 |
Description  |
|
|
BACKGROUND OF THE INVENTION
This invention relates to the detection of relatively weak signals against
a background of noise, and typical uses are in the acoustic detection of
aircraft, submarines, and land vehicles.
The invention is the subject of my currently copending Canadian application
Ser. No. 115,983, filed June 18, 1971.
Two problems are involved in target detection, firstly the actual detection
of the presence of a target, and secondly the location or
direction-finding of that target. These two requirements are
contradictory, since a narrow beam or sector of maximum sensitivity, which
is desirable for direction-finding, leads to lack of sensitivity in
neighboring directions. Thus an acoustic detection system using a narrow
beam requires constant scanning by that beam, at a suitably low speed for
detection to take place, if detection (as distinct from direction-finding)
is important.
The present invention is directed to detection, rather than
direction-finding, of a target.
Another of my copending Canadian patent applications No. 115,982, filed on
June 18, 1971 describes a direction-finding system utilizing two
microphones and a phase-difference detector which receives the outputs
from the two microphones and combines those two outputs in a particular
manner in a discriminator which enables the system to be used as a
highly-directional device for direction-finding. It also describes an
arrangement in which a greater number of pairs of microphones are combined
in a similar manner. Such an arrangement provides a compact microphone
system for a given narrowness of the beam produced.
It is possible to provide a beam of the same narrowness merely by using a
sufficiently large array of microphones with their outputs combined in an
additive manner, and for that given beam, the ability to detect a weak
signal against background noise is better with the additive arrangement
than with the more compact arrangement using discriminators.
An object of the present invention is to improve the detection of weak
signals against a background of noise for any given number of
signal-receiving transducers.
SUMMARY OF THE INVENTION
According to the present invention, a signal processing circuit
particularly adapted for use in the detection of a selected signal against
background noise, comprises separate inputs which comprise at least first,
second and third inputs which provide respectively the selected signal
plus a first noise signal, the selected signal plus a second noise signal,
and the selected signal plus a third noise signal (the three noise signals
being uncorrelated); first combining means arranged to produce from the
first and second inputs a fourth signal from which the selected signal has
been eliminated and which comprises the difference between the first and
second noise signals; second combining means arranged to produce from the
second and third inputs a fifth signal from which the selected signal has
been eliminated and which comprises the difference between the second and
third noise signals; means arranged to compare the fourth and fifth
signals, to select the signal which has an instantaneous value closer to
zero, and to present that signal as an instantaneous intermediate output;
means arranged to compare the fourth and fifth signals, and when the two
signals are of opposite polarity, to present zero as the said
instantaneous intermediate output; and combining means by which one of the
said inputs is combined with the said intermediate output in a manner
tending to eliminate the noise component therein; said intermediate signal
containing the selected signal with a higher signal-to-noise ratio than
any of the incoming signals.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention will now be described, by way of example, with reference to
the accompanying largely diagrammatic drawings, in which:
FIG. 1 is a block diagram of a three-input, signal-processing circuit
utilized in an aural target detection system;
FIGS. 2, 3 and 4 are graphical representations of two input signals and an
output signal of a discriminator shown in FIG. 1;
FIG. 5 is a block diagram of one embodiment of the discriminator of FIG. 1;
FIG. 6 is a more detailed circuit diagram of the discriminator of FIG. 5;
FIG. 7 is a graphical representation of the manner in which the
discriminator of FIG. 1 combines three noise inputs;
FIG. 8 is a circuit diagram of a second embodiment of the invention in
which four input signals are utilized;
FIG. 9 is a graphical representation illustrating the beam-forming
properties of 3-input, 4-input and 6-input arrangements according to the
present invention;
FIG. 10 is a diagram showing how discriminators of FIG. 8 can be utilized
in a direction finding, rather than a signal detection, role;
FIG. 11 is a block diagram of a multistage filter utilizing a discriminator
circuit shown in FIG. 1;
FIG. 12 is a graphical representation of observed gains of the three input
discriminator used in the filter mode;
FIG. 13 is a graphical indication of gain for the three input discriminator
used in the filter mode; and
FIG. 14 is a block diagram of a multistage filter a four-input
discriminator circuit such as that shown in FIG. 8.
