Signals and Systems (eBook)

Theory and Practical Explorations with Python

Fatos Tunay Yarman Vural, Emre Akbas (Autoren)

eBook Download: EPUB

2024
897 Seiten
Wiley (Verlag)
978-1-394-21577-5 (ISBN)

Infos

Introductory course textbook on signals and systems with numerous examples and code snippets implemented in Python

Supported by code examples, Signals and Systems: Theory and Practical Explorations with Python is a textbook resource for a complete introductory course in systems and signals, enabling readers to run Python programs for convolution, discrete time Fourier transforms and series, sampling, and interpolation for a wide range of functions. Readers are guided step-by-step through basic differential equations, basic linear algebra, and calculus to ensure full comprehension of the exercises.

This book is supported by a companion website, hosting interactive material to draw functions, and run programs in Python; it is enriched with audiovisual material via linking to related videos. Links to resources that provide a deeper explanation about the important concepts in the book, such as the systems approach, complex numbers, harmony, the Euler equation, and Hilbert spaces, are also included.

Written by two highly qualified academics, topics covered include:

• Systems approach for modeling the natural and manmade systems and some application areas
• Representation of complex and real signals by basic functions, such as real and complex exponentials, unit step and unit impulse functions
• Properties of signals, such as symmetry, harmony, energy, power, continuity and discreteness
• Convolution and correlation operations for continuous time and discrete time signals and systems
• Representation of systems by impulse response, frequency response, transfer function, block diagram, differential and difference equations
• Properties of systems, such as linearity, time invariance, memory, invertibility, stability and causality
• Continuous time and discrete time Fourier analysis in Hilbert space and their extension to Laplaca transform and z-transform
• Filtering by Linear Time Invariant systems in time and frequency domains, covering low pass, high pass band pass and band reject filters
• Sampling theorems for continuous time and discrete time systems, covering A/D and D/A conversion, sampling and interpolation

Signals and Systems is an ideal textbook resource for a one semester introductory course on signals and systems for upper level undergraduate and graduate students in computer science, electrical engineering and data science. It is also a useful reference for professionals working in bioinformatics, robotics, remote sensing, and related fields.

Fato? Tunay Yarman Vural is a Professor in the Department of Computer Engineering at Middle East Technical University, Turkey. She is a Senior Member of the IEEE and received her PhD from Princeton University, USA, in 1981.

Emre Akba? is an Associate Professor in the Department of Computer Engineering at Middle East Technical University, Turkey. Dr. Akba? received his PhD from the University of Illinois at Urbana-Champaign, USA, in 2011.

Textauszug

1
Introduction to Systems and Signals

“There is nothing more practical than a good theory!”

Vladimir Vapnik

This book is about the mathematical representation of systems and signals.

Let us start by describing the meaning of the words systems and signals.

The origin of the word systems dates back to 15th century, when it was used as a Latin word systema, which means the entire universe. Since then, this very wide meaning has narrowed to a set of connected items or devices that operate together. In the context of this book, a system can be defined as a unified collection of interrelated and interdependent parts. And in many cases, it is more than the summation of its parts.

The aforementioned definition is quite flexible and may cover both natural or human-made systems. It can be as large as a planet, a star, or a galaxy, or as small as a single cell, a molecule, or a microchip.

In this book, we shall use the systems approach to model, analyze and investigate the natural systems, and design and implement human-made systems.

Motivating Question: What is the systems approach?

The systems approach is a holistic paradigm to mathematically represent a system. Holism is the philosophy, which accepts a system as a whole, not only as a collection of its parts. It is the opposite of the reductionist paradigm, which assumes that a complex system can be represented by its simpler components. For example, in a reductionist paradigm, a puzzle can be represented by the collection of its pieces, which come in a box. However, when we turn the box of puzzle over a table, we see all the pieces, but we cannot perceive the theme of it. On the other hand, in the systems approach, we need to do the puzzle and look at the ordered puzzle to see that it consists of a picture (Figure 1.1).

In order to model a system using the holistic paradigm, we not only represent the attributes of its multiple components, but also formulate their inter-relationships, considering the objective of the entire system. This approach implicitly models the synergy created by a system.

 Learn more about the systems approach @ https://384book.net/v0101 

Figure 1.1 Waterfall by M.C. Escher1 The puzzle on the left consists of the pieces of the entire lithograph, but have no meaning. In order to observe the falling water of the watermill, we need to solve the puzzle.

Source: The M.C. Escher Company B.V/https://mcescher.com/gallery/impossible-constructions/#iLightbox[galleryimage1]/5/last accessed March 09, 2024.

The origin of the word signal is even older than that of systems, dating back to 13th. century. It comes from the Latin word signale, which means anything that serves to indicate or communicate information.

When we observe a signal, we assume that there is a source system, which generates the signal. Thus, signals can be considered as partial information about the systems. In most cases, systems can be modeled and represented by a collection of subsystems. The interrelations among the subsystems of a system can be modeled by the received input signal(s) and the generated output signal(s), i.e., signals, of each subsystem.

