AES New York 2009
Tutorial T7

Monday, October 12, 4:00 pm — 5:00 pm

T7 - The Manifold Joys, Uses, and Misuses of Polynomial Mapping Functions in Signal Processing

Robert Bristow-Johnson, audioImagination - Burlington, VT, USA

In digital audio signal processing, we “do math” upon samples of audio signals, but also with parameters associated with audio signals. These parameters can perhaps be loosely divided into two groups: numbers that are important and recognizable to the user of the DSP algorithm (loudness in dB, frequency in Hz, pitch or bandwidth in octaves, RT60 in seconds), and numbers that are of direct concern to the DSP algorithm itself (coefficients, thresholds, displacements in samples). There are relationships between these groups of parameters that involve mysteriously designed transcendental functions that may not be available to the processor being used in the implementation. This is about how to implement such mappings without the use of the ubiquitous look-up table (LUT) by fitting polynomials to functions, where it's useful in audio DSP, a little about the different fitting criteria, and methods of fitting.