DETAILED DESCRIPTION
Referring first to FIG. 1, three microphones 11, 13, and 15 are equally
spaced along a straight line 17, and each of these is sensitive to sound
approaching the microphone from the left in FIG. 1.
Considering the sound received by the microphones from a single sound
source, typically two or three miles from the microphones, each microphone
will receive a common signal S and a noise signal which will be different
for each microphone, and will be designated by X, U and Y, respectively,
for the three microphones. Thus the three outputs from the microphones
will be referred to as follows:
______________________________________
From microphone 11 Output is S + X
From microphone 13 Output is S + U
From microphone 15 Output is S + Y
______________________________________
It is important to realize that in the arrangement described the three
noise signals X, U and Y, although possessing identical statistical
characteristics, are uncorrelated.
In FIG. 1, the output S+U from microphone 13 is passed through an inverter
19 the output of which is thus -S-U, and this output is applied as one
input to an adder 23. The other input to adder 23 is the output from
microphone 11, i.e., the signal S+X. Thus the output from adder 23 is X-U.
Similarly, the output S+Y from microphone 15 is applied to an inverter 21,
the output of which is thus -S -Y, and this output is applied as one input
to an adder 25. The other input to adder 25 is the output from microphone
11, i.e., the signal S+X. Thus the output from adder 25 is X-Y.
The outputs from the two adders are applied respectively as first and
second inputs to a discriminator 27. This discriminator is one of two
discriminators described and claimed in my Canadian patent application No.
115,982.
The discriminator used in a circuit which obeys the following two rules:
(i) when input signals 1 and 2 are both of the same polarity, the circuit
selects the input closer to zero and presents it at the output;
(ii) when the input signals are of opposite polarity, the circuit presents
zero at the output.
FIGS. 2, 3 and 4 shown this effect pictorially: In FIG. 2, the two inputs 1
and 2 are equal and in phase: since they are never of opposite polarity,
rule (ii) does not apply, and the output is identically similar to each
input.
In FIG. 3, the two inputs 1 and 2 are equal but input 2 lags input 1 by 90
degrees: during period 0 to 90 degrees of input 1, since the two input are
of opposite polarity, the output is zero: from 90 degrees to about 135
degrees, input 1 is larger than input 2, so that the output follows input
2; from about 135 degrees to 180 degrees, input 1 is smaller than input 2,
and therefore the output follows input 1: from 180 degrees to 270 degrees,
the two inputs are of opposite polarity, and therefore the output is zero;
from 270 degrees to about 315 degrees, input 1 is larger than input 2, and
the output follows input 2, so that the output follows input 1.
In FIG. 4, where input 2 lags input 1 by 180 degrees, as all times (except
the crossover points) input 1 and input 2 are of opposite polarity, so
that the output remains at zero.
It will be seen that the change in the output from the discriminator is
from maximum to zero over a phase difference in the inputs of zero to 180
degrees.
FIG. 5 shows in block diagram form one form of the discriminator 27 of FIG.
1, and FIG. 6 shows the complete circuit diagram for this embodiment. The
blocks shown in FIG. 5 are all well known and commercially available logic
circuit components. Thus each of the comparators 40, 42 and 50 is a form
of analog-to-digital coverter. It receives two analog inputs, and compares
them with one another. If the algebraic sum of the two analog inputs is
positive, then the logic output is HIGH (i.e. 1). If the algebraic sum of
the two analog inputs is zero or negative, then the logic out is LOW (0).
Thus the output is binary in nature, and will always be either "1" or "0".
Each of the two modulus circuits 46 and 48 is in effect a full wave
rectifier circuit without any smoothing, so that the shape of both
positive and negative parts of the parts of the output waveform are
similar to those of the input waveform, but the negative parts of the
waveform are rendered as positive parts. Each GATE 58 and 60 acts as a
high-speed relay which controls the passage of an analog signal according
to the binary logic level applied to its driving input. As usual, each
gate is a transistor switching circuit, rather than an electromagnetic
relay.
The AND gates 54 and 56 each provide a "0" output unless both of their
inputs carry a "1" input. The "exclusive OR" circuit 44 has two inputs,
and provides a "0" output except when both of its inputs have the same
input signal, i.e., when both are "1" or when both are "0". When the
inputs are the same, the output is a "1". The inverter 52 provides as its
output a binary signal opposite to its input binary signal, i.e., a "1"
input signal produces a "0" output signal and a "0" input signal produces
a "1" output signal. The amplifier 62 is an operational amplifier used as
a summing amplifier.
