The application of cepstral techniques to the measurement of transfer functions and acoustical reflection coefficients

Abstract

Cepstral processing techniques in principle allow the separation of superposed pulses, such as those which occur in acoustic reflection, where a reflected pulse is a delayed and distorted version of the incident pulse. Additionally, the impulse response of the reflecting system, or equivalently its reflection coefficient, can also be determined. In practice, the accurate extraction of the impulse response is rendered difficult by the mathematical and computational properties of the power cepstrum procedure. In particular, spectral irregularity of the incident pulse, experimental noise and cepstral aliasing can cause the impulse response in the cepstrum to be masked. However, by careful selection of the incident signal, anti-aliasing filter, sampling frequency and echo delay in relation to the total sampling time, and the use of signal processing techniques such as time domain averaging, recursive filtering in the cepstral domain and zero padding, it is possible to produce good quality cepstra in which the reflector impulse response appears as an isolated feature. Experiments conducted on an electrical analogue of the acoustical reflection process have allowed the cepstral technique to be developed and evaluated. The acoustical reflector is simulated by a passive electrical filter network; the objective of the measurement and subsequent processing is the determination of the transfer function of this network. Good agreement is obtained between theoritical and measured transfer functions for a variety of filter networks indicating that cepstral techniques may be useful for acoustical reflection measurements given adequate transducer properties and environmental conditions.