For expository convenience, the present invention is illustrated with reference to the matching of characteristics of microphones used in a probe for measuring sound intensity. It should be recognized, however, that the invention can advantageously be applied in a number of other situations requiring precise matching of phase and/or amplitude characteristics.
Sound intensity is a vector measurement of the average rate of sound energy transmitted in a specified direction through a unit area normal to this direction at a specific point. Such measurements are commonly used to quantify, for example, the noise emitted from industrial equipment or machinery.
Sound intensity measurements are conventionally made using a pair of precisely matched, closely spaced microphones (commonly known as a sound intensity "probe"). As explained more fully in Pope, J., "The Two-Microphone Sound Intensity Probe," Journal of Vibration, Stress, and Reliability in Design, Vol. 110, January, 1988, pp. 97-103, sound intensity is related to the cross-spectrum detected by the two microphones in the frequency domain according to the following formula: EQU I.sub.r (.omega.)=-Im(G.sub.AB)/.pi..omega..DELTA.r (1)
The equivalent expression in the time domain is: ##EQU1## where: .pi.is the density of the acoustic medium;
.omega.is the frequency in radians; PA1 .DELTA.r is the effective microphone separation; PA1 p.sub.a is the sound pressure at microphone a; PA1 p.sub.b is the sound pressure at microphone b; PA1 I.sub.r is sound intensity in direction r from a to b; and PA1 Im(G.sub.AB) represents the imaginary part of the cross-spectrum between p.sub.a and p.sub.b.
The measurements necessary to make the above-detailed calculations can be performed using two different types of instruments: Fast Fourier Transform (FFT) spectrum analyzers and real time octave analyzers. Each has its respective advantages and disadvantages.
An FFT analyzer, such as the Hewlett-Packard HP 35660A and 35665A, operates by digitally sampling an analog input signal and performing a fast Fourier transform on the sampled data to determine its spectral composition. The results of the Fourier analysis are a series of spectral coefficients, one corresponding to each of a plurality of frequency "bins."
A drawback of the FFT analyzer technique is that the frequency bins into which the Fourier analysis resolves the spectral composition are uniformly spaced in frequency. A 400 bin analysis of the spectrum between 0 and 10 KHz, for example, results in bins that each correspond to 25 Hz. While such resolution is more than adequate for higher frequencies, it is inadequate at low frequencies.
To provide adequate resolution at low frequencies, a second FFT measurement spanning a smaller range (such as 0-1 KHz) is generally required. The results of the two measurements are then combined to yield a final result. This procedure, however, is problematical since a single instrument cannot make both measurements at the same time. The combined measurement instead reflects two different measurements made at two different times. This non-real time operation is often unacceptable.
Real time octave analyzers, in contrast, use a series of bandpass filters (often implemented digitally in a sampled data system) to determine spectral composition. These filters are generally centered at logarithmically-spaced frequencies (often in one-third octave steps), thereby providing increasingly finer resolution at increasingly lower frequencies.
(The human ear perceives sound in a logarithmic fashion, making octave-based analysis a popular mode of measurement. Further, most acoustic standards, such as the IEC 1043 Instruments for the Measurement of Sound Standard, are specified in this fashion.)
Several real time octave analyzers are known, including the Bruel & Kjaer 2133 and the HP 35665A. (The HP 35665A, which was noted above as an FFT analyzer, combines FFT and real time octave analysis capability in a single instrument.) In the B&K 2133, sound intensity is calculated by combining the outputs of the bandpass filters to perform a sampled data counterpart to the operation described in equation (2) above.
In order for the cross-channel data acquired in either an FFT or real time octave analyzer measurement setup to be useful, the characteristics of the probe microphones must be precisely matched. Amplitude matching is relatively easy to obtain. (Further, the sound intensity calculation is less sensitive to amplitude mismatch. Cf. Pope, supra.) Phase matching, however, is difficult.
Two primary mechanisms contribute to phase mismatches between otherwise identical microphones. The first relates to variability in diaphragm damping. This phenomenon is particularly evidenced at frequencies above a few hundred Hz. Due to manufacturing tolerances, otherwise identical microphones may commonly exhibit a difference in phase response of several degrees when measured at one kilohertz.