In FIG. 5, several points on the diagram are denoted by the various letters
A through F, and the following "Truth Table" indicates the signals at
these various points for varying inputs 1 and 2.
__________________________________________________________________________
Input
Polarity Amplitudes
Logic Signals
Case I/P.sub.1
I/P.sub.2
(inputs)
A
B
C D E F Output
__________________________________________________________________________
1 + + .vertline.I/P.sub.1 .vertline. > .vertline.I/P.sub.2 .vertline.
1 1 1 1 1 0 1 I/P.sub.2
2 + + .vertline.I/P.sub.2 .vertline. > .vertline.I/P.sub.1 .vertline.
2 1 1 1 0 1 0 I/P.sub.1
3 + - .vertline.I/P.sub.1 .vertline. > I/P.sub.2 .vertline.
1 0 0 1 0 0 0
4 + - .vertline.I/P.sub.2 .vertline. > .vertline.I/P.sub.1 .vertline.
. 1 0 0 0 0 0 0
5 - + .vertline.I/P.sub.1 .vertline. > .vertline.I/P.sub.2 .vertline.
0 1 0 1 0 0 0
6 - + .vertline. I/P.sub.2 .vertline. > .vertline. I/P.sub.1
.vertline.
0 1 0 0 0 0 0
7 - - .vertline.I/P.sub.1 .vertline. > .vertline.I/P.sub.2
0 0 1 1 0 1 I/P.sub.2
8 - - .vertline.I/P.sub.2 .vertline. > .vertline.I/P.sub.1 .vertline.
0 0 1 0 1 0 I/P.sub.1
9 + + .vertline.I/P.sub.2 .vertline. = .vertline.I/P.sub.1 .vertline.
1 1 1 1 0 1
- - .vertline.I/P.sub.2 .vertline. = .vertline.I/P.sub.1 .vertline.
0 0 1 1 0 1 I/P.sub.2
__________________________________________________________________________
In practice, the input 1 may not have exactly the same amplitude as the
input 2, but the modification of the output by practical differences in
these inputs are small, and for simplicity it will be assumed that the
amplitudes are the same.
In operation, the comparator 40 will provide a digital signal at A which
will be "1" while input 1 is positive, and will otherwise be "0".
Comparator 42 will provide a similar output at B depending upon the
polarity of input 2. The Exclusive OR circuit 44 will then provide at C a
binary signal which will be "1" when both inputs 1 and 2 are positive, or
negative, and a signal "0" when the inputs are of opposite sign. As long
as the signal at C is "0", neither of the AND gates 54 and 56 will be
enabled, so that both gates 58 and 60 will be non-conducting, so that the
output applied to amplifier 62 will be zero and the output from the whole
circuit will be zero.
When the signal at C is "1", then for each of the AND gates 54 and 56 one
input is provided.
The comparator 50 receives at all times a full-wave rectified but
unsmoothed version of the input 1 as a first input, and a full-wave
rectified but unsmoothed version of the input 2 as a second input. If the
instantaneous numerical value of input 1 is greater than the instantaneous
numerical value of input 2, then the output of comparator 50, i.e. at the
point D, is "1". On the other hand, if the opposite is true, the signal at
point D is "0". The signal at D is applied directly as the second input to
AND gate 56 while an inversion of the signal is applied directly as the
signal to AND gate 54. Thus if signal input 1 is greater than signal input
2 (and they are of the same polarity) at point F appears a signal "1" so
that gate 60 is enabled and the analog signal on input 2 is applied to the
amplifier 62. On the other hand, if signal input 2 is greater than input
signal 1 (and they are of the same polarity) at point E appears a "1"
signal and gate 58 is enabled so that the analog signal input 1 is applied
to the amplifier 60.
It will be seen that the smaller of the two input signals is applied to the
amplifier 62 as long as the signals are of the same polarity. In the case
of FIG. 2, when the two signals are equal and of the same polarity, the
output is input 2. This result is necessary to avoid the occurrence of
zero output when the sound locator is precisely directed at the target,
and is achieved by setting comparator 50 to give a "1" output when its
input 1 is equal to input 2.
