An analysis of a noise reduction neural network

An analysis of the four-layer, feedforward, noise-reduction neural network proposed by S. Tamura author and A. Waibel (Int. Conf. Acoust., Speech and Signal Proc., p.553-6, 1988) is described. Each layer has 60 units and is fully interconnected with the next higher layer. The input of the network is given by a 60-point-long (at 12-kHz sampling rate) noisy waveform, and the output is a 60-point-long noise-free waveform. The network was trained using the back-propagation learning algorithm. The network is divided into three subelements for the analysis. Each element stands for a transformation from a layer output to the next higher layer output. First, the transformation from the input layer to the first hidden layer is analyzed, showing that the linear part of the transformation performs linear noise reduction as well as linear speech/noise-characteristic extraction. It is also shown that the transformation from the first hidden layer to the second hidden layer greatly compresses the noise region of the first hidden layer by sigmoid nonlinearities, while preserving its speech region, and the transformation from the second hidden layer to the output layer linearly suppresses the noise components. The spectra of basis vectors spanning an output waveform space show poor higher formant structures