An electronic noise-reducing system which includes a plurality of adaptive filters forming multiple stages of noise reduction and producing greatly increased signal-to-noise ratio. The input for the primary channel of the first adaptive filter, which forms the first noise-reducing stage, is the signal including multitones buried in noise. The reference channel ideally uses signal-free noise as input. The output of the first adaptive filter is used as the input to the primary channel of the second or final adaptive filter, whereas the reference channel thereof is fed with "clean noise". The clean noise can be obtained as the output of the intermediate adaptive filter by feeding simultaneously both the primary and reference channels of the intermediate filter with the noise-reduced waveform present at the output of the first noise-reducing filter.

BACKGROUND OF THE INVENTION 
(1) Field of the Invention 
Subject invention is related to signal processing in general and more 
particularly to a multi-stage system using adaptive filters for canceling 
noise without affecting the signal and thereby increasing signal-to-noise 
ratio, i.e., S/N. 
(2) Description of the Prior Art 
In my U.S. Pat. No. 4,589,137 and my pending patent application, Ser. No. 
220,692, filed July 5, 1988 which are both incorporated here in entirety, 
one-stage noise-reducing systems were discussed wherein a single tone's 
S/N ratio was increased 17 dB by causing the noise in nearby frequency 
bands to attenuated by 17 dB. Extension of this work resulted in the 
"unmasking" of four tones (masked by broadband noise) at normalized 
frequencies of, roughly: 1, 2, 3 and 5 spread over a decade. The original 
masking noise was reduced over more than a decade of frequency by anywhere 
from 15 dB to 25 dB. 
The adaptive filter using the Least Mean Squares (LMS) algorithm favors 
noise peak region's and tends not to favor noise dip-regions, so that the 
15 dB attenuation occurred at dip regions while the 25 dB attenuation 
occurred at peak regions. A reasonable number would be 20 dB for the 
average attenuation of noise attained across a broadband. However, 20 dB 
attenuation is not sufficient for many applications, and so an attempt to 
cascade two or more stages of adaptive filters seemed worthwhile in order 
to try to attain 35 dB or 40 dB of attenuation. 
SUMMARY OF THE INVENTION 
We start with the output of a one-stage noise-canceling system. A reduction 
of about 20 dB in broadband noise over a band greater than a decade was 
accomplished routinely, using either a time-domain adaptive filter or a 
frequency-domain adaptive filter. But this noise floor, which we will 
arbitrarily call -20 dB, would not drop lower. In addition, if the 
original noise spectrum had a fairly sharp dip somewhere, this was ignored 
by the adaptive filter so that it became a residual peak, which we named a 
stalagmite. So the goal of the present invention was to start with the 
output O.sub.1 of a first adaptive filter F.sub.1 and to feed it in tandem 
into a second adaptive filter F.sub.2, with the assistance of a third or 
"intermediate" adaptive filter F.sub.int, and thereby lower the noise 
floor by perhaps an additional 13 dB, thus lowering the noise overall to 
-33 dB (-20 dB and -13 dB), all without greatly attenuating the N tones 
already unmasked in the output of the first filter. 
An object of subject invention is to have a noise-canceling system which 
does not require a large volume of sound-absorbing material. 
Another object of subject invention is to have a noise-canceling system 
which reduces the noise over a wide frequency bandwidth. 
Still another object of subject invention is to have a noise-canceling 
system which uses multiple adaptive filters in order to obtain larger 
overall noise reduction. 
Other objects, advantages and novel features of the invention may become 
apparent from the following detailed description of the invention when 
considered in conjunction with the accompanying drawings wherein:

DESCRIPTION OF THE PREFERRED EMBODIMENT 
It should be noted that throughout our discussion each of the adaptive 
filters has a primary (P) channel and a reference (R) channel with 
subscripts designating the adaptive filter under discussion. The problem 
in a two-stage noise canceler is: what to feed into the reference channel 
R.sub.2 of adaptive filter F.sub.2. The input to the primary channel 
P.sub.2 of adaptive filter F.sub.2 should be the output of F.sub.1. The 
desired input to reference channel R.sub.2, which is always the output of 
an adaptive filter called intermediate adaptive filter F.sub.int, would be 
a near-duplicate to the output of adaptive filter F.sub.1 except with the 
N tones removed, so that the reference channel could truly be said to 
contain only signal-free noise. We will refer to this as "clean noise". 
FIG. 1 shows the amplitude of sound pressure over a frequency range 
between f.sub.low and f.sub.high including both signal and wide band 
noise, the input sound pressure wave (signal+noise) being represented by 
curve 10 and the output of the first adaptive filter which is also the 
input to the second filter being represented by curve 12. 