Referring now to FIG. 6, it will be seen that the Exclusive Or circuit 44
includes three AND gates 70, 72 and 74 and five inverters 76, 78, 80, 82
and 84. The modulus circuit 46 makes use of an operational amplifier 88
used as a differential amplifier to the non-inverting input of which is
applied input 1, the inverting input being supplied with the same signal
which however is inverted in an amplifier 90 and then gated by gate 92
which is driven by the output on lead A. Modulus circuit 48 includes
differential operational amplifier 96 inverting amplifier 98 and gate 100.
Returning now to FIG. 1, it will be appreciated that only "noise" is
processed through the discriminator 27. The output from the discriminator
is passed through a further inverter 29 the output of which is applied as
one of the two inputs to an adder 31. The output from microphone 11 is
applied directly to the second input of adder 31. The output from adder 31
is applied to a band-pass filter 33, the pass-band of which is centered on
the frequency of desired signals, and the output from that filter is the
useful output which is monitored to ascertain the presence of signal S.
Certain assumptions are made regarding the operation of the system shown in
FIG. 1, and naturally circuit components and values are selected which
will make these assumptions tenable. Thus the signal component S is
assumed to have the same phase and amplitude in all three inputs. This
will be true as long as the wavefront of the incoming sound wave is
substantially parallel to the line 17, and as long as the three
microphones have equal responses. Small deviations from parallelism will
have little effect since the phase difference varies inversely as the
wavelength of the sound signal S; and as regards amplitudes, microphones
can be suitably matched. Further, the noises are assumed to have the same
RMS amplitude at each input, but to be mutually incoherent, i.e., on the
assumption that the "noise" comes from a different bearing than that of
the target, "noise" signals X, U and Y will have equal RM amplitudes but
will have different phases. Since the signal is processed linearly in the
adder 31 and the filter 33, and since the noises are fixed in RMS
amplitude, the output signal-to-noise gain will not vary with input
signal-to-noise ratio. This "noise" is then inverted and added to signal
S+X in adder 31. The resultant complex waveform is then filtered in filter
33.
FIG. 7 shows the three original "noise" inputs at A, B and C in FIG. 1 and
the resultant "noise" output at E in FIG. 1. The effect of "adding" an
inversion of the selected "noise" signal is partly to cancel noise signal
"X" from the signal passing to filter 33.
One of the problems in the processing of signals is that the amplitude
statistics at the output tend to be decidely nongaussian, but tests show
that with the arrangement of FIG. 1 the output amplitude statistics for
noise are very close to gaussian so that measured RMS gains in
signal-to-noise ratio are not degraded in the detection process. The
measured RMS gains depend on input bandwidth, the number of inputs, and
the nature of the processed signal, as the table below indicates.
______________________________________
Octave 1% No. of
SIGNAL Band Bandwidth Inputs
______________________________________
Sinewave 4.6 db 6.2 db 3
Noise (at stated bandwidth)
4.1 5.7 3
Sinewave 5.5 7.2 4
Noise (at stated bandwidth)
5.0 6.7 4
Sinewave 7.3 8.6 6
Noise (at stated bandwidth)
6.8 8.1 6
______________________________________
As indicated by the above table, the arrangement of FIG. 1 can be modified
to accept 4 input or 6 inputs from a corresponding number of microphones.
FIG. 8 is a diagrammatic representation of a detection circuit having four
inputs 131, 133, 135 and 137 derived respectively from four microphones
arranged on a common line in the manner indicated in FIG. 1 for the three
microphone arrangement. The input 131 is applied to first and second
operational amplifiers AMP. 101 and AMP. 103. The input 133 is applied to
first, second and third operational amplifiers 105, 107 and 108. The input
135 is applied to a single operational amplifier 109. The input 137 is
applied to a single operation amplifier 111. In FIG. 8, each amplifier
shown has associated with it, for these inputs, a series input resistor
indicated by XXX.S (where XXX is the number of the amplifier) and a
feedback resistor XXX.F (where XXX is the number of the amplifier).
