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Claims  |
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We claim:
1. A method for providing a differential microphone with a desired
frequency response, the differential microphone coupled to a filter having
a frequency response which is adjustable, the method comprising the steps
of:
receiving one or more output signals from the differential microphone;
determining a distance between the differential microphone and a source of
sound based on the received one or more output signals;
determining a filter frequency response, based on the determined distance,
to provide the differential microphone with the desired response; and
adjusting the filter to exhibit the determined response.
2. The method of claim 1 wherein the distance comprises an operating
distance.
3. The method of claim 1 wherein one or more values of a function of the
differential microphone outputs are determined at known distances and
wherein the step of determining a distance comprises the steps of:
observing a value of the function based on the received one or more output
signals; and
comparing the observed value with the one or more determined values to
determine the distance.
4. The method of claim 3 wherein the function comprises a ratio of outputs.
5. The method of claim 1 wherein the step of determining a filter frequency
response further comprises the step of determining a half-power frequency
of the filter based on a determined distance.
6. The method of claim 1 wherein the step of determining a distance is
performed in response to a user command.
7. The method of claim 1 wherein the step of determining a distance is
performed periodically.
8. The method of claim 1 wherein the step of determining a filter frequency
response comprises the step of determining a substantial inverse of the
frequency response of the differential microphone.
9. The method of claim 1 wherein the filter comprises a Butterworth filter.
10. The method of claim 1 wherein the step of determining a filter
frequency response is performed only when the one or more output signals
are produced in response to an active source of sound to be detected by
the microphone.
11. The method of claim 1 wherein the filter comprises and amplifier having
an adjustable gain and wherein the step of determining a filter frequency
response further comprises the steps of:
determining an amplifier gain, based on the determined distance for
providing the differential microphone with a desired output level; and
adjusting the amplifier to exhibit the determined gain.
12. An apparatus for providing a cardioid microphone with a desired
frequency response, the apparatus comprising:
an adjustable low-pass filter, coupled to the cardioid microphone; and
a controller, coupled to the cardioid microphone and the low-pass filter,
for adjusting the low-pass filter to provide the cardioid microphone with
the desired response based on one or more signals received from the
cardioid microphone.
13. An apparatus for providing a differential microphone with a desired
frequency response, the apparatus comprising:
an adjustable filter, coupled to the differential microphone; and
a controller, coupled to the differential microphone and the filter for
determining a distance between the differential microphone and a source of
sound based on one or more output signals received from the microphone and
for adjusting the filter to provide the differential microphone with the
desired response.
14. The apparatus of claim 13 wherein the controller comprises:
a detector for determining average values of the one or more signals
received from the differential microphone; and
a divider for determining a ratio of average signal values.
15. The apparatus of claim 13 wherein the filter is adjusted to exhibit a
frequency response which is a substantial inverse of the frequency
response of the differential microphone.
16. The apparatus of claim 13 wherein the filter comprises a Butterworth
filter.
17. The apparatus of claim 13 further comprising a threshold detector for
determining when a source of sound to be detected by the microphone is
active.
18. The apparatus of claim 13 wherein the differential microphone comprises
a pressure differential microphone and the filter comprises a low-pass
filter.
19. The apparatus of claim 13 wherein the differential microphone comprises
a velocity differential microphone and the filter comprises a high-pass
filter.
20. The apparatus of claim 13 wherein the differential microphone comprises
a velocity differential microphone and the filter comprises a band-pass
filter.
21. The apparatus of claim 13 wherein the differential microphone comprises
a displacement differential microphone and the filter comprises a
high-pass filter.
22. The apparatus of claim 13 wherein the differential microphone comprises
a cardioid microphone and the filter comprises a low-pass filter.
23. The apparatus of claim 13 wherein the filter comprises an amplifier
having a gain which is adjustable by the controller based on the
determined distance.
