Applications of Quaternion Fourier and Wavelet Transforms, and Radon Transform

This chapter presents an application of the quaternion Fourier transform for preprocessing for neural computing. In a new way, the 1D acoustic signals of French spoken words are represented as 2D signals in the frequency and time domains. These kinds of images are then convolved in the quaternion Fourier domain with a quaternion Gabor filter for the extraction of features. This approach allows us to greatly reduce the dimension of the feature vector. Two methods of feature extraction are tested. The feature vectors were used for the training of a simple MLP, a TDNN, and a system of neural experts. The improvement in the classification rate of the neural network classifiers is very encouraging, which amply justifies the preprocessing in the quaternion frequency domain. This work also suggests the application of the quaternion Fourier transform for other image processing tasks.