Amplifier 105 serves merely as no-loss inverter and its output is applied
through a series resistor 101X to amplifier 101. The amplifier 101 serves
as an adder and receives signal S+P (where S is the desired signal and P
is the noise) from input 131 and the inverted signal -S -Q (where Q is the
noise on input 133) and its output P -Q is applied to one input of a
discriminator 119.
Amplifier 109 serves merely as a no-loss inverter and its output is applied
through a first series resistor 103X to amplifier 103 and through a second
series resistor 107X to amplifier 107. The input 135 consists of the
signal S and noise "R", and the output from amplifier 109 is thus -S -R.
Amplifier 103 acts as an adder, and its output is thus P-R. This is
applied to discriminator 119 Amplifier 107 also acts as an adder, and its
output is thus Q-R, and this is applied to a discriminator 121. Amplifier
111 serves as a no-loss inverter of the signal S+T (T is the noise) from
input 137 and its output -S -T is applied through series resistor 108X to
amplifier 108. Amplifier 108 acts as an adder, and its output is thus Q-T,
and this is applied to the discriminator 121.
Each of the discriminators 119 and 121 operates in the manner described
above in connection with discriminator 27 of FIG. 1. The output from
discriminator 119 is applied through a series resistor 113X to an
operational amplifier 113, and the input 131 is also applied to this
amplifier through a series resistor 113S. The output from discriminator
121 is applied through a series resistor 115X to an operation amplifier
115, and the input 133 is applied through a series resistor 115S to this
amplifier.
Each of the amplifiers 113 and 115 acts as an adder, and their outputs are
applied respectively through series resistors 117S and 117X to an
operational amplifier 117. The output from that amplifier is passed
through a band-pass filter 123 to provide the useful output from the
circuit.
In the circuit of FIG. 8, all the operational amplifiers are integrated
circuits sold under the type number AMELCO 809 CE, and all the resistors
shown have a resistance of 100,000 ohms.
The manner of operation of the circuit of FIG. 8 will be seen to be similar
to that of the circuit of FIG. 1. First, pairs of inputs are combined to
eliminate the target signal S, and then the "noise" difference signals are
applied in pairs to discriminators.
However, although the three input system of FIG. 1 is effective for target
detection, the four-input system of FIG. 8 is required for beam forming,
since the phase response curve for the three-input system of FIG. 1 is at
maximum at 180 degrees relative phase difference between the three inputs.
Referring to FIG. 1, when the line 7 is mis-oriented so that the incoming
wavefront is not parallel to the line, then there will be a
phase-difference between the signals arriving from a target at the various
microphones. The phase difference will depend upon the angle by which line
7 is mis-oriented, and the distance between the microphones in terms of
wave-lengths of the sound from the target. As far as the circuits of FIGS.
1 and 8 are concerned, it is the phase difference between the various
inputs which is critical, and the curves in FIG. 9 show how the output,
expressed as voltage for 3-input systems according to FIG. 1, for 4-input
systems according to FIG. 8, and a 6-input system using the same method of
detection, vary with the phase difference between the inputs. It will be
clear to those skilled in the art that from the curves of FIG. 9 it is
possible to draw beam patterns for the three devices concerned. It can be
shown that all three devices produce wider beams than would be produced by
a simple additive arrangment of the same number of inputs. On the other
hand, the side lobes produced are smaller than with such additive arrays.
Such an arrangement provides a wide beam useful for the initial detection
of a target.
It has been found that the arrangements described are particularly
efficient when dealing with sinewave-like signals processed in a narrow
band, when the gain obtained is compared with that given by additive
processing (on an equal-beam-width basis). In a multi-microphone
arrangement it is found that a slightly larger number of microphones is
needed to produce a given beam width, compared with an additive system.
In an experimental array according to FIG. 8, band widths of 41 degrees
with side lobes 15 and 19 dB down have been achieved.
FIG. 10 illustrates an arrangement in which four microphones 201, 203, 205
and 207 are grouped in pairs, the outputs of the first pair of microphones
being fed to a discriminator 209 and the outputs of the second pair of
microphones being fed to a discriminator 211. The output from
discriminator 209 is passed through a band-pass filter 213 whose pass band
is centered on the frequency of the target signal, and the output of
discriminator 211 is passed through a similar bandpass filter 215. The
outputs from the two filters are combined in a further discriminator 217,
the output of which is passed through a third similar band-pass filter 219
to an output terminal 221. In this circuit, the discriminators are of the
type described above and shown in the earlier drawings. This circuit is
also shown and described in my Canadian application No. 115,982, and that
arrangement produces a narrow beam having a 10 degree beam width and with
side lobes which are 25 dB down. It provides a very useful arrangement for
direction-finding, as distinct from target detection.