The second mechanism that contributes to microphone phase mismatch is an interaction between a cavity behind the microphone diaphragm and a hole venting this cavity to the atmosphere, effectively creating an acoustical low pass filter. Differences in this static pressure equalization between microphones can cause a phase variance between otherwise matched microphones of up to three degrees at twenty hertz. (Twenty hertz is typically the low frequency limit for sound intensity measurements.)
In order for a pair of microphones to be successfully utilized for sound intensity measurements, their phase characteristics should generally be matched to within less than 0.3 degrees throughout the measurement span of interest. (This 0.3 degree figure is highly application dependent. In some instances a variance of up to 1 degree may be acceptable. In others, a variance of less than 0.1 degrees may be required.). As noted, current manufacturing processes can only reliably match microphones to within about 3 degrees, an order of magnitude higher than this approximate threshold requirement. Accordingly, microphones must generally be matched by a tedious manual selection process.
Low frequency phase error is usually the most critical in making sound intensity measurements. As noted, sound intensity is a vector measurement. The direction of the measured sound is determined by the phase delay with which the same sound reaches the two microphones. Since, at low frequencies, the sound wavelength is several meters long, and the microphones may only be spaced by a centimeter or two, the cos .phi. phase delay associated with off-axis sound vectors is quite small and would be masked by even small phase errors (.phi. is here the angle between the intensity vector and the center line of the microphones).
If the problem of low frequency phase error could be solved, the remaining task of selecting microphones by manually matching high frequency responses would be considerably simplified.
While in real time octave analyzers, the microphones themselves must be precisely matched, in FFT analyzers it is possible to match the microphones using correction factors internal to the analyzer. In particular, it is possible to determine the phase error between a pair of microphones in the frequency domain, and then multiply the cross spectrum between the microphones by the complex conjugate of this error term to effect correction. This method has been used for many years in FFT instruments.
(To determine the phase error between a pair of microphones, a number of different methods may be employed. Exemplary are those disclosed in Chung, J. Y., "Cross-Spectral Method of Measuring Acoustic Intensity Without Error Caused by Instrument Phase Mismatch," Journal of the Acoustical Society of America, Vol. 64, No. 6, 1978, pp. 1613-16, and Seybert, A. F., "Measurement of Phase Mismatch Between Two Microphones," NOISE-CON 85 Proceedings, 1985, pp. 423-28.)
Real time octave analyzers have not previously been susceptible to this type of phase correction. Consequently, extensive research has been conducted in methodologies of producing closely matched microphones. Exemplary of this work are: Frederiksen, E., "Phase Characteristics of Microphones for Intensity Probes,"Proceedings of 2nd International Congress on Acoustic Intensity, Senlis, 1985, pp. 50-57; and Frederiksen, E., et al, "Pressure Microphones for Intensity Measurements with Significantly Improved Phase Properties," Bruel & Kjaer Technical Review, No. 4, 1986, pp. 11-21. The latter paper proposed a solution to low frequency phase mismatch by mechanical compensation--namely the addition of two additional cavities behind the diaphragm to attenuate the effect of low frequency vent-cavity resonances, and hence minimize phase variabilities between microphones. Microphones optimized for phase accuracy are also shown in U.S. Pat. Nos. 4,887,300 and 4,777,650. While effective, such approaches result in significantly increased manufacturing costs.
In accordance with the present invention, a real time octave analyzer is equipped with an adaptive time domain phase compensation filter whose poles and zeros are selected to counteract the low frequency phase error associated with any given pair of microphones. Precise equalization of unmatched microphone phase errors is thereby achieved without resort to elaborate mechanical compensation schemes. In the preferred embodiment, the transfer function for the adaptive filter is determined using a pole/zero curve fitting technique based on cross spectrum data acquired in an FFT spectral analysis of the probe microphones.
The foregoing and additional features and advantages of the present invention will be more readily apparent from the following detailed description, which proceeds with reference to the accompanying drawings.
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