This class addresses the representation, analysis, and design of discrete time signals and systems. The major concepts covered include: Discrete-time processing of continuous-time signals; decimation, interpolation, and sampling rate conversion; flowgraph structures for DT systems; time-and frequency-domain design techniques for recursive (IIR) and non-recursive (FIR) filters; linear prediction; discrete Fourier transform, FFT algorithm; short-time Fourier analysis and filter banks; multirate techniques; Hilbert transforms; Cepstral analysis and various applications.
Acknowledgements
I would like to express my thanks to Thomas Baran, Myung Jin Choi, and Xiaomeng Shi for compiling the lecture notes on this site from my individual lectures and handouts and their class notes during the semesters that they were students in the course. These lecture notes, the text book and included problem sets and solutions will hopefully be helpful as you learn and explore the topic of Discrete-Time Signal Processing.

Increasingly volatile climate and weather; vulnerable drinking water supplies; shrinking wildlife habitats; widespread deforestation due to energy and food production. These are examples of environmental challenges that are of critical importance in our world, both in far away places and close to home, and are particularly well suited to inquiry using geographic information systems. In GEOG 487 you will explore topics like these and learn about data and spatial analysis techniques commonly employed in environmental applications. After taking this course you will be equipped with relevant analytical approaches and tools that you can readily apply to your own environmental contexts.

This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra.

This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations and direct and iterative methods in linear algebra.

This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions.
This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.024. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.29.

In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize the aspects that play an important role in practical problems. We confine ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation. The techniques discussed in the intro-ductory chapters, for instance interpolation, numerical quadrature and the solution to nonlinear equations, may also be used outside the context of differential equations. They have been in-cluded to make the book self-contained as far as the numerical aspects are concerned. Chapters, sections and exercises marked with a * are not part of the Delft Institutional Package.
The numerical examples in this book were implemented in Matlab, but also Python or any other programming language could be used. A list of references to background knowledge and related literature can be found at the end of this book. Extra information about this course can be found at http://NMODE.ewi.tudelft.nl, among which old exams, answers to the exercises, and a link to an online education platform. We thank Matthias Moller for his thorough reading of the draft of this book and his helpful suggestions.

In this activity, students will analyze raw data obtained from an experiment that explores the effect of overexpressing the Ssk protein in order to strengthen the intestinal barrier and prevent bacteria from leaking out of the gut and into the hemolymph, which is the fruit fly equivalent to blood in the circulatory system. Using Excel, students will fit an exponential function to the few known data points and will then interpolate the missing data points and extrapolate a few future data points. They will also learn how they can fit a linear model by transforming the data (applying the logarithmic function) and use that model to estimate the missing data points. This activity involves both statistical analysis and mathematical modeling as well as displaying the usefulness of mathematical models for biological data analysis.

This is an interdisciplinary lesson that incorporates tools learned in Algebra about analyzing data representations to apply to historical and literary purposes.

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat’s pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.

Students act as food science engineers as they explore and apply their understanding of cooling rate and specific heat capacity by completing two separate, but interconnected, tasks. In Part 1, student groups conduct an experiment to explore the cooling rate of a cup of hot chocolate. They collect and graph data to create a mathematical model that represents the cooling rate, and use an exponential decay regression to determine how long a person should wait to drink the cup of hot chocolate at an optimal temperature. In Part 2, students investigate the specific heat capacity of the hot chocolate. They determine how much energy is needed to heat the hot chocolate to an optimal temperature after it has cooled to room temperature. Two activity-guiding worksheets are included.