The Effect of Fixed-point Arithmetic on Low Frequency Sound Zone Control

By use of several loudspeakers it is possible to create constructive and destructive acoustic interference leading to spatial sound zones with high (bright zone) and low (dark zone) sound pressure levels, respectively. The loudspeaker control signals are commonly created by filtering the audio signals using Finite Impulse Response (FIR) control filters. We are interested in using finite precision multiply-accumulate arithmetic in the FIR filter operations in order to reduce the complexity of a potential hardware implementation. In a simulation study based on a setup with 8 loudspeakers and for the frequency range 50 – 600 Hz, we demonstrate that using only 8 and 12 bits signed fixed-point arithmetic for the multiplier and adder, respectively, reduces the mean acoustic contrast ratio between the bright and the dark zones by only 0.1 dB as compared to when using 32 bits arithmetic. Reducing the word length of the adder below 12, significantly increases the sound pressure in the dark zone.

Keywords: sound zones, fixed point arithmetic, FIR filtering, variable word length simulation.