The z-domain Adaptive Modeling of Finite-lenght Acoustic Waveguide Fed by the Loudspeaker (With Application on Active Noise Control)

The finite length acoustic waveguide was opened on one end, and on the other end a loudspeaker is mounted. Inside the waveguide, a microphone is axially mounted. The loudspeaker is excited with low-pass filtered white noise. The low-pass filter was 20th order Buttherworth-type , sampling frequency was 8 kHz and cut-off frequency was 1.5 kHz, below the first cut-off mode of the duct. Sampled microphone signal was used as the desired signal, and low-pass filtered white noise signal was reference (training) signal for adaptive lest mean square (LMS) modeling of the whole system. The obtained finite-impulse-response (FIR) transfer function is compared with continuous time frequency response and impulse response of the whole system. Modeling error and influence of the modeling conditions are discussed. The similar complex systems, consisted of acoustic and electromechanical parts are secondary and feedback transfer functions in active noise control. The application of some control approaches with estimated transfer functions are discussed.