tap coefficient a.sub.n is given by a sampling value of an
interval T/2 of an inverse Fourier transform a(t) of A(.omega.). If it is
assumed that A(.omega.)=0 in .vertline..omega..vertline.>2.pi./T, then
##EQU6##
The above equation (5), however, holds true when impulses are introduced.
When rectangular pulses whose spectrum is given by sin .omega.T/4
/.omega.T/4 are to be introduced, the inverse of this spectrum function is
multiplied into the integrand to make the rectangular pulses equivalent to
impulse inputs. The equation (5), therefore, can be rewritten as
##EQU7##
Accordingly, values of the resistors R.sub.-n to R.sub.n connected to each
of the stages of the shift register 21 of FIG. 4A should be so selected
that they will be proportional to the inverses of their respective tap
coefficients a.sub.-n to a.sub.n.
When M=2, from the above equation (4), there is obtained a relation
H(.omega.)=A(.omega.) 2 cos (.omega.T/4) (7)
Therefore, the value H(.omega.) necessarily becomes zero at
.omega.=2.pi./T, 6.pi./T, 10.pi./T. Consequently, the frequency components
of clock pulses of 1/T can be suppressed irrespective of the tap
coefficients.
The dotted lines of diagrams (c) and (e) of FIG. 5 represent impulse
responses a(t+T/4) and a(t-T/4), and the solid arrows represent impulse
trains for taking sampling values at an interval T/2. Diagrams (d) and (f)
of FIG. 5 illustrate frequency spectra of the impulse trains of the
sampled values. Diagrams (g) and (h) of FIG. 5 illustrate impulse trains
for taking sampling values of the resultant impulse response and its
frequency spectrum. Diagram (i) of FIG. 5 shows a resultant output (input
of the low-pass filter 25) produced under practical operating conditions,
i.e., when an NRZ signal is introduced, and the diagram (j) of FIG. 5
shows a frequency spectrum of the resultant output. Here, A'(.omega.)
=A(.omega.) when .vertline..omega..vertline.<2.pi./T or, otherwise,
A'(.omega.)=A'(.omega.+n4.pi./T) and H'(.omega.)=H(.omega.) when
.vertline..omega..vertline.<2.pi./T or, otherwise,
H'(.omega.)=H'(.omega.+n. 4.pi./T).
As illustrated in detail in the foregoing, according to the present
invention, in which the input NRZ signals are directly fed to the shift
register, there is no need of employing the means for converting NRZ
signals into RZ signals which is used in the conventional binary
transversal filters. When the shift registers are driven by timing signals
of a frequency two times that of clock pulses of the input NRZ signals,
the transfer characteristics become zero at a clock frequency 1/T, as
given by the equation (7), making it possible to suppress clock
components.
When M is not 2, the term cos .omega.T/4 in the equation (3) should be
replaced by
##EQU8##
Therefore, when M=3, the equation corresponding to the equation (7) can be
given by
H(.omega.)=A(.omega.) A(.omega.) (1+2 cos .omega.T/3) (8)
and when M=4, the equation corresponding to the equation (7) can be given
by
H(.omega.)=4A(.omega.) cos (.omega.T/4) cos (.omega.T/8) (9)
Thus, as will be understood from the equations (8) and (9), when M is an
even number, there are present two effects, i.e., suppressing the clock
frequency components and obviating the need for NRZ-RZ conversion. When M
is an odd number, however, the clock components are not suppressed, but
the NRZ-RZ conversion is still not required.
* * * * *
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