24. A microphone system comprising:
a differential microphone for providing one or more output signals;
a filter, coupled to the differential microphone and having a frequency
response which is adjustable, for filtering the output signals; and
a controller, coupled to the differential microphone and the filter, for
determining a distance between the differential microphone and a source of
sound based on the one or more output signals received from the
differential microphone and for adjusting the frequency response of the
filter based on the determined distance to provide a desired frequency
response for the system.
25. The microphone system of claim 24 wherein the filter comprises an
amplifier having a gain which is adjustable by the controller based on the
determined distance.
26. A communication device comprising:
a differential microphone for providing one or more output signals;
a filter, coupled to the differential microphone and having a frequency
response which is adjustable, for filtering the output signals; and
a controller, coupled to the differential microphone and the filter, for
determining a distance between the differential microphone and a source of
sound based on the one or more output signals received from the
differential microphone and for adjusting the frequency response of the
filter based on the determined distance to provide a desired frequency
response for the system.
27. The communication device of claim 26 wherein the filter comprises an
amplifier having a gain which is adjustable by the controller based on the
determined distance.
28. A method for providing a differential microphone with a desired
frequency response, the differential microphone coupled to a filter having
a frequency response which is adjustable, the method comprising the steps
of:
receiving one or more output signals from the differential microphone;
determining a filter frequency response based on the received one or more
output signals to provide the differential microphone with the desired
response, wherein the determined frequency response reflects a substantial
inverse of the frequency response of the differential microphone; and
adjusting the filter to exhibit the determined response.
29. A method for providing a differential microphone with a desired
frequency response, the differential microphone coupled to a Butterworth
filter having a frequency response which is adjustable, the method
comprising the steps of:
receiving one or more output signals from the differential microphone;
determining a Butterworth filter frequency response, based on the received
one or more output signals, to provide the differential microphone with
the desired response; and
adjusting the Butterworth filter to exhibit the determined response.
30. An apparatus for providing a differential microphone with a desired
frequency response, the apparatus comprising:
an adjustable filter, coupled to the differential microphone; and
a controller, coupled to the differential microphone and the filter, for
adjusting the filter to provide the differential microphone with the
desired response based on one or more signals received from the
differential microphone, the controller including
a detector for determining average values of the one or more signals
received from the differential microphone, and
a divider for determining a ratio of average signal values.
31. An apparatus for providing a differential microphone with a desired
frequency response, the apparatus comprising:
an adjustable filter, coupled to the microphone; and
a controller, coupled to the microphone and the filter, for adjusting the
filter to exhibit a frequency response based on one or more signals
received from the differential microphone, which frequency response is a
substantial inverse of the frequency response of the differential
microphone, to provide the differential microphone with the desired
response.
32. An apparatus for providing a differential microphone with a desired
frequency response, the apparatus comprising:
an adjustable Butterworth filter, coupled to the microphone; and
a controller, coupled to the microphone and the Butterworth filter, for
adjusting the Butterworth filter to provide the differential microphone
with the desired response based on one or more signals received from the
differential microphone.
33. An apparatus for providing a pressure differential microphone with a
desired frequency response, the apparatus comprising:
an adjustable low-pass filter, coupled to the pressure differential
microphone; and
a controller, coupled to the pressure differential microphone and the
low-pass filter, for adjusting the low-pass filter to provide the pressure
differential microphone with the desired response based on one or more
signals received from the pressure differential microphone.
34. An apparatus for providing a velocity differential microphone with a
desired frequency response, the apparatus comprising:
an adjustable high-pass filter, coupled to the velocity differential
microphone; and
a controller, coupled to the velocity differential microphone and the
high-pass filter, for adjusting the frequency response of the high-pass
filter to provide the velocity differential microphone with the desired
response based on one or more signals received from the velocity
differential microphone.
35. An apparatus for providing a displacement differential microphone with
a desired frequency response, the apparatus comprising:
an adjustable high-pass filter, coupled to the displacement differential
microphone; and
a controller, coupled to the displacement differential microphone and the
high-pass filter, for adjusting the frequency response of the high-pass
filter to provide the displacement differential microphone with the
desired response based on one or more signals received from the
displacement differential microphone.