The four inputs 131, 133, 135 and 137 of FIG. 8 can be used simultaneously
as the four input microphones 201, 203, 205 and 207 of FIG. 10. The
circuit of FIG. 8 is then used to effect early detection of the target,
and once the presence of a target has been established, the circuit of
FIG. 10 can be used to obtain an accurate bearing reading on the target.
If desired, switching can be provided so that two of the discriminators and
the filter of FIG. 10 can be utilized in the circuit of FIG. 8, in which
case the circuit of FIG. 8 is used to detect the target, and then the
circuit of FIG. 10 is established to locate the target.
The three-input discriminator arrangement of FIG. 1 and the 4- and 6-input
modifications described in connection with FIG. 8 provide arrangements in
which the signal-to-noise gain is independent of input-signal-to-noise
ratio; the output amplitude statistics are essentially gaussian; and the
signal to noise gain is superior to that of an adder for equal beam widths
for sinewave signals processed in narrow band where the noise background
is random or flow noise.
Of course, distant in-beam noise is processed as if it is a part of the
useful signal S, and for that type of noise the performance is very much
like that of a simple additive array. As in an additive array, in-beam
noise which differs considerably in frequency from the target frequency
can be reduced considerably by use of the various band-pass filters.
As mentioned above, in the case of the 4 microphone array both the
"detection" mode and the "direction finding" mode can be used, either
simultaneously, or sequentially by suitable switching. Thus the 41 degree
beam is used to detect the target, and then the target bearing is
ascertained using the alternative mode with its narrow pointed beam. For
this number (4) of microphones, the signal-to-noise gains for both modes
are about the same. Larger arrays using the "detection" mode can be built.
Thus 13 microphones designated 601 thru 613 can be arranged with
microphones 601 through 604 connected to a first 4-input discriminator
(e.g. FIG. 8) with microphones 604 through 607 connected to a second
discriminator; with microphones 607 through 610 connected to a third
discriminator; and with microphones 610 through 613 connected to a fourth
discriminator. The outputs of the discriminators can be passed through
suitable band pass filters, and the four outputs combined in a further
discriminator. The output from this last discriminator, after passing
through a band pass filter, serves as the useful output from the circuit.
In large sizes, arrays of this type can be appreciably superior to
additive arrays especially for small input bandwidths.
One useful feature of the apparatus described is its ability to operate
properly in a windy environment, in which there is much wind-induced noise
to contend with.
Non-acoustic system applications can include ECM and radio monitoring, and
low frequency radar.
It has been found that, in the absence of any bandpass filters, the noise
output bandwidth is appreciably greater than the noise input band-width.
It follows that if a final bandwidth filter has the same bandwidth as an
input bandwidth filter, since the noise frequencies have been band spread
in the non-linear processing, that the final bandpass filter provides a
distinct gain in signal-to-noise ratio.
The signal processing circuit or discriminator which has been described
above also finds application in the filtering of noise from a single input
signal.
Linear filtering is an extremely common operation in electronic systems,
and the basic idea of limiting the bandwidth of a system so as to include
the signal and exclude unwanted wide band noise has proven extremely
valuable.
An observed phenomena in the output spectrum levels of the three-input
discriminator device provides the key to a superior type of filtering in
which not only is the bandwidth limited in the normal way but noise within
the desired output bandwidth is reduced with respect to a signal. Signal
here refers to a sine wave having a relatively narrow bandwidth, that is
of long duration, whose frequency and amplitude remain essentially
constant. Real signals may have slight frequency and amplitude variations.
However, the signal bandwidth is assumed to be small compared with the
bandwidths of the noise within the output bandwidth of the filter being
considered. The signal characteristics will set the ultimate limit to the
bandwidth of this proposed type of filter just as they do in the linear
type of filter.
