Week 1 Help Center
Welcome to the first week of class!
Please consult the "Start Here" page for all practical information about the class, the homework deadlines and the grading. Also, please don't forget to fill in the initial survey if you haven't done so already; this will help us know our student base better and will allow you to better tailor our class to your needs.
Each Monday we will release two days' worth of lectures, together with homework sets and a varying amount of additional material. It's up to you to spread the week's workload as it best fits your schedule. Remember however that all homework sets are due 14 days from their release date, as detailed in the submission guidelines. Please don't forget to fill in the feedback section for each homework set as well.
Each week, to complement the video lectures, we will also release a video of an example of signal processing that we call the "Signal of the Day". Our aim is to show you cool real life applications of signal processing in a large variety of fields, from environmental sciences to music, image processing and more.
Each week we will also release one or two "practice" homework sets; these sets are not graded and their solution will be made available immediately.
Each week you will be able to look at one or two numerical examples. These are examples of actual working signal processing code, which you can run in Python. Please see the section on Numerical Examples in the "Start Here" page for details. This week we have also prepared an introductory tutorial that will help you installing a suitable computational environment on your PC to run the samples.
Finally, you will be able to download the slides of each lecture video as the videos are released.
And so, without further ado, let's get started with our journey into Digital Signal Processing!
Day 1
After a brief introduction to signal processing, with historical digressions to put things in perspective, we will start by describing what we mean by the term "signal" and, in particular, by "discrete-time" signal. We will then introduce probably the most famous of discrete-time signals, the complex exponential and we will wrap up the module with a playful digression into the mechanics of bank accounts and the inner working of music synthesizers: they have more in common than you may think!
Video lectures:
- 0 - Welcome!
- 1 - Introduction to signal processing
- 2.1 - Discrete time signals
- 2.2 - The complex exponential
- 2.3 - The Karplus-Strong Algorithm
Signal of the day:
Numerical example:
Please review the "Start Here" page for information about numerical examples and computing environments. We have prepared minimalistic tutorials to get you started with Python or FreeMat. Then, in this first numerical example we will build our first application, namely an implementation of the Karplus-Strong algorithm, which allows you to simulate the sound of a hammered or plucked string.
Practice homework:
Homework (due Monday November 2, 5:00pm CET):
Day 2
The way we teach signal processing is a little bit different than most. The fundamental idea is to express most signal processing concepts in terms of linear algebra: signals are vectors in a suitable vector space and transformations become changes of basis. While this may seem a little abstract at first, it will pay off handsomely in the end by providing us with very simple proofs of complex results (such as the sampling theorem). The price to pay is that we must endure a little dryness while we lay down the foundations of our framework... Bear with us, it's worth the effort!
Video lectures:
- 3.1 - From Euclid to Hilbert
- 3.2 - Hilbert Space, properties and bases
- 3.3 - Hilbert Space and approximation
Numerical example:
- A basis for grayscale images (Python)
Practice homework:
Homework (due Monday November 2, 5:00pm CET):
Notes and external resources
Module 1 is based on Chapter 1 in our textbook (''What is Digital Signal Processing''). For a beautiful history of information, from the earliest times to contemporary technology, see:
- James Gleick, "The Information: A History, a Theory, a Flood,'' New York: Pantheon Books, 2011.
Module 2 is based on Chapter 2 in our textbook ("Discrete-time Signals"). For a quick introduction on signal processing, digital signal processing and discrete-time signal processing, these Wikipedia pages are a good start:
Wikipedia has become a widely-referenced resource for Digital Signal Processing. DSP articles on Wikipedia, in some senses, have become a knowledge representation of DSP on the Internet. These articles form an impressive knowledge network worth exploring.
Module 3 is based on Chapter 3 in our textbook (''Signals and Hilbert Spaces'').
The book shown in the introduction video is a facsimile copy of "Six Books of Euclid", by Oliver Byrne (Taschen). For Euclid's Elements, see wikipedia.org/Euclid_Elements
For a fun read about thinking in geometrical spaces, there is the all time classic "Flatland: A Romance of Many Dimensions'' , by Edwin Abbott Abbott.
If you would like to dig deeper into Hilbert Spaces, there are many books available. For a free online version with a point of view similar to what is done in this class, we recommend Chapter 2, ''From Euclid to Hilbert'', in ''Foundation of Signal Processing,'' by M.Vetterli, J.Kovacevic and V.K.Goyal, downloadable at http://www.fourierandwavelets.org/. The book is published by Cambridge University Press.
Last Modified Mon 19 Oct 2015 5:31 PM CEST