36. The apparatus of claim 13 wherein the distance comprises an operating
distance.
37. The microphone system of claim 24 wherein the distance comprises an
operating distance.
38. The communication device of claim 26 wherein the distance comprises an
operating distance. |
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Claims |
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Description |
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FIELD OF THE INVENTION
This invention relates generally to differential microphones and more
specifically to adjusting the frequency response of differential
microphones to provide a desired response.
BACKGROUND OF THE INVENTION
Directional microphones offer advantages over omnidirectional microphones
in noisy environments. Unlike omnidirectional microphones, directional
microphones can discriminate against both solid-borne and air-borne noise
based on the direction from which such noise emanates, defined with
respect to a reference axis of the microphone. Differential microphones,
sometimes referred to as gradient microphones, are a class of directional
microphones which offer the additional advantage of being able to
discriminate between sound which emanates close to the microphone and
sound emanating at a distance. Since sound emanating at a distance is
often classifiable as noise, differential microphones have use in the
reduction of the deleterious effects of both off-axis and distant noise.
Differential microphones are microphones which have an output proportional
to a difference in measured quantities. There are several types of
differential microphones including pressure, velocity and displacement
differential microphones. An exemplary pressure differential microphone
may be formed by taking the difference of the output of two microphone
sensors which measure sound pressure. Similarly, velocity and displacement
differential microphones may be formed by taking the difference of the
output of two microphone sensors which measure particle velocity and
diaphragm displacement, respectively. Differential microphones may also be
of the cardioid type, having characteristics of both velocity and pressure
differential microphones.
As a general matter, differential microphones exhibit a frequency response
which is a function of the distance between the microphone and the source
of sound to be detected (e.g., speech). For example, when a pressure
differential microphone is located in the near field of a speech source
(that area of the sound field exhibiting a large spatial gradient and a
large phase shift between acoustic pressure and particle velocity, e.g.,
less than 2 cm. from the source), its frequency response is essentially
flat over some specified frequency range. At somewhat greater distances
from the speech source, the frequency response tends to over-emphasize
high frequencies. When a velocity differential microphone is in the near
field of a speech source, its frequency response tends to over-emphasize
low frequencies, while at somewhat greater distances, its response is
essentially flat for some specified frequency range.
Because their frequency response varies with distance, differential
microphones are ideally suited for use at a constant distance from a
source, for example, at a distance where microphone response is flat. In
practice, however, users of pressure differential microphones often vary
the distance between microphone and mouth over time, causing the
microphone to exhibit an undesirable, variable gain to certain frequencies
present in speech. For a pressure differential microphone, unless a close
constant distance is maintained, high frequencies present in speech will
be emphasized. For a velocity differential microphone, unless somewhat
greater distances are maintained, lower frequencies will be emphasized.
SUMMARY OF THE INVENTION
A method and apparatus are disclosed for providing a desired frequency
response of a differential microphone of order n. A desired response is
provided by operation of a controller in combination with an adjustable
filter. The controller receives microphone output and determines, based on
the output, a filter frequency response needed to provide any desired
response. For example, the controller may determine a filter frequency
response which equals or approximates the inverse of the microphone
response to provide an overall flat response. Alternatively, an exemplary
response could be provided which is optimal for telephony. The
determination by the controller can include a complete definition of the
filter response (including absolute output level) or a definition of just
those parameters used in modifying one or more aspects of a given or
quiescent response. The filter is adjusted by the controller to exhibit
the determined frequency response thereby providing a desired response for
the microphone.
In an illustrative embodiment of the present invention for a pressure
differential microphone, the controller makes an automatic determination
of distance between microphone and sound source (this distance being
referred to as the "operating distance") and adjusts a low-pass filter to
compensate for the gain to high frequencies exhibited by the microphone at
or about the determined distance. The operating distance may be determined
one or more times (e.g., periodically) during microphone use. Automatic
distance determination may be accomplished by comparing observed
microphone output at an unknown operating distance to known outputs at
known distances.
