Page 11 - Summer 2008

300 Hz with corresponding propagation speed of 1500 m/sec. The sensor data are generated at 0 dB SNR. The results of applying a modern parametric estimator (maxi- mum entropy method (MEM))5 developed for harmonic (sinusoidal) waves in noise are shown in Fig. 3, where we observe the ensemble results of the 16-sensor channel spec- tral estimates. The results demonstrate that the algorithms are capable of providing reasonable DOA estimates in such a noisy environment.
Steps 2 & 3: Parametric signal processing (black/gray- box approach)
Perhaps even a more reasonable application of modern signal processing follows directly from the black/gray-box or parametric approach. In this realm of processing the acousti- cian can choose from a set of models that reasonably approx- imate the underlying phenomenology and essentially “fit” the model to the data through a variety of estimation algorithms. This type of processing evolves from the signal processing lit- erature, from applications in speech (e.g., linear prediction, coding, recognition, etc.),10 and controls called system identi-
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In this domain the parametric approach is to: (1) select a represen- tative model set (e.g., transfer function, autoregressive (all- pole), moving average (all-zero), autoregressive moving aver-
fication (e.g., adaptive control, noise cancelling, etc.).
age (pole-zero), state-space, etc.); (2) estimate the model parameters from the data; and (3) construct the signal esti- mate (e.g., spectrum, impulse response, etc.) from these parameters.7 Again this can represent the “black-box” step if the parameters have no physical interpretation or the “gray- box” step if they do have physical relations.
Parametric signal processing for prosthetic heart valve classification application
As a parametric processing application, consider the problem of estimating flaws or cracks in prosthetic heart valves (see Fig. 4a). By placing microphones on a patient’s chest and listening to the sounds radiated by the valve, its condition can be determined. From the structure of the pros- thetic value and its interacting components, it is possible to isolate the sounds associated with each component and clas- sify potential problems. Since these sounds are essentially vibrational resonances, an all-pole (autoregressive) model is selected to perform parametric signal processing and investi- gate the condition of the valve under test through a variety of statistical tests. Note how the acoustical problem is dictating the processing approach and potential solution. The process- ing is illustrated in Fig. 4. The approach selected in this appli- cation is to construct a classifier to determine in which class (failure or normal) the valve belongs (Fig. 4b). The heart
Fig. 4. Prosthetic heart valve acoustic analysis and condition detection using parametric signal processing (black/gray-box) techniques: (a) prosthetic heart valve under test; (b) overall processing paradigm to detect and classify condition; (c) parametric (all-pole) model and estimated signal/spectrum; and (d) ensemble spectrum, instantaneous spectrogram (power versus time versus frequency) image, and peak frequency probability distribution or histogram (feature) for condition classification.
10 Acoustics Today, July 2008