Extreme temperature events analyzed with Fast Fourier Transform

Extreme weather and climate events have received increased attention in the last few years, due to the often large loss of agriculture business and exponentially increasing costs associated with them and insurance planning. This increased attention raises the question as to whether extreme weather and climate events are truly increasing, whether this is only a perceived increase exacerbated by enhanced media coverage, or both. There are a number of ways extreme climate events can be defined, such as extreme daily temperatures, extreme daily rainfall amounts, and large areas experiencing unusually warm monthly temperatures, among others. In this study, we will focus our attention in frost and heatstroke events measuring it as the number of days under 0 ºC and number of days with daily maximum over 30ºC monthly respectively. We have studied the trends in these extreme events applying a Fast Fourier Transform to the series to clarify the tendency. Lack of long-term climate data suitable for analysis of extremes is the single biggest obstacle to quantifying whether extreme events have changed over the twentieth century, including high temporal and spatial resolution observations of temperatures. However, several series have been grouped in different ways: chosen the longest series independently, by provinces, by main watersheds and altitude. On the other hand, synthetic series generated by Luna and Balairón (AEMet) were also analyzed. The results obtained by different pooling data are discussed concluding the difficulties to assess the extreme events tendencies and high regional variation in the trends.

Estimation of Symmetric Channels for Discrete Cosine Transform Type-I Multicarrier Systems: A Compressed Sensing Approach

The problem of channel estimation for multicarrier communications is addressed. We focus on systems employing the Discrete Cosine Transform Type-I (DCT1) even at both the transmitter and the receiver, presenting an algorithm which achieves an accurate estimation of symmetric channel filters using only a small number of training symbols. The solution is obtained by using either matrix inversion or compressed sensing algorithms. We provide the theoretical results which guarantee the validity of the proposed technique for the DCT1. Numerical simulations illustrate the good behaviour of the proposed algorithm.

The DLMT. An alternative to the DCT

In the last recent years, with the popularity of image compression techniques, many architectures have been proposed. Those have been generally based on the Forward and Inverse Discrete Cosine Transform (FDCT, IDCT). Alternatively, compression schemes based on discrete “wavelets” transform (DWT), used, both, in JPEG2000 coding standard and in the next H264-SVC (Scalable Video Coding), do not need to divide the image into non-overlapping blocks or macroblocks. This paper discusses the DLMT (Discrete Lopez-Moreno Transform). It proposes a new scheme intermediate between the DCT and the DWT (Discrete Wavelet Transform). The DLMT is computationally very similar to the DCT and uses quasi-sinusoidal functions, so the emergence of artifact blocks and their effects have a relative low importance. The use of quasi-sinusoidal functions has allowed achieving a multiresolution control quite close to that obtained by a DWT, but without increasing the computational complexity of the transformation. The DLMT can also be applied over a whole image, but this does not involve increasing computational complexity. Simulation results in MATLAB show that the proposed DLMT has significant performance benefits and improvements comparing with the DCT

The DLMT hardware implementation. A comparative study with the DCT and the DWT

In the last recent years, with the popularity of image compression techniques, many architectures have been proposed. Those have been generally based on the Forward and Inverse Discrete Cosine Transform (FDCT, IDCT). Alternatively, compression schemes based on discrete "wavelets" transform (DWT), used, both, in JPEG2000 coding standard and in H264-SVC (Scalable Video Coding) standard, do not need to divide the image into non-overlapping blocks or macroblocks. This paper discusses the DLMT (Discrete Lopez-Moreno Transform) hardware implementation. It proposes a new scheme intermediate between the DCT and the DWT, comparing results of the most relevant proposed architectures for benchmarking. The DLMT can also be applied over a whole image, but this does not involve increasing computational complexity. FPGA implementation results show that the proposed DLMT has significant performance benefits and improvements comparing with the DCT and the DWT and consequently it is very suitable for implementation on WSN (Wireless Sensor Network) applications.

Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given

Diseño de algoritmos de guerra electrónica y radar para su implementación en sistemas de tiempo real

Esta tesis se centra en el estudio y desarrollo de algoritmos de guerra electrónica {electronic warfare, EW) y radar para su implementación en sistemas de tiempo real. La llegada de los sistemas de radio, radar y navegación al terreno militar llevó al desarrollo de tecnologías para combatirlos. Así, el objetivo de los sistemas de guerra electrónica es el control del espectro electomagnético. Una de la funciones de la guerra electrónica es la inteligencia de señales {signals intelligence, SIGINT), cuya labor es detectar, almacenar, analizar, clasificar y localizar la procedencia de todo tipo de señales presentes en el espectro. El subsistema de inteligencia de señales dedicado a las señales radar es la inteligencia electrónica {electronic intelligence, ELINT). Un sistema de tiempo real es aquel cuyo factor de mérito depende tanto del resultado proporcionado como del tiempo en que se da dicho resultado. Los sistemas radar y de guerra electrónica tienen que proporcionar información lo más rápido posible y de forma continua, por lo que pueden encuadrarse dentro de los sistemas de tiempo real. La introducción de restricciones de tiempo real implica un proceso de realimentación entre el diseño del algoritmo y su implementación en plataformas “hardware”. Las restricciones de tiempo real son dos: latencia y área de la implementación. En esta tesis, todos los algoritmos presentados se han implementado en plataformas del tipo field programmable gate array (FPGA), ya que presentan un buen compromiso entre velocidad, coste total, consumo y reconfigurabilidad. La primera parte de la tesis está centrada en el estudio de diferentes subsistemas de un equipo ELINT: detección de señales mediante un detector canalizado, extracción de los parámetros de pulsos radar, clasificación de modulaciones y localization pasiva. La transformada discreta de Fourier {discrete Fourier transform, DFT) es un detector y estimador de frecuencia quasi-óptimo para señales de banda estrecha en presencia de ruido blanco. El desarrollo de algoritmos eficientes para el cálculo de la DFT, conocidos como fast Fourier transform (FFT), han situado a la FFT como el algoritmo más utilizado para la detección de señales de banda estrecha con requisitos de tiempo real. Así, se ha diseñado e implementado un algoritmo de detección y análisis espectral para su implementación en tiempo real. Los parámetros más característicos de un pulso radar son su tiempo de llegada y anchura de pulso. Se ha diseñado e implementado un algoritmo capaz de extraer dichos parámetros. Este algoritmo se puede utilizar con varios propósitos: realizar un reconocimiento genérico del radar que transmite dicha señal, localizar la posición de dicho radar o bien puede utilizarse como la parte de preprocesado de un clasificador automático de modulaciones. La clasificación automática de modulaciones es extremadamente complicada en entornos no cooperativos. Un clasificador automático de modulaciones se divide en dos partes: preprocesado y el algoritmo de clasificación. Los algoritmos de clasificación basados en parámetros representativos calculan diferentes estadísticos de la señal de entrada y la clasifican procesando dichos estadísticos. Los algoritmos de localization pueden dividirse en dos tipos: triangulación y sistemas cuadráticos. En los algoritmos basados en triangulación, la posición se estima mediante la intersección de las rectas proporcionadas por la dirección de llegada de la señal. En cambio, en los sistemas cuadráticos, la posición se estima mediante la intersección de superficies con igual diferencia en el tiempo de llegada (time difference of arrival, TDOA) o diferencia en la frecuencia de llegada (frequency difference of arrival, FDOA). Aunque sólo se ha implementado la estimación del TDOA y FDOA mediante la diferencia de tiempos de llegada y diferencia de frecuencias, se presentan estudios exhaustivos sobre los diferentes algoritmos para la estimación del TDOA, FDOA y localización pasiva mediante TDOA-FDOA. La segunda parte de la tesis está dedicada al diseño e implementación filtros discretos de respuesta finita (finite impulse response, FIR) para dos aplicaciones radar: phased array de banda ancha mediante filtros retardadores (true-time delay, TTD) y la mejora del alcance de un radar sin modificar el “hardware” existente para que la solución sea de bajo coste. La operación de un phased array de banda ancha mediante desfasadores no es factible ya que el retardo temporal no puede aproximarse mediante un desfase. La solución adoptada e implementada consiste en sustituir los desfasadores por filtros digitales con retardo programable. El máximo alcance de un radar depende de la relación señal a ruido promedio en el receptor. La relación señal a ruido depende a su vez de la energía