In the illustrative embodiment, the frequency response of the low-pass
filter is dependent upon the frequency response of the pressure
differential microphone as a function of operating distance and microphone
order. Pressure differential microphones have a frequency response which
is flat at close operating distances and at large operating distances
increases at a rate of 6 n dB per doubling of frequency (i.e., per
octave), where n is an integer equal to the order of the pressure
differential microphone. For a given determined distance, the filter
frequency response is adjusted, and this may include an adjustment to
absolute output level.
In the case of the illustrative embodiment for use with a first or second
order pressure differential microphone, the filter is a first or second
order Butterworth low-pass filter, respectively, with a half-power
frequency adjustable to the microphone's 3 dB gain frequency, which is a
function of operating distance.
Brief Description of the Drawings
FIG. 1 presents an exemplary block diagram embodiment of the present
invention.
FIG. 2 presents a relative frequency response plat of first through fifth
order pressure differential microphones as a function of kr, where k is
the acoustic wave number and r is the operating distance to a source.
FIG. 3 presents a schematic view of a first order pressure differential
microphone in relation to a point source of sound.
FIG. 4 presents a relative frequency response plot for a first order
pressure differential microphone as a function of kr.
FIG. 5 presents a schematic view of a second order pressure differential
microphone in relation to a point source of sound.
FIG. 6 presents a relative frequency response plot for a second order
pressure differential microphone as a function of kr.
FIG. 7 presents a schematic view of a first order pressure differential
microphone in relation to an on-axis point source of sound.
FIG. 8 presents sound pressure level ratio plots for two zeroth order
pressure differential microphones which form a first order pressure
differential microphone.
FIG. 9 presents a schematic view of a second order pressure differential
microphone in relation to an on-axis point source of sound.
FIG. 10 presents sound pressure level ratio plots for two first order
pressure differential microphones which form a second order pressure
differential microphone.
FIG. 11 presents a detailed exemplary block diagram embodiment of the
present invention.
DETAILED DESCRIPTION
Introduction
FIG. 1 presents an illustrative embodiment of the present invention. In
FIG. 1, a differential microphone 1 of order n provides an output 3 to a
filter 5. Filter 5 is adjustable (i.e., selectable or tunable) during
microphone use. A controller 6 is provided to adjust the filter frequency
response. The controller 6 can be operated via a control input 9.
In operation, the controller 6 receives from the differential microphone 1
output 4 which is used to determine the operating distance between the
differential microphone 1 and the source of sound, S. Operating distance
may be determined once (e.g., as an initialization procedure) or multiple
times (e.g., periodically). Based on the determined distance, the
controller 6 provides control signals 7 to the filter 5 to adjust the
filter to the desired filter frequency response. The output 3 of the
differential microphone 1 is filtered and provided to subsequent stages as
filter output 8.
Frequency Response of Pressure Differential Microphones
One illustrative embodiment of the present invention involves pressure
differential microphones. In general, the frequency response of a pressure
differential microphone of order n ("PDM(n)") is given in terms of the nth
derivative of acoustic pressure, p=P.sub.o e.sup.-jkr /r, within a sound
field of a point source, with respect to operating distance, where P.sub.o
is source peak amplitude, k is the acoustic wave number (k=2.pi./.lambda.,
where .lambda. is wavelength and .lambda.=c/f, where c is the speed of
sound and f is frequency in Hz), and r is the operating distance. That is,
##EQU1##
FIG. 2 presents a plot of the magnitude of Eq. 1 for n=1 to 5. The figure
shows the gain exhibited by a PDM(n), n=1 to 5, at high frequencies and
large distances, i.e., at increasing values of kr.