A few methods will be described, which were used to lower the noise floor 
and/or to remove the stalagmites. 
a. Mirror-Image Method: It had been observed that any adaptive filter such 
as F.sub.1 did not "go after" the whole band of noise, designated by 14 in 
FIG. 2, simultaneously, but rather that it worked on the peak regions 
first, and the dip regions later. This tends to create a mirror-image of 
14, the input 18's (P.sub.1) noise, at the output O.sub.1 or 24 of F.sub.1 
(disregarding the signal for the moment), as shown in FIG. 2. Note that 
the tones survive undiminished. The output at O.sub.1, namely sound 
pressure wave 25, then feeds into the input P.sub.2 (26) of a second 
adaptive filter F.sub.2 (28). 
Simultaneously the "signal-free noise" or "noise plus residual signal" 
designated as 16 at reference input 23 (R.sub.1) of adaptive filter 
F.sub.1 (22) as shown in FIG. 2, feeds also into an adaptive filter called 
F.sub.intermediate or 30 (F.sub.int). This noise 16 feeds into both input 
channels 32 (P.sub.int) and 34 (R.sub.int), as shown in FIG. 2, via a tee 
connection. 
To define a term called "partial convergence" which we will use presently, 
we first define another term, "full convergence", as a term used to 
describe the action from an adaptive filter when it has canceled noise as 
much as possible. If full convergence is aborted, we call the process 
"partial convergence". When partial convergence is used in F.sub.int, the 
output at 36 (output.sub.int), namely 38, tends to be a mirror-image of 
the input 16 at 34 (R.sub.int input) as seen in FIG. 2 and thus is almost 
identical with sound pressure wave 25 at output 24 (O.sub.1) of F.sub.1 
(except for the virtual absence of signal components). We call the sound 
pressure wave 38 "clean noise". 
If now the sound pressure wave 38 at output.sub.int 36 is fed into 
reference input or channel 42 (R.sub.2) of adaptive filter 28 (F.sub.2), 
any stalagmites existing in sound pressure wave 25 at Output 24 (O.sub.1) 
will cancel at appreciably at Output 46 (O.sub.2) of adaptive filter 28 
(F.sub.2). The output at 46 has a wave form 48 where tones 50, 52, 54 and 
56 are unattenuated and the stalagmites 58 are low. Additionally some of 
the residual noise will cancel further, across the whole band. This is 
also shown in FIG. 3, using experimental data, wherein curve 60 shows a 
noise-spectrum plus a hidden tone, i.e., input S+N. Curve 62 shows the 
results of a first cancellation (observe the stalagmites on either side of 
the tone 66 of FIG. 3). Curve 64 shows the results of a second 
cancellation, where the stalagmites are much reduced. Since the 
mirror-image method works best for an "unwhitened" noise spectrum, it is 
advisable to "pre-unwhiten" the noise spectrum, via a spectral shaper of 
both magnitude and phase, into a first set of mountains and valleys 
feeding into a first noise-reduction system; and simultaneously 
"pre-unwhiten" the noise spectrum into a second set of mountains and 
valleys staggered or offset from the first set. 
b. The Noise-Decorrelation Method. In the mirror-image method the "clean 
noise" was generated in the intermediate adaptive filter by supplying its 
P.sub.int and R.sub.int inputs (via a tee connection) with the same raw 
input that was used in filter F.sub.1 's R.sub.1 channel as shown in FIG. 
2. In the noise-decorrelation method, as shown in FIG. 4, the "clean 
noise" curve 105 of FIG. 4D is generated in the intermediate filter 
F.sub.1 or 90 by supplying its P.sub.int and R.sub.int inputs (via a tee 
connection) with the noise-reduced Output.sub.1, namely curve 88, of 
filter F.sub.1 (100) as shown in FIG. 4. It should be noted that curve 87 
represents the input signal-plus-noise as shown in FIGS. 4A-4E. The 
signal, e.g., the four tones which exist superposed on the noise, as seen 
in the solid curve 88 of FIG. 4C, entering 90 (F.sub.int) must be removed 
in order to produce "clean noise" at the output of adaptive filter 90 
(F.sub.int). This can be done by one of the following methods. 
1. A delay of say 20 msec can be inserted within the reference channel 92 
(R.sub.int). This shifts the signal and the noise (in the reference 
channel) by 20 msec, in the time domain, enough to decorrelate the noise 
from its counterpart in P.sub.int (94), but with no effect on a repetitive 
signal, e.g., a tone, which keeps repeating its time-domain signature. 
