The spatial coherence of noise fields evoked by continuous source distributions

Area of Science:

• Acoustics
• Wave Propagation
• Signal Processing

Background:

• Understanding spatial coherence is crucial for characterizing noise fields.
• Sparse representations offer efficient ways to describe complex acoustic phenomena.
• Existing methods may lack the flexibility to handle arbitrary pressure distributions.

Purpose of the Study:

• To derive analytic expressions for spatial coherence in the modal domain.
• To develop a sparse representation of sound fields using orthogonal basis functions.
• To enable prediction of spatial coherence without direct measurement.

Main Methods:

• Expressing sound fields using pressure distributions on virtual surfaces (cylindrical/spherical).
• Applying the Huygens-Fresnel principle with elementary sources.
• Proposing orthogonal basis functions with limited angular support for windowed distributions.
• Investigating special cases of circular and spherical distributions.

Main Results:

• Analytic expressions for spatial coherence in the modal domain were successfully derived.
• Orthogonal basis functions with limited angular support were proposed for arbitrary pressure distributions.
• Circular and spherical distributions with uncorrelated, equal-power source modes result in cylindrically and spherically isotropic (diffuse) noise fields, respectively.
• The derived expressions enable prediction of spatial coherence at any point within a region of interest.

Conclusions:

• The derived analytic expressions provide a powerful tool for analyzing spatial coherence in noise fields.
• The proposed method allows for efficient, sparse representation of sound fields.
• This approach eliminates the need for extensive sensor placement in the region of interest, simplifying acoustic measurements and predictions.