For purposes of this discussion, it is instructive to examine the frequency
response of a PDM as a function of kr. Therefore, two illustrative
developments are provided below. The developments address the frequency
response of both first and second order PDMs as functions of kr, and are
made in terms of a finite difference approximation for
##EQU2##
In light of Eq. 1 and the developments which follow, it will be apparent
to the ordinary artisan that the analysis can be extended in a
straight-forward fashion to any order PDM. Also, because the response of
velocity and displacement microphones is related to that of a pressure
differential microphone by factors of 1/j.omega. and 1/(j.omega.).sup.2,
respectively, the ordinary artisan will recognize that Eq. 1 and the
developments which follow are adaptable to systems employing velocity and
displacement differential microphones, as well as cardioid microphones.
First Order Pressure Differential Microphones
A schematic representation of a first order PDM in relation to a source of
sound is shown in FIG. 3. The microphone 10 typically includes two sensing
features: a first sensing feature 11 which responds to incident acoustic
pressure from a source 20 by producing a positive response (typically, a
positively tending voltage), and a second sensing feature 12 which
responds to incident acoustic pressure by producing a negative response
(typically, a negatively tending voltage). These first and second sensing
features 11 and 12 may be, for example, two pressure (or "zeroth" order)
microphones. The sensing features are separated by an effective acoustic
distance 2d, such that each sensing feature is located a distance d from
the effective acoustic center 13 of the microphone 10. A point source 20
is shown to be at an operating distance r from the effective acoustic
center 13 of the microphone 10, with the first and second sensing features
located at distances r.sub.1 and r.sub.2, respectively, from the source
20. An angle .theta. exists between the direction of sound propagation
from the source 20 and the microphone axis 30.
For a spherical wave generated by source 20 at operating distance r from
the center 13 of the microphone 10, the acoustic pressure incident on the
first sensing feature 11 is given by:
##EQU3##
The acoustic pressure incident on the second sensing feature 12 is given
by:
##EQU4##
The distances r.sub.1 and r.sub.2 are given by the following expressions:
##EQU5##
If r>>d (when the microphone is in the far field of source 20) or
.theta..apprxeq.0.degree. (when source 20 is located near microphone axis
30), then
r.sub.1 .apprxeq.r-d cos .theta. (4a)
and
r.sub.2 .apprxeq.r+d cos .theta. (4b)
The response of the microphone can then be approximated by a first-order
difference of acoustic pressure, .DELTA.p, and is given by:
##EQU6##
The magnitude of .DELTA.p, .vertline..DELTA.p.vertline., is:
##EQU7##
For kd<<1,
sin (kd cos .theta.).apprxeq.kd cos .theta., (7)
and
cos (kd cos .theta.).apprxeq.1. (8)
Therefore,
##EQU8##
For a near-field source, i.e., kr<<1,
##EQU9##
and for a far-field source, i.e., kr>>1 and r>>d,
##EQU10##
Note that Eq. 11 contains no frequency dependent terms. That is, Eq. 11 is
independent of the wave number, k (wave number is proportional to
frequency, i.e.,
##EQU11##
where f is frequency in Hz and c is the speed of sound). As such, a first
order PDM in the near field of a point source 20 has a frequency response
which is substantially flat. On the other hand, Eq. 12 does depend on the
acoustic wave number, k. FIG. 4 shows the frequency dependence of the
first order PDM for values of kr from 0.1 to 10. For values of kr<0.2 the
response is substantially uniform or flat. Above kr=1.0 the response rises
at 6 dB per doubling kr. (For this figure, kd<<1 and r>>d.)
