Fast nonorthogonal wavelet transforms and reconstructions for detonation detection

Fast schemes for wavelet transforms and their inversion are presented for real-time computation of nonorthogonal wavelet transforms. The processing architecture for the transform/reconstruction is of the frequency sampling structure. The computational complexity of the fast computation is independent of specific scales of wavelets. The parallel processing of the fast transform is readily implemented for real-time applications. The fast wavelet transforms are applied to detecting detonation in a vehicle engine for real-time control of ignition advancement. The basic wavelet in this experiment is the modulated Gaussian wavelet. 714 complex multiplications are needed to compute the fast transform over 51 scales in this experiment, which is less than one tenth of that required for the convolution method. Experimental results show 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