Probability and data analysis Introduction to statistical modeling Signals and systems Linear algebra

The main objective of this course is that the student is able to extract relevant information contained in the signals under study with the aid of statistical signal processing tools. To achieve this, the student will study the main techniques of: - Random signals analysis - Estimation - Detection

K3: To know fundamental contents in their area of study starting from the basis of general secondary education and reaching a level proper of advanced textbooks, including also some aspects of the forefront of their field of study. K4: Knowledge of basic scientific and technical subjects that qualify for the learning of new methods and technologies, as well as providing a great versatility to adapt to new situations, in the field of data storage, management and processing. K5: Ability to understand and relate fundamental concepts of probability and statistics and be able to represent and manipulate data to extract meaningful information from them K11: Understand the modeling, prediction, filtering and smoothing of random signals and stochastic processes, with applications in time series analysis, pattern detection, and optimization of models in Data Science and Engineering. S3: Ability to solve technological, computer, mathematical and statistical problems that may arise in data engineering and science, applying knowledge of mathematics, probability and statistics, programming, databases, and languages, grammars and automata. S4: Ability to solve mathematically formulated problems applied to various subjects, using numerical algorithms and computational techniques, and applying knowledge of: algebra; geometry; differential and integral calculus; numerical methods; numerical algorithms; statistics and optimization C5: Be able to analyze and synthesize basic problems related to engineering and data science, elaborate, defend and efficiently communicate solutions individually and professionally, applying the knowledge, skills, tools and strategies acquired or developed in their area of study.

This course introduces the fundamental tools for the estimation, detection, and prediction of discrete-time random signals INTRODUCTION and FOUNDATIONS: · Detection and estimation · Calculus, probability, and linear systems PART 1: Stochastic processes · Introduction and examples · First and second order statistics · Stationarity and ergodicity · Power spectral density PART 2: Estimation theory · Parameter estimation · Bayesian estimation · Time series · Filtering, prediction and smoothing · Power spectral density estimation PART 3: Detection theory · Introduction and examples · Performance metrics for detectors · Detector design · Sequential detection

AF1: THEORETICAL-PRACTICAL CLASSES. They will present the knowledge that students should acquire. They will receive the class notes and will have basic texts of reference to facilitate the follow-up of the classes and the development of the subsequent work. Exercises, practical problems on the part of the student will be solved and workshops and evaluation test will be held to acquire the necessary skills. AF2: Updated to allegation AF3: INDIVIDUAL OR GROUP WORK OF THE STUDENT. AF9: FINAL EXAM. In which the knowledge, skills and abilities acquired throughout the course will be assessed globally. MD1: CLASS THEORY. Exhibitions in the teacher's class with support of computer and audiovisual media, in which the main concepts of the subject are developed and the materials and bibliography are provided to complement the students' learning. MD2: LABS. Resolution of practical cases, problems, etc. raised by the teacher individually or in groups. MD3: STUDENT CONSULTATION. Individualized assistance or in group to students by the teacher.