Second Order Pressure Differential Microphones
A second order PDM is formed by combining two first order PDMs in
opposition. Each first order PDM can have a spacing of 2d.sub.1 and an
acoustic center 65,67. The PDMs can be arranged in line and spaced a
distance 2d.sub.2 apart as shown in FIG. 5. The response of the second
order PDM can be approximated by a second order difference of acoustic
pressure, .DELTA..sup.2 p, in a sound field of a spherical radiating
source 70 at operating distance r from the acoustic center 60 of the
microphone 35:
.DELTA..sup.2 p=p.sub.1 -p.sub.2 -p.sub.3 +p.sub.4 (13)
where
##EQU12##
and r.sub.i, for i=1 to 4 are:
##EQU13##
If r>>d.sub.3 and r>>d.sub.4 or .theta..apprxeq.0.degree., then:
r.sub.1 .apprxeq.r-d.sub.4 cos .theta.; (19)
r.sub.2 .apprxeq.r-d.sub.3 cos .theta.; (20)
r.sub.3 .apprxeq.r+d.sub.3 cos .theta.; (21)
and
r.sub.4 .apprxeq.r+d.sub.4 cos .theta.. (22)
Therefore,
##EQU14##
For kd.sub.4 <1,
##EQU15##
Equations similar to Eqs. 24 and 25 can be written for cos (kd.sub.3 cos
.theta.) and sin (kd.sub.3 cos .theta.) when kd.sub.3 <<1. For kd.sub.4
<<1 and kd.sub.3 <<1 then:
##EQU16##
For a near-field source (kr<<1),
##EQU17##
and for a far-field source (kr>>1; r>>d.sub.3 ; r>>d.sub.4),
##EQU18##
As is the case with Eq. 11, Eq. 28 contains no frequency dependent terms.
Thus, a second order PDM 35 in the near field of a point source 70 has a
frequency response which is flat. Like Eq. 12, Eq. 29 does depend on
frequency. However, Eq. 29 exhibits a rise in response at high frequencies
at twice the rate of that exhibited by Eq. 12.
FIG. 6 shows the relative frequency response of a second order PDM versus
kr. For kr<1, the response is substantially flat. Above kr=1, the response
rises at 12 dB per doubling of kr. (For this Figure, kd.sub.3 <<1 and
kd.sub.4 <<1 and r>>d.sub.3 and r>>d.sub.4, for a far field source, or
.theta..apprxeq.0.degree..)
Automatic Distance Determination
The illustrative embodiment of the present invention includes an automatic
determination of operating distances by the controller 6. This embodiment
facilitates determining operating distance continuously or at periodic or
aperiodic points in time.
For a first order PDM, the controller 6 can use ratios of output levels
from two zeroth order PDMs (of the first order PDM) to estimate the
operating distance between source and microphone. This approach involves
making a predetermined association between ratios of zeroth order PDM
output levels and operating distances at which such ratios are found to
occur. At any time during microphone operation, a ratio of zeroth order
PDM output levels can be compared to the predetermined ratios at known
distances to determine the then current operating distance.
Consider the first order PDM 75 which comprises zeroth order PDMs A 11 and
B 12 shown in FIG. 3. The response of zeroth order PDMs A 11 and B 12 can
be written (from Eqs. 2a and 2b) as
##EQU19##
Using Eqs 4a,b, Eqs. 30 and 31 can be rewritten as follows:
##EQU20##
The magnitude of the response of the microphones A 11 and B 12 (for
r>d.vertline.cos.theta..vertline.) is therefore:
##EQU21##
For an illustrative configuration of FIG. 7, .theta.=0 and the ratio of
Eqs. 34 and 35 is:
##EQU22##
Ratio A.sub.r is a function of operating distance r (between source 73 and
microphone acoustic center 78) and d, a physical parameter of the PDM
design. For a given first order PDM, the parameter d is fixed such that
A.sub.r varies with r only.
A plot of A.sub.r (Eq. 36) for two exemplary first order PDM array
configurations (d=1 cm and d=2 cm) is shown in FIG. 8. The figure shows
that changes in A.sub.r are sizeable for a range of r. With knowledge of
this data, operating distances for measured A.sub.r values may be
determined.
In determining operating distance, the controller of the illustrative
embodiment makes a determination of the ratio of observed microphone
output levels. This ratio represents an observed value for A.sub.r : Ar.