In summary, the response of a system to a specific set of input signals provides information about the properties of systems. Signals describe the interrelations among the parts of a system. Loosely speaking, signals are the measurements of our varying observations about a system and/or its parts.

1.1 Example Applications

Models for representing signals and systems are widely used in electrical engineering and computer science for filter design, control, communications, computer vision, machine learning, speech, image, and video processing. The formalism of signals and systems is also used in a wide range of multidisciplinary areas, including bioinformatics, robotics, neuroscience, remote sensing, aeronautics, seismology, biomedical engineering, chemical process control, energy and mechatronics, astronomy, and cosmology.

Let us give some examples, where the methodologies of the systems approach are intensively utilized, in the modeling, design, and implementation stages of natural and human-made systems. Most of these models are generated by using the signals measured at the input and/or output of the systems.

Figure 1.2 Digital terrain model of a transportation area obtained from LIDAR scanning.

Source: black_mts/Adobe Stock.

1.1.1 Three-Dimensional World Models by LIDAR Signals

Light detection and ranging (LIDAR) signals are generated by a source that emits laser beams. These signals bounce off the surrounding objects and return to a sensor. Systems approach is, then, used to create a three-dimensional representation of the physical environment by measuring the elapsed time for each laser pulse to return to the sensor (Figure 1.2).

 Learn more about the LIDAR example @ https://384book.net/v0102 

1.1.2 Modeling the Brain Networks from the Brain Signals

Functional magnetic resonance imaging (fMRI) technique records the brain signals, which indirectly measure the activities in the anatomical regions. It is possible to model and analyze the cognitive processes, such as vision, speech, and memory of the human brain from the fMRI signals.

Representing brain activities by networks is crucial to understand various cognitive states. It is possible to extract brain networks from the fMRI recorded while the subjects perform a predefined cognitive task. Figure 1.3 shows two brain networks for planning and execution phases, while the subject solves a complex problem. The suggested computational network model can successfully discriminate the planning and execution phases of complex problem-solving process with more than 90% accuracy, when the estimated dynamic networks, extracted from the fMRI data, are classified by a machine learning algorithm.

Figure 1.3 Visualizing anatomical regions during both the planning (a) and execution (b) phases while the selected subject solves a complex problem.2

Source: With permission of IEEE.

Figure 1.4 Example of building detection using remote sensing applications.3

Source: With permission of IEEE.

 An example: speech synthesis from neural decoding of spoken sentences @ https://384book.net/v0103 

1.1.3 Detecting the Buildings from the Remote-Sensed Satellite Images

Remote sensing images are recorded by measuring the signals of several electromagnetic waveforms reflected from the earth’s surface. These signals are used to extract various information, such as measuring environmental pollution or climate change, the growth rate of cities or green areas, etc.

One important application of remote sensing is to detect the buildings in municipalities. For this purpose, a multidimensional signal measured from the earth’s surface is modeled to filter the buildings in the remotely sensed data, as shown in Figure 1.4.

1.1.4 Noise Reduction in Old Records

Due to the technological limitations of their time, the old gramophone recordings are mostly noisy. These recordings can be cleaned by using methodologies of signal processing. Additive noise is partially eliminated by estimating a mathematical model for the noise and subtracting it from the corrupted signal. An example of noise reduction can be found in the companion website of the book.

 Noise reduction on “O’sole mio” @ https://384book.net/v0104 

1.2 Relationship Between Signals and Systems

The aforementioned brief descriptions and examples of signals and systems show that there is a remarkable relationship between the signals and the underlying system, which generates the signal. Philosophically, one may consider the signals as the manifestation of systems. We, humans, can perceive the physical world through these manifestations. Heraclitus of Ephesus summarizes this view by his famous saying:

which translates to English as:

All flows!

Almost 2500 years ago, Heraclitus claimed that everything changes. Since then, as we study the nature, we discover some invariant laws, which lie behind the changes. Although we can only perceive the world of flux, these invariant laws govern our changing observations. In other words, we can only perceive variances, generated by the invariant laws, which govern the natural systems. Our aim is to find these invariant laws, manifested through our varying observations.

To analyze and understand a natural system or design and implement a human-made system, we need rigorous mathematical representations of signals, which correspond to our varying observations. Based on these observations, we can model the invariant rules of a system, which administers a set of prescribed tasks.

Motivating Question: How can we analyze and understand the laws that govern the natural systems? How can we design a human-made system to achieve a specific goal?

The answers to these questions require mathematical representation of systems and/or their...

Produkt-Details

• Erscheint lt. Verlag: 24.12.2024
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Schlagworte: Block Diagram • Continuous-time • convolution • Difference Equations • Differential Equations • Discrete-Time • filtering • fourier analysis • Frequency Response • impulse response • python code • Sampling • Signals • Systems
• ISBN-10: 1-394-21577-0 / 1394215770
• ISBN-13: 978-1-394-21577-5 / 9781394215775