This thesis is concerned with future trend prediction on capital markets on the basis of neural networks. Usage of convolutional and recurrent neural networks, Elliott wave theory and scalograms for capital market's future trend prediction is discussed. The aim of this thesis is to propose a novel approach to future trend prediction based on Elliott's wave theory. The proposed approach will be based on the principle of classification of chosen patterns from Elliott's theory by the way of convolutional neural network. To this end scalograms of the chosen Elliott patterns will be created through application of continuous wavelet transform on parts of historical time series of price for chosen stocks.

To handle potentially large size and complicated nonstationary functional data, we present the wavelet-based methodology in data mining for process monitoring and fault classification. Since traditional wavelet shrinkage methods for data de-noising are ineffective for the more demanding data reduction goals, this thesis presents data reduction methods based on discrete wavelet transform. Our new methods minimize objective functions to balance the tradeoff between data reduction and modeling accuracy. Several evaluation studies with four popular testing curves used in the literature and with two real-life data sets demonstrate the superiority of the proposed methods to engineering data compression and statistical data de-noising methods that are currently used to achieve data reduction goals. Further experimentation in applying a classification tree-based data mining procedure to the reduced-size data to identify process fault classes also demonstrates the excellence of the proposed methods. In this application the proposed methods, compared with analysis of original large-size data, result in lower misclassification rates with much better computational efficiency. This thesis extends the scalogram's ability for handling noisy and possibly massive data which show time-shifted patterns. The proposed thresholded scalogram is built on the fast wavelet transform, which can effectively and efficiently capture non-stationary changes in data patterns. Finally, we present a SPC procedure that adaptively determines which wavelet coefficients will be monitored, based on their shift information, which is estimated from process data. By adaptively monitoring the process, we can improve the performance of the control charts for functional data. Using a simulation study, we compare the performance of some of the recommended approaches.

Visualization, processing and editing of audio, directly on a time-frequency surface, is the scope of this thesis. More precisely the scalogram produced by a Gabor Wavelet transform is used, which is a powerful alternative to traditional techinques where the wave form is the main visual aid and editting is performed by parametric filters. Reconstruction properties, scalogram design and enhancements as well audio manipulation algorithms are investigated for this audio representation.The scalogram is designed to allow a flexible choice of time-frequency ratio, while maintaining high quality reconstruction. For this mean, the Loglet is used, which is observed to be the most suitable filter choice.  Re-assignmentare tested, and a novel weighting function using partial derivatives of phase is proposed.  An audio interpolation procedure is developed and shown to perform well in listening tests.The feasibility to use the transform coefficients directly for various purposes is investigated. It is concluded that Pitch shifts are hard to describe in the framework while noise thresh holding works well. A downsampling scheme is suggested that saves on operations and memory consumption as well as it speeds up real world implementations significantly. Finally, a Scalogram 'compression' procedure is developed, allowing the caching of an approximate scalogram.