As previously discussed, the output spectra of the 3 and 4-input
discriminators effectively bandspread the noise whereas the linearly
processed signal was not bandspread. It was also shown that this effect
became proportionately much greater in narrow bandwidths. The basic
mechanism is related to the rate of change of amplitude and originates in
the non-linear discriminating process itself. Finally, it was shown that
the 3-input device proved to be highly efficient especially in narrow
bands where efficiency is defined by signal to noise gain for a given
beamwidth in array processing.
These characteristics and the following expression show that the
linear-non-linear processing has a useful application in filtering. The
autocorrelation function R.sub.x (t) is given by:
##EQU1##
where:
W.sub.1 =2.pi.f.sub.1, f.sub.1 is the lower frequency limit in the band
W.sub.2 =2.pi.f.sub.2, f.sub.2 is the upper frequency limit in the band
##EQU2##
T=delay time
A solution for this equation shows that for a value of T equal to the
period of one hertz at f.sub.o, the auto-correlation function is near zero
for a bandwidth equal to the center frequency. That is the
auto-correlation coefficient of a noise whose bandwidth is somewhat
greater than a octave band (i.e. BW=f.sub.o) will be near zero when
comparing the input and the output of a delay line of length T, the period
of 1 hertz at f.sub.o. This means that two delay lines of equal length
connected in series will provide the required three input for a
three-input processor. Assuming the proper relationship between bandwidth
and delay nT, the noises at all three inputs will be uncorrelated.
Referring now to FIG. 11, this is a block diagram showing the use of the
three-input discriminator in three basically similar stages of a filter.
An input terminal 401 is arranged to receive the noise-containing signal
to be processed, and is connected to an orthodox band-pass filter 403 with
a one-octave bandwidth approximately equal to 70% f.sub.o. The output of
this filter is applied to two series-connected delay lines 405 and 407 to
provide three inputs as shown to a discriminator circuit 409. Each delay
line produces a delay time T equal to the period of one cycle at the
center frequency, and the discriminator is the three input arrangement of
inverters, adders and discriminator shown in FIG. 1. The output from the
discriminator circuit is applied to a further filter 411 having a
bandwidth approximately equal to the bandwidth of the input noise to this
stage of the circuit, i.e. approximately 70% f.sub.o. The output from
filter 411 is applied in a similar manner as the input to stage 2, being
applied to two series connected delay lines 413 and 415 each producing a
delay time 2T (i.e. equal to twice the delay time T) and so providing the
three inputs shown to a further discriminator circuit 417. An output
filter 419 with a band width of only 35% f.sub.o is connected between
circuit 417 and two series connected delay lines 421 and 423 each
producing a time delay of 4T (i.e. equal to four times the delay time T).
This arrangement provides three inputs for discriminator circuit 425, the
output of which is connected through an output filter 427 having a
bandwidth of only 18% f.sub.o to an output terminal 429.
It will be seen that a one octave bandwidth is used at the input with unit
T rather than the calculated 100% f.sub.o bandwidth. The reason for this
is the phase response characteristic of the three-input device, which
peaks at 180.degree. phase difference. By limiting the noise bandwidth to
one octave for this value of T, this peak of the phase response curve
cannot occur, but as the above formula shows the auto-correlation function
is now greater than zero.
The effective filtering per stage can be calculated from the phase response
curve for the three-input device and extensive measurements with a swept
sine wave at the input confirm the calculations. However, these apparent
bandwidths cannot be used in calculating the signal-to-noise gain of each
stage because of the bandspreading effect of the non-linear processing of
noise. It was found that the filter mode arrangement of FIG. 11 yields the
best result. Great care must be used in measuring the input and output
noise spectra, together with the RMS change involved, to determine the
correct gain per stage. A measurement of the auto-correlation function of
the noise at the output of a linear-non-linear filter stage checked with
the measured noise bandwidth. In addition the amplitude distribution was
virtually gaussian. There were no measureable differences between the
output noise and an equivalent bandwidth of noise after linear filtering.
This allows the calculation of multistage performance of a
linear-non-linear filter design.
In linear filtering the correct gain is given by G=10 log Bwi/Bwo in dB,
where signal gain is assumed to be unity.
where Bw =input noise bandwidth
Bwo=output noise bandwidth
In this linear-non-linear type of filtering the gain per stage was measured
directly using the RMS measuring circuits. A value of X was calculated
from
##STR1##
using measured values of Bwi, Bwo and G, and this value is plotted on FIG.