de señal transmitida, potencia multiplicado por la anchura de pulso. Cualquier cambio hardware que se realice conlleva un alto coste. La solución que se propone es utilizar una técnica de compresión de pulsos, consistente en introducir una modulación interna a la señal, desacoplando alcance y resolución. ABSTRACT This thesis is focused on the study and development of electronic warfare (EW) and radar algorithms for real-time implementation. The arrival of radar, radio and navigation systems to the military sphere led to the development of technologies to fight them. Therefore, the objective of EW systems is the control of the electromagnetic spectrum. Signals Intelligence (SIGINT) is one of the EW functions, whose mission is to detect, collect, analyze, classify and locate all kind of electromagnetic emissions. Electronic intelligence (ELINT) is the SIGINT subsystem that is devoted to radar signals. A real-time system is the one whose correctness depends not only on the provided result but also on the time in which this result is obtained. Radar and EW systems must provide information as fast as possible on a continuous basis and they can be defined as real-time systems. The introduction of real-time constraints implies a feedback process between the design of the algorithms and their hardware implementation. Moreover, a real-time constraint consists of two parameters: Latency and area of the implementation. All the algorithms in this thesis have been implemented on field programmable gate array (FPGAs) platforms, presenting a trade-off among performance, cost, power consumption and reconfigurability. The first part of the thesis is related to the study of different key subsystems of an ELINT equipment: Signal detection with channelized receivers, pulse parameter extraction, modulation classification for radar signals and passive location algorithms. The discrete Fourier transform (DFT) is a nearly optimal detector and frequency estimator for narrow-band signals buried in white noise. The introduction of fast algorithms to calculate the DFT, known as FFT, reduces the complexity and the processing time of the DFT computation. These properties have placed the FFT as one the most conventional methods for narrow-band signal detection for real-time applications. An algorithm for real-time spectral analysis for user-defined bandwidth, instantaneous dynamic range and resolution is presented. The most characteristic parameters of a pulsed signal are its time of arrival (TOA) and the pulse width (PW). The estimation of these basic parameters is a fundamental task in an ELINT equipment. A basic pulse parameter extractor (PPE) that is able to estimate all these parameters is designed and implemented. The PPE may be useful to perform a generic radar recognition process, perform an emitter location technique and can be used as the preprocessing part of an automatic modulation classifier (AMC). Modulation classification is a difficult task in a non-cooperative environment. An AMC consists of two parts: Signal preprocessing and the classification algorithm itself. Featurebased algorithms obtain different characteristics or features of the input signals. Once these features are extracted, the classification is carried out by processing these features. A feature based-AMC for pulsed radar signals with real-time requirements is studied, designed and implemented. Emitter passive location techniques can be divided into two classes: Triangulation systems, in which the emitter location is estimated with the intersection of the different lines of bearing created from the estimated directions of arrival, and quadratic position-fixing systems, in which the position is estimated through the intersection of iso-time difference of arrival (TDOA) or iso-frequency difference of arrival (FDOA) quadratic surfaces. Although TDOA and FDOA are only implemented with time of arrival and frequency differences, different algorithms for TDOA, FDOA and position estimation are studied and analyzed. The second part is dedicated to FIR filter design and implementation for two different radar applications: Wideband phased arrays with true-time delay (TTD) filters and the range improvement of an operative radar with no hardware changes to minimize costs. Wideband operation of phased arrays is unfeasible because time delays cannot be approximated by phase shifts. The presented solution is based on the substitution of the phase shifters by FIR discrete delay filters. The maximum range of a radar depends on the averaged signal to noise ratio (SNR) at the receiver. Among other factors, the SNR depends on the transmitted signal energy that is power times pulse width. Any possible hardware change implies high costs. The proposed solution lies in the use of a signal processing technique known as pulse compression, which consists of introducing an internal modulation within the pulse width, decoupling range and resolution.

