The effects of contaminating noise on the calculation of active acoustic intensity for pressure gradient methods

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Calculation of acoustic intensity using the phase and amplitude gradient estimator (PAGE) method has been shown to increase the effective upper frequency limit beyond the traditional p-p method when the source of interest is broadband in frequency [Torrie, Whiting, Gee, Neilsen, and Sommerfeldt, Proc. Mtgs. Acoust. 23, 030005 (2015)]. PAGE processing calculates intensity for narrowband sources without bias error up to the spatial Nyquist frequency [Succo, Sommerfeldt, Gee, and Neilsen, Proc. Mtgs. Acoust. 30, 030015 (2018)]. The present work demonstrates that for narrowband sources with frequency content above the spatial Nyquist frequency, additive low-level broadband noise can improve intensity calculations. To be effective, the angular separation between the source and additive noise source should be less than 30 , while using phase unwrapping with a smaller angular separation will increase the usable bandwidth. The upper frequency limit for the bandwidth extension depends on angular separation, sound speed, and probe microphone spacing. Assuming the signal-to-additive-noise ratio (SNR a) is larger than 10 dB, the maximum level and angular bias errors incurred by the additive broadband noise beneath the frequency limit-or up until probe scattering effects must be taken into account-are less than 0.5 dB and 2:5 , respectively. Smaller angular separation yields smaller bias errors. V

Section: Signal-to-noise Ratiosmentioning

confidence: 99%

Section: Derivationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bandwidth extension of narrowband-signal intensity calculation using additive, low-level broadband noise

Cook

Succo

Gee

et al. 2019

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Bandwidth extension of intensity-based sound power estimates

Mortenson

Gilbert

Neilsen

et al. 2020

The traditional method for intensity-based sound power estimates often used in engineering applications is limited in bandwidth by microphone phase mismatch at low frequencies and by microphone spacing at high frequencies. To overcome these limitations, the Phase and Amplitude Gradient Estimator (PAGE) method [Gee, Neilsen, Sommerfeldt, Akamine, and Okamoto, J. Acoust. Soc. Am. 141(4), EL357–EL362 (2017)] is applied to sound power for a reference sound source, a blender, and a vacuum cleaner. Sound power measurements taken according to ISO 3741:2010 (2010) are compared against traditional- and PAGE-processed intensity-based sound power estimates measured according to ANSI S12.12-1992 (R2017). While the traditional method underestimates the sound power at the spatial Nyquist frequency by 7–10 dB, the PAGE-based sound power is accurate up to the spatial Nyquist frequency, and above when phase unwrapping is successful.

A coherence-based phase and amplitude gradient estimator method for calculating active acoustic intensity

Cook

Gee

Sommerfeldt

2022

The phase and amplitude gradient estimator (PAGE) method [Thomas, Christensen, and Gee, J. Acoust. Soc. Am. 137, 3366–3376 (2015)] has been developed as an alternative to the traditional p-p method for calculating energy-based acoustic measures such as active acoustic intensity. While this method shows many marked improvements over the traditional method, such as a wider valid frequency bandwidth for broadband sources, contaminating noise can lead to inaccurate results. Contaminating noise degrades performance for both the traditional and PAGE methods and causes probe microphone pairs to exhibit low coherence. When coherence is low, better estimates of the pressure magnitude and gradient can be obtained by using a coherence-based approach, which yields a more accurate intensity estimate. This coherence-based approach to the PAGE method, known as the CPAGE method, employs two main coherence-based adjustments. The pressure magnitude adjustment mitigates the negative impact of uncorrelated contaminating noise and improves intensity magnitude calculation. The phase gradient adjustment uses coherence as a weighting to calculate the phase gradient for the probe and improves primarily the calculation of intensity direction. Though requiring a greater computation time than the PAGE method, the CPAGE method is shown to improve intensity calculations, both in magnitude and direction.