12 (curve 431) as a function of bandwidth for five different input
bandwidths; 70%, 35%, 30%, 11% and 1% of f.sub.o. It will be seen that the
value of X increases with decreasing bandwidth. For comparison purposes
the standard value of X=10 for linear filtering is also shown (curve 433)
on FIG. 12.
Clearly there is a measurable gain using linear-non-linear processing when
compared to standard filtering. This gain derives partly from the normal
out-of-band rejection based on the phase response curves for the 3-input
device. It also derives, in part, from the bandspreading of noise from
within the pass band of the filter stage itself to outside of the final
pass band which the terminal filter elimates. This latter part of the gain
is very small at wide bandwidths but becomes increasingly important at
narrow bandwidths. Measurements of improvements were easy but unimpressive
at octave bandwidths. The gains recorded at 1% bandwidths were difficult
to measure but were entirely convincing. A special very narrow band pass
measurement filter which could be swept across the output spectra had to
be constructed. A linear regenerative delay line filter was used whose
band pass was held constant at 0.3% f.sub.o.
Using the measured values of X at various bandwidths and the calculated
number of stages required to achieve narrow bandwidths, the accumulated
gain of this filter as a function of bandwidth is plotted on FIG. 13. The
bottom curve 435 is the result of standard linear filtering over the three
decades of bandwidth change shown. Curve I shows the result of
linear-non-linear filtering and is supported by measurements to the 1%
bandwidth point, and is an extrapolation beyond that point. Curves II and
III are the results of starting with initially narrower bandwidths and are
largely extrapolations of the measured data. Since it is clear that this
type of filtering works best in narrow bands, it is always possible to
heterodyne wide band low frequency energy into relatively narrow band
higher frequency energy for more efficient processing.
Standard linear filtering is one dimensional filtering in that the transfer
function is related to frequency only. In the linear-non-linear type of
filtering just described, the device is both phase sensitive and amplitude
sensitive. As a result, the transfer function involves both frequency or
phase differences across a delay line and amplitude differences across the
same delay line. The mechanism of noise bandspreading from within the
output pass band can and does occur because the noise is not fully
correlated across the delay line even within the output pass band. This is
a fundamentally different situation from the in-beam distant noise case
which arises in spatial processing. Such in-beam noise is almost fully
correlated and is processed as signal. For this reason, the gains
achievable vis-a-vis the additive processing are limited to sources of
noise which are uncorrelated at each microphone. When filtering no such
restriction applies as the degree of noise correlation across the delay
line is determined by the auto-correlation function or by the relationship
of the noise bandwidth and the value of delay involved.
In FIG. 11, the 3-input discriminator is employed. It has the disadvantage
of using expensive and, in higher stages, very long delay lines. The
terminal filter in each stage has to be carefully set to achieve a proper
balance between the apparent gain of a given stage and the correct input
bandwidth to the next stage. A 4-input discriminator circuit arrangement
such as that shown in FIG. 14 using the circuit of FIG. 8 requires an
additional delay line per stage but would be less critical in its terminal
filter requirements and would require fewer stages to achieve a narrow
band output. Measurements on the 4-input arrangement showed a lower
efficiency, i.e. gain in signal-to-noise ratio per unit change in
bandwidth, than the 3-input arrangement. The values of T must be increased
by a factor of 3 rather than 2 per stage. The lower efficiency was more
apparent at wide bandwidths that at narrow bandwidths.
A final point concerns the rise time of this type of filtering. For a
multistage linear-non-linear filter the rise time is approximately twice
as long as the rise time for a standard linear filter of equal bandwidth.
This means that for signals of finite length, any post detector time
averaging gain will be 1.5 dB less for the linear-non-linear filter than
for the standard filter. This loss is relatively small when compared to
potential improvement of 10 to 30 dB.
The phase response for the three-input device or multiples thereof produces
wide main beams when used in an array. Side lobes are 18 dB down which is
lower than the corresponding additive processing for four-inputs. The wide
beam is useful in search and hence this is called the search mode of
operation.
The signal-to-noise gain is independent of input signal-to-noise ratio in
the 3-input device but depends on the input bandwidth | | |