By rewriting Eq. 36, an estimate for r as a function of the observed ratio
A.sub.r is: is:
##EQU23##
Eq. 37 could be implemented by the controller 6 of the illustrative
embodiment in either analog or digital form, or in a form which is a
combination of both. For example, the controller 6 may use a
microprocessor to determine r either by scanning a look-up table
(containing precomputed values of r as a function of A.sub.r), or by
calculating r directly in a manner specified by Eq. 37, to provide control
for analog or digital filter 5. Distance determination by the controller 6
can be performed once or, if desired, continually during operation of the
PDM.
For a second order PDM, the controller 6 can use ratios in output levels
between two first order PDMs (of the second order PDM) to estimate the
operating distance between source and microphone. If a predetermined
association is made between ratios of first order PDM output levels and
operating distances at which such ratios are found to occur, an observed
ratio of first order PDM output levels can be compared to the
predetermined ratios at known distances to determine the then current
operating distance.
Consider the second order PDM which comprises first order PDMs A and B
shown in FIG. 9 for .theta.=0. The response of first order PDMs A 80 and B
90 can be written (from Eq. 10) as
##EQU24##
respectively, for kd.sub.1 <<1, and where r.sub.A and r.sub.B are
operating distances from source 100 to the acoustic centers, 81 and 91, of
PDMs A and B, respectively. If the signal from each of the microphones A
and B is low-pass filtered by the controller 6, then kr.sub.A <<1 and
kr.sub.B <<1, and:
##EQU25##
Since,
r.sub.A =r-d.sub.2 (42)
and
r.sub.B =r+d.sub.2, (43)
then
##EQU26##
where r is the operating distance from source 100 to the acoustic center
95 of the second order PDM.
The ratio of Eq. 44 to Eq. 45 is:
##EQU27##
Ratio A.sub.r is a function of operating distance r and other physical
parameters of the PDM design. For a given second order PDM the parameters
d.sub.1 and d.sub.2 are fixed such that A.sub.r varies with r only.
A plot of A.sub.r (Eq. 46) for two exemplary second order PDM array
configurations (d.sub.2 =0.5 cm, d.sub.2 =1.0 cm, and d.sub.1 =0.5 cm) is
shown in FIG. 10. The figure shows that changes in A.sub.r are quite
sizeable for the range of r. With knowledge of this data, operating
distances may be determined.
In determining an operating distance, the controller 6 of the illustrative
embodiment makes a determination of the ratio of observed microphone
output levels (after low pass filtering). This ratio represents an
observed value for A.sub.r :A.sub.r. By rewriting Eq. 46, an estimate for
r as a function of the observed ratio A.sub.r is:
##EQU28##
As with the case above, Eq. 47 could be implemented by the controller 6 of
the illustrative embodiment in either in analog or digital form, or in a
form which is a combination of both. Again, distance determination by the
controller 6 can be performed once or, if desired, continually during the
operation of the PDM.
Regardless of which order PDM an embodiment uses, it is preferred that the
controller 6 determine operating distance only when the source of sound to
be detected is active. Limiting the conditions under which calibration may
be performed can be accomplished by calibrating only when the PDM output
signal equals or exceeds a predetermined threshold. This threshold level
should be greater than the PDM output resulting from the level of expected
background noise.
The low-pass filtering performed by the controller 6 on the outputs of each
microphone insures that, as a general matter, only those frequencies for
which the microphone's response is flat are considered for the
determination of distance. This has been expressed as kr<<1 in the
developments above. The cutoff frequency for this filter can be determined
in practice by, for example, determining an outer bound operating distance
and then solving for the frequency below which the microphone response is
flat. Thus, with reference to FIG. 2, the frequency response of various
microphones is flat for kr less than 0.5, approximately. Given an outer
bound distance, r.sub.OB, the cutoff frequency should be less than
##EQU29##
Filter Selection
Once distance determination by the controller 6 is performed, a filter 5 is
selected. As discussed above, the filter 5 provides a frequency response
which provides the desired frequency response of the PDM(n). So, for
example, the combination of the microphone and a selected filter 5 may
exhibit a frequency response which is substantially uniform (or flat).
