Constrained Spectral Conditioning for the Spatial Mapping of Sound
Spalt, Taylor Brooke
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In aeroacoustic experiments of aircraft models and/or components, arrays of microphones are utilized to spatially isolate distinct sources and mitigate interfering noise which contaminates single-microphone measurements. Array measurements are still biased by interfering noise which is coherent over the spatial array aperture. When interfering noise is accounted for, existing algorithms which aim to both spatially isolate distinct sources and determine their individual levels as measured by the array are complex and require assumptions about the nature of the sound field. This work develops a processing scheme which uses spatially-defined phase constraints to remove correlated, interfering noise at the single-channel level. This is achieved through a merger of Conditioned Spectral Analysis (CSA) and the Generalized Sidelobe Canceller (GSC). A cross-spectral, frequency-domain filter is created using the GSC methodology to edit the CSA formulation. The only constraint needed is the user-defined, relative phase difference between the channel being filtered and the reference channel used for filtering. This process, titled Constrained Spectral Conditioning (CSC), produces single-channel Fourier Transform estimates of signals which satisfy the user-defined phase differences. In a spatial sound field mapping context, CSC produces sub-datasets derived from the original which estimate the signal characteristics from distinct locations in space. Because single-channel Fourier Transforms are produced, CSC's outputs could theoretically be used as inputs to many existing algorithms. As an example, data-independent, frequency-domain beamforming (FDBF) using CSC's outputs is shown to exhibit finer spatial resolution and lower sidelobe levels than FDBF using the original, unmodified dataset. However, these improvements decrease with Signal-to-Noise Ratio (SNR), and CSC's quantitative accuracy is dependent upon accurate modeling of the sound propagation and inter-source coherence if multiple and/or distributed sources are measured. In order to demonstrate systematic spatial sound mapping using CSC, it is embedded into the CLEAN algorithm which is then titled CLEAN-CSC. Simulated data analysis indicates that CLEAN-CSC is biased towards the mapping and energy allocation of relatively stronger sources in the field, which limits its ability to identify and estimate the level of relatively weaker sources. It is also shown that CLEAN-CSC underestimates the true integrated levels of sources in the field and exhibits higher-than-true peak source levels, and these effects increase and decrease respectively with increasing frequency. Five independent scaling methods are proposed for correcting the CLEAN-CSC total integrated output levels, each with their own assumptions about the sound field being measured. As the entire output map is scaled, these do not account for relative source level errors that may exist. Results from two airfoil tests conducted in NASA Langley's Quiet Flow Facility show that CLEAN-CSC exhibits less map noise than CLEAN yet more segmented spatial sound distributions and lower integrated source levels. However, using the same source propagation model that CLEAN assumes, the scaled CLEAN-CSC integrated source levels are brought into closer agreement with those obtained with CLEAN.
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