Fast wavelet transform is presented for realtime processing of wavelet transforms. A processor for the fast wavelet transform is of the frequency sampling structure in architectural level. The fast wavelet transform owes its parallelism both to the frequency sampling structure and parallel tapping of a series of delay elements. Computational burden of the fast transform is hence independent of specific scale values in wavelets and the parallel processing of the fast transform is readily implemented for real-time applications. This point is quite different from the computation of wavelet transforms by convolution. We applied the fast wavelet transform to detecting detonation in a vehicle engine for precise real-time control of ignition advancement. The prototype wavelet for this experiment was the Gaussian wavelet (i.e. Gabor function) which is known to have the least spread both in time and in frequency. The number of complex multiplications needed to compute the fast wavelet transform over 51 scales is 714 in this experiment, which is less than one tenth of that required for the convolution method. Experimental results have shown that detonation is successfully detected from the acoustic vibration signal picked up by a single knock sensor embedded in the outer wall of a V/8 engine and is discriminated from other environmental mechanical vibrations.

We investigated suitable spatial inverse filters for cortical dipole imaging from the scalp electroencephalogram (EEG). The effects of incorporating statistical information of signal and noise into inverse procedures were examined by computer simulations and experimental studies. The parametric projection filter (PPF) and parametric Wiener filter (PWF) were applied to an inhomogeneous three-sphere volume conductor head model. The noise covariance matrix was estimated by applying independent component analysis (ICA) to scalp potentials. The present simulation results suggest that the PPF and the PWF provided excellent performance when the noise covariance was estimated from the differential noise between EEG and the separated signal using ICA and the signal covariance was estimated from the separated signal. Moreover, the spatial resolution of the cortical dipole imaging was improved while the influence of noise was suppressed by including the differential noise at the instant of the imaging and by adjusting the duration of noise sample according to the signal to noise ratio. We applied the proposed imaging technique to human experimental data of visual evoked potential and obtained reasonable results that coincide to physiological knowledge.