Temporal self-imaging effect for periodically modulated trains of pulses

In this paper, the mathematical description of the temporal selfimaging effect is studied, focusing on the situation in which the train of pulses to be dispersed has been previously periodically modulated in phase and amplitude. It is demonstrated that, for each input pulse and for some specific values of the chromatic dispersion, a subtrain of optical pulses is generated whose envelope is determined by the Discrete Fourier Transform of the modulating coefficients. The mathematical results are confirmed by simulations of various examples and some limits on the realization of the theory are commented.

DCT Type-III for Multicarrier Modulation

In this paper we propose the use of Discrete Cosine Transform Type-III (DCT3) for multicarrier modulation. There are two DCT3 (even and odd) and, for each of them, we derive the expressions for both prefix and suffix to be appended into each data symbol to be transmitted. Moreover, DCT3 are closely related to the corresponding inverse DCT Type-II even and odd. Furthermore, we give explicit expressions for the 1-tap per subcarrier equalizers that must be implemented at the receiver to perform the channel equalization in the frequency-domain. As a result, the proposed DCT3-based multicarrier modulator can be used as an alternative to DFT-based systems to perform Orthogonal Frequency-Division Multiplexing or Discrete Multitone Modulation

Accelerating FPGA-based evolution of wavelet transform filters by optimized task scheduling

Adaptive embedded systems are required in various applications. This work addresses these needs in the area of adaptive image compression in FPGA devices. A simplified version of an evolution strategy is utilized to optimize wavelet filters of a Discrete Wavelet Transform algorithm. We propose an adaptive image compression system in FPGA where optimized memory architecture, parallel processing and optimized task scheduling allow reducing the time of evolution. The proposed solution has been extensively evaluated in terms of the quality of compression as well as the processing time. The proposed architecture reduces the time of evolution by 44% compared to our previous reports while maintaining the quality of compression unchanged with respect to existing implementations. The system is able to find an optimized set of wavelet filters in less than 2 min whenever the input type of data changes.

On the use of discrete cosine transforms for multicarrier communications

In this correspondence, the conditions to use any kind of discrete cosine transform (DCT) for multicarrier data transmission are derived. The symmetric convolution-multiplication property of each DCT implies that when symmetric convolution is performed in the time domain, an element-by-element multiplication is performed in the corresponding discrete trigonometric domain. Therefore, appending symmetric redun-dancy (as prefix and suffix) into each data symbol to be transmitted, and also enforcing symmetry for the equivalent channel impulse response, the linear convolution performed in the transmission channel becomes a symmetric convolution in those samples of interest. Furthermore, the channel equalization can be carried out by means of a bank of scalars in the corresponding discrete cosine transform domain. The expressions for obtaining the value of each scalar corresponding to these one-tap per subcarrier equalizers are presented. This study is completed with several computer simulations in mobile broadband wireless communication scenarios, considering the presence of carrier frequency offset (CFO). The obtained results indicate that the proposed systems outperform the standardized ones based on the DFT.