Full convergence is allowed to take place in all three adaptive filters 
90, 100 and 102. Only the original tone peaks subtract because only they 
are still correlated. They decrease to small values. The spectrum at 
Output.sub.int (104) is then called "clean noise" and is shown as curve 
105 of FIG. 4D and again as curve 110 of FIG. 5. The final adaptive filter 
102 (F.sub.2) receives the "clean noise" at input R.sub.2 and receives the 
original output (O.sub.1) at input P.sub.2. A second cancellation then 
occurs within adaptive filter 102 (F.sub.2). The result is curve 114, as 
shown in FIG. 6. 
2. Alternatively, a delay of say 20 msec can be inserted in the primary 
channel 94 (P.sub.int) of the intermediate filter 90 (F.sub.int) as seen 
in FIG. 4. Full convergence must be aborted, since otherwise the filter 90 
(F.sub.int) will slowly cancel everything that is residing within channel 
94 (P.sub.int). Partial convergence of F.sub.int must be used, with a 
duration time of, for example, only 4 seconds and then the convergence 
being frozen. Filters 100 (F.sub.1) and 102 (F.sub.2), however, are 
meanwhile allowed to fully converge, and then run continuously. The 
original tone peaks in channel 92 (R.sub.int) disappear by subtraction 
because they are still highly correlated with their counterparts in 
channel 94 (P.sub.int). The spectrum 105 from output.sub.int (104) is 
again called "clean noise". The final adaptive filter 102 (F.sub.2) 
receives the "clean noise" at input channel 120 (R.sub.2), and receives 
the noise-reduced wave 88 from Output.sub.1 at input channel 122 input 
(P.sub.2). A second cancellation then occurs within 102 (F.sub.2). The 
result is the same as shown in FIG. 6, where the noise floor has dropped 
by almost an additional 20 dB, to a level of -40 dB. Recapitulating the 
events, a signal-plus-noise input, the output of the first adaptive 
filter, and the combination of first stage and second stage cancellation 
are shown in FIG. 7 as curves 130, 132 and 134 respectively. 
3. A different method of achieving "clean noise" is to send the 
noise-reduced spectrum of FIG. 1 through a thresholding device which clips 
the magnitude of each spectral peak down to that of the neighboring noise 
level. That portion of the spectrum which fails to be clipped is 
preserved, and used as the "clean noise" input to R.sub.2 of a second 
adaptive filter 102 (F.sub.2). This method is especially useful when the 
"surviving spectrum" is nearly flat, like white noise, as seen in FIG. 5. 
In all these methods, the "clean noise" goes to R.sub.2 of adaptive filter 
102 (F.sub.2), while the Output.sub.1 of filter F.sub.1 goes to P.sub.2 of 
the second filter, and the resultant second cancellation at Output.sub.2 
is indicated as curve 114 of FIGS. 4(e) and 6. 
In each of the three noise cancellation methods discussed, a third stage of 
cancellation can be cascaded by adding two additional adaptive filters 
after adaptive filter F.sub.2, giving a total of five adaptive filters. 
And for N stages of cancellation, the number of adaptive filters required 
is 2N-1. However, a law of diminishing returns shows up. For, although the 
noise floor seems to drop an additional 6 or 7 dB with three stages of 
cancellation, a new digital noise arises from the signal processing 
itself, making the usefulness of multi-stage cancellation doubtful for 
three or more stages. 
Another advantage of a three-filter method is displayed in FIG. 8 wherein 
curve 140 shows the relative frequency response of four tones after a 
single noise-cancellation. Basically the autospectrum at the output of 
first adaptive filter 100 (F.sub.1) is mathematically divided by the 
"clean noise" autospectrum at the output of adaptive filter (F.sub.int) ; 
but since we are using logarithmic units, namely dB, we subtract (not 
divide) the two autospectra. Notice the straightened-out baseline. The 
three-filter method also allows other 2-channel comparisons to be made 
such as cross-correlation and coherence. 
Thus a multiple stage noise-cancelling system according to the teachings of 
subject invention comprises a first adaptive filter and a plurality of 
pairs of adaptive filters, each stage requiring one pair of adaptive 
filters (wherein each adaptive filter includes one primary channel and one 
reference channel). Thus each stage of noise cancellation is cascaded by 
using an additional pair of adaptive filters wherein "clean noise" becomes 
the input to the reference channel of the second filter. The noise 
cancellation of the two successive stages is logarithmically additive. 
Many modifications and variations of the presently disclosed invention are 
possible in light of the above teachings. As an example, the number of 
stages in the noise cancellation system can be varied without deviating 
from the teachings of subject invention. The number of signal tones buried 
in the noise may vary. Furthermore, the frequency range over which the 
signal tones are distributed may also vary. It is therefore understood 
that within the scope of the appended claims, the invention may be 
practiced otherwise than as specifically described.