HIGH PERFORMANCE, LOW COST SUBSPACE DECOMPOSITION AND POLYNOMIAL ROOTING FOR REAL TIME DIRECTION OF ARRIVAL ESTIMATION: ANALYSIS AND IMPLEMENTATION

This thesis develops high performance real-time signal processing modules for direction of arrival (DOA) estimation for localization systems. It proposes highly parallel algorithms for performing subspace decomposition and polynomial rooting, which are otherwise traditionally implemented using sequential algorithms. The proposed algorithms address the emerging need for real-time localization for a wide range of applications. As the antenna array size increases, the complexity of signal processing algorithms increases, making it increasingly difficult to satisfy the real-time constraints. This thesis addresses real-time implementation by proposing parallel algorithms, that maintain considerable improvement over traditional algorithms, especially for systems with larger number of antenna array elements. Singular value decomposition (SVD) and polynomial rooting are two computationally complex steps and act as the bottleneck to achieving real-time performance. The proposed algorithms are suitable for implementation on field programmable gated arrays (FPGAs), single instruction multiple data (SIMD) hardware or application specific integrated chips (ASICs), which offer large number of processing elements that can be exploited for parallel processing. The designs proposed in this thesis are modular, easily expandable and easy to implement. Firstly, this thesis proposes a fast converging SVD algorithm. The proposed method reduces the number of iterations it takes to converge to correct singular values, thus achieving closer to real-time performance. A general algorithm and a modular system design are provided making it easy for designers to replicate and extend the design to larger matrix sizes. Moreover, the method is highly parallel, which can be exploited in various hardware platforms mentioned earlier. A fixed point implementation of proposed SVD algorithm is presented. The FPGA design is pipelined to the maximum extent to increase the maximum achievable frequency of operation. The system was developed with the objective of achieving high throughput. Various modern cores available in FPGAs were used to maximize the performance and details of these modules are presented in detail. Finally, a parallel polynomial rooting technique based on Newton’s method applicable exclusively to root-MUSIC polynomials is proposed. Unique characteristics of root-MUSIC polynomial’s complex dynamics were exploited to derive this polynomial rooting method. The technique exhibits parallelism and converges to the desired root within fixed number of iterations, making this suitable for polynomial rooting of large degree polynomials. We believe this is the first time that complex dynamics of root-MUSIC polynomial were analyzed to propose an algorithm. In all, the thesis addresses two major bottlenecks in a direction of arrival estimation system, by providing simple, high throughput, parallel algorithms.

ON THE DIGITAL-POLITICAL TOPOGRAPHY OF MUSIC

The persuasive power of music is often relegated to the dimension of pathos: that which moves us emotionally. Yet, the music commodity is now situated in and around the liminal spaces of digitality. To think about how music functions, how it argues across media, and how it moves us, we must examine its material and immaterial realities as they present themselves to us and as we so create them. This dissertation rethinks the relationship between rhetoric and music by examining the creation, performance, and distribution of music in its material and immaterial forms to demonstrate its persuasive power. While both Plato and Aristotle understood music as a means to move men toward virtue, Aristotle tells us in his Laws, through the Athenian Stranger, that the very best kinds of music can help guide us to truth. From this starting point, I assess the historical problem of understanding the rhetorical potential of music as merely that which directs or imitates the emotions: that which “Soothes the savage breast,” as William Congreve writes. By furthering work by Vickers and Farnsworth, who suggest that the Baroque fascination with applying rhetorical figures to musical figures is an insufficient framework for assessing the rhetorical potential of music, I demonstrate the gravity of musical persuasion in its political weight, in its violence—the subjective violence of musical torture at Guantanamo and the objective, ideological violence of music—and in what Jacques Attali calls the prophetic nature of music. I argue that music has a significant function, and as a non-discursive form of argumentation, works on us beyond affect. Moreover, with the emergence of digital music distribution and domestic digital recording technologies, the digital music commodity in its material and immaterial forms allows for ruptures in the former methods of musical composition, production, and distribution and in the political potential of music which Jacques Attali describes as being able to foresee new political realities. I thus suggest a new theoretical framework for thinking about rhetoric and music by expanding on Lloyd Bitzer’s rhetorical situation, by offering the idea of “openings” to the existing exigence, audience, and constraints. The prophetic and rhetorical power of music in the aleatoric moment can help provide openings from which new exigencies can be conceived. We must, therefore, reconsider the role of rhetorical-musical composition for the citizen, not merely as a tool for entertainment or emotional persuasion, but as an arena for engaging with the political.