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This thesis examines applications of Digital Signal Processing to the analysis, transformation, and resynthesis of musical audio. First I give an overview of the human perception of music. I then examine in detail the requirements for a system that can analyse, transcribe, process, and resynthesise monaural polyphonic music. I then describe and compare the possible hardware and software platforms. After this I describe a prototype hybrid system that attempts to carry out these tasks using a method based on additive synthesis. Next I present results from its application to a variety of musical examples, and critically assess its performance and limitations. I then address these issues in the design of a second system based on Gabor wavelets. I conclude by summarising the research and outlining suggestions for future developments.

Recent research has shown that compressible signals can be recovered from a very limited number of measurements by minimizing nonconvex functions that closely resemble the L0-norm function. These functions have sparse minimizers and, therefore, are called sparsity-promoting functions (SPFs). Recovery is achieved by solving a nonconvex optimization problem when using these SPFs. Contemporary methods for the solution of such difficult problems are inefficient and not supported by robust convergence theorems. New signal-recovery methods for compressive sensing that can be used to solve nonconvex problems efficiently are proposed. Two categories of methods are considered, namely, sequential convex formulation (SCF) and proximal-point (PP) based methods. In SCF methods, quadratic or piecewise-linear approximations of the SPF are employed. Recovery is achieved by solving a sequence of convex optimization problems efficiently with state-of-the-art solvers. Convex problems are formulated as regularized least-squares, second-order cone programming, and weighted L1-norm minimization problems. In PP based methods, SPFs that entail rich optimization properties are employed. Recovery is achieved by iteratively performing two fundamental operations, namely, computation of the PP of the SPF and projection of the PP onto a convex set. The first operation is performed analytically or numerically by using a fast iterative method. The second operation is performed efficiently by computing a sequence of closed-form projectors. The proposed methods have been compared with the leading state-of-the-art signal-recovery methods, namely, the gradient-projection method of Figueiredo, Nowak, and Wright, the L1-LS method of Kim, Koh, Lustig, Boyd, and Gorinevsky, the L1-Magic method of Candes and Romberg, the spectral projected-gradient L1-norm method of Berg and Friedlander, the iteratively reweighted least squares method of Chartrand and Yin, the difference-of-two-convex-functions method of Gasso, Rakotomamonjy, and Canu, and the NESTA method of Becker, Bobin, and Candes. The comparisons concerned the capability of the proposed and competing algorithms in recovering signals in a wide range of test problems and also the computational efficiency of the various algorithms. Simulation results demonstrate that improved reconstruction performance, measurement consistency, and comparable computational cost are achieved with the proposed methods relative to the competing methods. The proposed methods are robust, are supported by known convergence theorems, and lead to fast convergence. They are, as a consequence, particularly suitable for the solution of hard recovery problems of large size that entail large dynamic range and, are, in effect, strong candidates for use in many real-world applications. / Graduate / 0544 / eng.flavio.teixeira@gmail.com

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configurable Computer system manufactured by SRC Computers Incorporated are discussed. Design and implementation of a fully functional prototype Quadrature Mirror Filter Bank is detailed, with a discussion for extending the functionality to larger more practical designs. Performance and device utilization results between the Quadrature Mirror Filter Bank implemented in VHDL, design elements implemented in the C programming language, and calculations made using high precision mathematical tools are compared, along with relative effort levels required to achieve results using the different hardware instantiation methods.

Three autonomous cropping and feature extraction algorithms are examined that can be used for classification of low probability of intercept radar modulations using time-frequency (T-F) images. The first approach, Erosion Dilation Adaptive Binarization (EDAB), uses erosion and a new adaptive threshold binarization algorithm embedded within a recursive dilation process to determine the modulation energy centroid (radar's carrier frequency) and properly place a fixed-width cropping window. The second approach, Marginal Frequency Adaptive Binarization (MFAB), uses the marginal frequency distribution and the adaptive threshold binarization algorithm to determine the start and stop frequencies of the modulation energy to locate and adapt the size of the cropping window. The third approach, Fast Image Filtering, uses the fast Fourier transform and a Gaussian lowpass filter to isolate the modulation energy. The modulation is then cropped from the original T-F image and the adaptive binarization algorithm is used again to compute a binary feature vector for input into a classification network. The binary feature vector allows the image detail to be preserved without overwhelming the classification network that follows. A multi-layer perceptron and a radial basis function network are used for classification and the results are compared. Classification results for nine simulated radar modulations are shown to demonstrate the three feature-extraction approaches and quantify the performance of the algorithms. It is shown that the best results are obtained using the Choi-Williams distribution followed by the MFAB algorithm and a multi-layer perceptron. This setup produced an overall percent correct classification (Pcc) of 87.2% for testing with noise variation and 77.8% for testing with modulation variation. In an operational context, the ability to process and classify LPI signals autonomously allows the operator in the field to receive real-time results.

Time-compression overlap-add (TC-OLA) is presented as a novel method of communications over a (wireless) channel, which is shown to have benefits over other methods in some applications. TC-OLA is initially explored in an experimental context using a custom wideband software-defined radio (SDR) to gain insight into some of the possibilities of this method. Basic analysis is developed showing the processing gain, transmitted spectrum, and behaviour in fading channels. The method is considered as a candidate for low power wide area network (LPWAN) applications, highlighting the equivalent channel property, channel averaging, and ability to handle more simultaneous users in the uplink than other schemes in this application area.The method is then considered as an alternative to single carrier frequency domain equalization (SC-FDE) for ultrawideband (UWB) applications, where the ability to reduce or eliminate the cyclic prefix (CP) overhead while still using frequency domain equalization (FDE) techniques is highlighted. Additional application areas for this technology are briefly considered, including cognitive radio and radar. The process of patenting this technology is outlined in an appendix. The issued patent can be found through the United States Patent and Trademark Office (USPTO) as U.S. Patent 9,479,216. / Graduate

This thesis scientifically investigates the setup and tuning of cylindrical membranophones as musical instruments. To date there has been very little quantitative analysis of drum tuning with respect to performance sound, studio recording and music production. Digital signal analysis has been used to quantify a number of acoustic related factors to drum setup and tuning. This is concerned with the evaluation of a drum's free vibration once excitation has occurred. Novel analysis of membranophone response is performed with respect to tuning an 'equalised drumhead'. Such analysis has not previously been performed on cylindrical drums with two heads. The findings show that it is indeed possible to tune a drum to a chosen, uniform frequency response and to a quantified accuracy. With reference to previous, non-scientific literature, the fundamental frequency of each drum in the modern drum kit is shown for the first time to be objectively tunable to correspond to a musical pitch. The research also investigates the role of the resonant head in tuning cylindrical drums. Unique analysis of the interaction between the two membranes shows for the first time that the ratios of the modal frequencies present in a drum sound are not fixed and can be manipulated to more desirable ratios. The fundamental frequently present is shown to be the same for both batter and resonant heads due to the strong coupling effect of the (01) modes. Furthermore the current research shows how this ability to manipulate the frequencies present in the drum can be extended to the drum kit as a whole and how the envelope profile of cylindrical drums with two heads can be manipulated via tuning and damping. This research therefore provides an original contribution to the knowledge of drum tuning for both scientific and musical purposes.

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