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A specialized fast cross-correlation for acoustical measurements using coded sequences.

John N Daigle1, Ning Xiang

  • 1Department of Electrical Engineering, Anderson Hall, University of Mississippi, University, Mississippi 38677, USA.

The Journal of the Acoustical Society of America
|February 4, 2006
PubMed
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This study introduces a new algorithm for acoustics system identification using Fast Fourier Transforms (FFTs). The method efficiently calculates cross-correlations for sequences not suitable for standard FFTs, enabling simultaneous impulse response measurements.

Area of Science:

  • Acoustics
  • Signal Processing
  • System Identification

Background:

  • Binary maximal-length sequences and related sequences are crucial for acoustics system identification.
  • These sequences have pulselike autocorrelation functions, beneficial for acoustical applications.
  • Existing methods face limitations with sequence lengths not compatible with Fast Fourier Transform (FFT)-based cross-correlation algorithms.

Purpose of the Study:

  • To develop a specialized algorithm for calculating cross-correlations between periodic finite-length sequences using standard FFTs.
  • To address the challenge of sequence lengths not being powers of 2 in FFT-based correlation.
  • To enable simultaneous impulse response measurements in complex acoustic environments.

Main Methods:

  • Exploration of standard FFTs for cross-correlation of equal-length, periodic finite sequences.

Related Experiment Videos

  • Development of a specialized correlation algorithm accommodating non-power-of-2 sequence lengths.
  • Application of the algorithm to analyze room-acoustic data.

    • Main Results:

    • Successful calculation of cross-correlations for sequences with lengths not suitable for standard FFT algorithms.
    • Demonstration of the algorithm's efficacy in a practical room-acoustic environment.
    • Simultaneous acquisition of impulse responses between multiple sources and receivers.

    Conclusions:

    • The developed algorithm overcomes limitations of standard FFT-based cross-correlation for specific sequence lengths.
    • This method enhances the capabilities for system identification in acoustics.
    • It facilitates efficient, simultaneous impulse response measurements in multi-input, multi-output acoustic systems.