In the illustrative embodiment for pressure differential microphones,
filter 5 exhibits a low-pass characteristic which equals or approximates
the inverse (i.e., mirror image) of PDM(n) frequency response. Such a
filter characteristic may be provided by any of the known low-pass filter
types. Butterworth low-pass filters are preferred for first and second
order PDMs since the frequency response of a first or second order PDM
exhibits a Butterworth-like high-pass characteristic.
In selecting a filter, the half-power frequency and roll-off rate of the
pass band should be determined. In the illustrative embodiment, the
half-power frequency, f.sub.hp, of filter 5 should match the 3 dB gain
point of the frequency characteristic of the PDM(n). Half-power frequency
can be determined directly from the equation for the frequency response of
the PDM(n), .vertline..DELTA..sup.n p.vertline., with knowledge of r from
the distance determination procedures described above. For example, the 3
dB frequency of a first order PDM is determined with reference to Eq. 10
by solving for the value of frequency for which:
##EQU30##
(all parameters on the right hand side of Eq. 10 other than
.sqroot.1+k.sup.2 r.sup.2 are constant for a given microphone
configuration and therefore contain no frequency dependence). Since
##EQU31##
an expression for the half-power frequency of the filter 5 (3 dB
frequency), f.sub.hp, as a function of distance is:
##EQU32##
where c is the speed of sound and r is the determined distance.
For a second order PDM, the 3 dB frequency is determined with reference to
Eq. 27 by solving for the value of frequency for which:
##EQU33##
Since
##EQU34##
an expression for the half-power frequency of the filter 5, f.sub.hp, as a
function of distance is:
##EQU35##
where c is the speed of sound and r is the determined distance.
Regarding low-pass filter 5 roll-off, a rate should be chosen which closely
matches (in magnitude) the rate at which the PDM high frequency gain
increases. In the illustrative case of low-pass Butterworth filters for
use with first and second order PDMs, this is accomplished by choosing a
filter of order equal to that of the microphone (i.e., a first order
filter for a first order PDM; a second order filter for second order PDM).
Roll-off rate may be fixed for filter 5, or it may be selectable by
controller 6.
In light of the above discussion, it will be apparent to one of ordinary
skill in the art that either analog or digital circuitry could be utilized
to implement the filter 5. Of course, if a digital filter is employed,
additional analog-to-digital and digital-to-analog converter circuitry may
be needed to process the microphone output 3. Moreover, control of an
adjustable filter 5 by the controller 6 can be achieved by any of several
well-known techniques such as the passing of filter constants from the
controller 6 to a finite impulse response or infinite impulse response
digital filter, or by the communication of signals from the controller 6
to drive voltage-controlled devices which adjust the values analog filter
components. Also, the division of tasks between the controller 6 and the
filter 5 described above is, of course, exemplary. Such division could be
modified, e.g., to require the controller 6 to determine distance, r, and
pass such information to the filter 5 to determine the requisite frequency
response.
Like relative frequency response, the absolute output level of a
differential microphone varies with operating distance r, as can be seen
in general from the magnitude of Eq. 1, and in particular, for first and
second order PDMs, from Eqs. 10 and 27, respectively. Since an estimate of
operating distance is already obtained by an embodiment of the present
invention for the purpose of adjusting the filter's relative frequency
response, this information can be employed for the purpose of determining
a gain to compensate for absolute output level variations.
The gain can be derived for any differential microphone of given order. For
the illustrative embodiments previously discussed, the first and second
order gain adjustment is determined as the inverse of the
frequency-invariant portion of Eqs. 10 and 27, respectively. For example,
if the source is located on-axis, then .theta.=0 and cos .theta.=1. In
this case, Eq. 10 shows that for the first order PDM, the gain would be
set proportional to
G.sub.1 =r.sup.2 -d.sup.2. (52)
An estimate of G.sub.1, G.sub.1, can be obtained by using the estimate r
previously obtained from Eq. 37, and d, a fixed design parameter.
Likewise, for | | |
