Error analysis and complexity optimization for the multiplier-less FFT-like transformation (ML-FFT)

This paper studies the effect of the signal round-off errors on the accuracies of the multiplier-less Fast Fourier Transform-like transformation (ML-FFT). The idea of the ML-FFT is to parameterize the twiddle factors in the conventional FFT algorithm as certain rotation-like matrices and approximate the associated parameters inside these matrices by the sum-of-power-of-two (SOPOT) or canonical signed digits (CSD) representations. The error due to the SOPOT approximation is called the coefficient round-off error. Apart from this error, signal round-off error also occurs because of insufficient wordlengths. Using a recursive noise model of these errors, the minimum hardware to realize the ML-FFT subject to the prescribed output bit accuracy can be obtained using a random search algorithm. A design example is given to demonstrate the effectiveness of the proposed approach.published_or_final_versio

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

FPGA-based implementation of real-time identification procedures for adaptive control in photovoltaic applications

2013 - 2014In this thesis two adaptive Maximum Power Point Tracking (MPPT) techniques for PhotoVoltaic (PV) applications, which are based on two different real-time identification procedures are proposed. The algorithms are implemented on the same low-cost Field Programmable Gate Array (FPGA) device in charge of controlling the switching converter that processes the power produced by the PV array. The Perturb & Observe (P&O) algorithm is the most common MPPT technique. Its efficiency is mainly related to two parameters: the perturbation amplitude and the perturbation period Tp. The optimal values of such parameters depend on the PV array type and on the irradiance and temperature conditions thereof, as well as on the parameters of the power processing circuit. Thus, a method for dynamically adapt the P&O parameters would be very useful for increasing the P&O MPPT performances. Several approaches presented in the current literature are focused on the adaptation of the perturbation amplitude. In this thesis, on the contrary, the on-line optimization of the value of Tp is proposed. The effects of such a parameter on both the tracking speed and the stationary MPPT efficiency are pointed out. Besides, the need for a real-time identification technique for identifying the minimum acceptable value of Tp in the actual PV operating conditions is demonstrated. Two different identification procedures aimed at developing the aforementioned adaptive MPPT controllers have been studied: the Cross-Correlation Method (CCM) and the Dual Kalman Filter (DKF). The first one belongs to the non-parametric techniques and allows identifying the impulse response and the frequency response of the PV system. Instead, the DKF is a model-based approach which estimates the states and the parameters of the system. One of the aims of this thesis is to demonstrate the usefulness of these identification procedures for the optimization of the PV P&O MPPT performances. In order to achieve a good trade-off between the desired performances and the cost of the controller, hardware digital solutions, such as FPGA, are adopted. They are able to reduce the execution time by exploiting the intrinsic parallelism of the algorithm to be implemented. Then, in this work, the challenging design of a high performances hardware architecture for the identification algorithms is dealt with. Moreover, the implemented identification techniques are compared in terms of accuracy, identification time and used hardware resources. Several simulations and experimental tests demonstrate the feasibility of the developed identification procedures. In fact, the proposed adaptive MPPT controllers suitably change in few tens of milliseconds the value of Tp ensuring a stable MPPT behaviour. The developed FPGA-based architectures of both the identification techniques is promising for embedding other functions that are of interest in the field of PV systems, e.g. related to on-line monitoring or diagnostic purposes. The work has been developed in co-tutorship between the Systèmes et Applications des Technologies de l’Information et de l’Energie (SATIE) laboratory in the Université de Cergy-Pontoise (France) and the Circuiti Elettronici di Potenza laboratory in the Universitá degli Studi di Salerno (Italy). The work has been supported by the Université Franco-Italienne by means the Vinci project 2013 n. C2-29. [edited by author]XIII n.s

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Error analysis and efficient realization of the multiplier-less FFT-like transformation (ML-FFT) and related sinusoidal transformations

This paper studies the round-off analysis, design and implementation, and applications of the multiplier-less Fast Fourier Transform-like (ML-FFT) transformation proposed by Chan et al. [1, 2]. The ML-FFT parameterizes the twiddle factors in the conventional FFT algorithm as certain rotation-like matrices and approximates the associated parameters inside these matrices by the sum-of-power-of-two (SOPOT) or canonical signed digits representations, hence avoiding expensive multiplications. The error due to the SOPOT approximation is called the coefficient round-off error and it has been studied in [1, 2]. This paper studies the signal round-off error arising from internal rounding and develops a recursive noise model for ML-FFT. Using this model, a random search algorithm is proposed to minimize the hardware resources for realizing the ML-FFT subject to a prescribed output bit accuracy. To address the irregular structure of the ML-FFT due to the varying number of SOPOT terms used, a framework for its software implementation is also developed. The resulting algorithm has a regular implementation structure and is shown to offer a good performance similar to their floating-point counterpart. Finally, a new ML-FFT for real-valued input, called the ML-RFFT, is proposed. Because of the symmetry in the algorithm, it only requires about half the number of additions as required by the ML-FFT. Using the mappings between the DFT and the DCTs and DWTs, new ML-FFT-based transformations called ML-DCTs and ML-DWTs are derived. Design examples are given to demonstrate the usefulness of the proposed methods. © 2006 Springer Science + Business Media, LLC.link_to_subscribed_fulltex