The work describes a novel multiresolution signal decomposition method using wavelets and neural networks. The neural network is trained by the supervision of the bandwise decomposed main signal components at the output as well as at the input. The training algorithm is Kalman filtering since fast training is required due to the stochastic signals applied to the network. The signal characteristics having been learned by the network including their orthogonality among themselves, the network can be employed for fault detection using the stationary stochastic signal in multiresolution form. Since the learning part comprises components of the decomposed signals, the implication of the process for unknown signal with anomaly is effectively the estimation of those components of the signal without anomaly at the output. Hence the differences between the inputs with the corresponding outputs would identify the anomaly together with the relevant frequency band involved. In this respect the concise work presented here briefly demonstrates the accurate estimation of each component of the wavelet decomposed signal with neural network. The performance of the method is demonstrated.