Modelado en alto nivel con SystemC

El presente proyecto final de carrera titulado “Modelado de alto nivel con SystemC” tiene como objetivo principal el modelado de algunos módulos de un codificador de vídeo MPEG-2 utilizando el lenguaje de descripción de sistemas igitales SystemC con un nivel de abstracción TLM o Transaction Level Modeling. SystemC es un lenguaje de descripción de sistemas digitales basado en C++. En él hay un conjunto de rutinas y librerías que implementan tipos de datos, estructuras y procesos especiales para el modelado de sistemas digitales. Su descripción se puede consultar en [GLMS02] El nivel de abstracción TLM se caracteriza por separar la comunicación entre los módulos de su funcionalidad. Este nivel de abstracción hace un mayor énfasis en la funcionalidad de la comunicación entre los módulos (de donde a donde van datos) que la implementación exacta de la misma. En los documentos [RSPF] y [HG] se describen el TLM y un ejemplo de implementación. La arquitectura del modelo se basa en el codificador MVIP-2 descrito en [Gar04], de dicho modelo, los módulos implementados son: · IVIDEOH: módulo que realiza un filtrado del vídeo de entrada en la dimensión horizontal y guarda en memoria el video filtrado. · IVIDEOV: módulo que lee de la memoria el vídeo filtrado por IVIDEOH, realiza el filtrado en la dimensión horizontal y escribe el video filtrado en memoria. · DCT: módulo que lee el video filtrado por IVIDEOV, hace la transformada discreta del coseno y guarda el vídeo transformado en la memoria. · QUANT: módulo que lee el video transformado por DCT, lo cuantifica y guarda el resultado en la memoria. · IQUANT: módulo que lee el video cuantificado por QUANT, realiza la cuantificación inversa y guarda el resultado en memoria. · IDCT: módulo que lee el video procesado por IQUANT, realiza la transformada inversa del coseno y guarda el resultado en memoria. · IMEM: módulo que hace de interfaz entre los módulos anteriores y la memoria. Gestiona las peticiones simultáneas de acceso a la memoria y asegura el acceso exclusivo a la memoria en cada instante de tiempo. Todos estos módulos aparecen en gris en la siguiente figura en la que se muestra la arquitectura del modelo: Figura 1. Arquitectura del modelo (VER PDF DEL PFC) En figura también aparecen unos módulos en blanco, dichos módulos son de pruebas y se han añadido para realizar simulaciones y probar los módulos del modelo: · CAMARA: módulo que simula una cámara en blanco y negro, lee la luminancia de un fichero de vídeo y lo envía al modelo a través de una FIFO. · FIFO: hace de interfaz entre la cámara y el modelo, guarda los datos que envía la cámara hasta que IVIDEOH los lee. · CONTROL: módulo que se encarga de controlar los módulos que procesan el vídeo, estos le indican cuando terminan de procesar un frame de vídeo y este módulo se encarga de iniciar los módulos que sean necesarios para seguir con la codificación. Este módulo se encarga del correcto secuenciamiento de los módulos procesadores de vídeo. · RAM: módulo que simula una memoria RAM, incluye un retardo programable en el acceso. Para las pruebas también se han generado ficheros de vídeo con el resultado de cada módulo procesador de vídeo, ficheros con mensajes y un fichero de trazas en el que se muestra el secuenciamiento de los procesadores. Como resultado del trabajo en el presente PFC se puede concluir que SystemC permite el modelado de sistemas digitales con bastante sencillez (hace falta conocimientos previos de C++ y programación orientada objetos) y permite la realización de modelos con un nivel de abstracción mayor a RTL, el habitual en Verilog y VHDL, en el caso del presente PFC, el TLM. ABSTRACT This final career project titled “High level modeling with SystemC” have as main objective the modeling of some of the modules of an MPEG-2 video coder using the SystemC digital systems description language at the TLM or Transaction Level Modeling abstraction level. SystemC is a digital systems description language based in C++. It contains routines and libraries that define special data types, structures and process to model digital systems. There is a complete description of the SystemC language in the document [GLMS02]. The main characteristic of TLM abstraction level is that it separates the communication among modules of their functionality. This abstraction level puts a higher emphasis in the functionality of the communication (from where to where the data go) than the exact implementation of it. The TLM and an example are described in the documents [RSPF] and [HG]. The architecture of the model is based in the MVIP-2 video coder (described in the document [Gar04]) The modeled modules are: · IVIDEOH: module that filter the video input in the horizontal dimension. It saves the filtered video in the memory. · IVIDEOV: module that read the IVIDEOH filtered video, filter it in the vertical dimension and save the filtered video in the memory. · DCT: module that read the IVIDEOV filtered video, do the discrete cosine transform and save the transformed video in the memory. · QUANT: module that read the DCT transformed video, quantify it and save the quantified video in the memory. · IQUANT: module that read the QUANT processed video, do the inverse quantification and save the result in the memory. · IDCT: module that read the IQUANT processed video, do the inverse cosine transform and save the result in the memory. · IMEM: this module is the interface between the modules described previously and the memory. It manage the simultaneous accesses to the memory and ensure an unique access at each instant of time All this modules are included in grey in the following figure (SEE PDF OF PFC). This figure shows the architecture of the model: Figure 1. Architecture of the model This figure also includes other modules in white, these modules have been added to the model in order to simulate and prove the modules of the model: · CAMARA: simulates a black and white video camera, it reads the luminance of a video file and sends it to the model through a FIFO. · FIFO: is the interface between the camera and the model, it saves the video data sent by the camera until the IVIDEOH module reads it. · CONTROL: controls the modules that process the video. These modules indicate the CONTROL module when they have finished the processing of a video frame. The CONTROL module, then, init the necessary modules to continue with the video coding. This module is responsible of the right sequence of the video processing modules. · RAM: it simulates a RAM memory; it also simulates a programmable delay in the access to the memory. It has been generated video files, text files and a trace file to check the correct function of the model. The trace file shows the sequence of the video processing modules. As a result of the present final career project, it can be deduced that it is quite easy to model digital systems with SystemC (it is only needed previous knowledge of C++ and object oriented programming) and it also allow the modeling with a level of abstraction higher than the RTL used in Verilog and VHDL, in the case of the present final career project, the TLM.