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SignalProcessingAndInformationTheory

This is a class for the Bachelor of Science in Bioinformatics. The course is in English, so this page is in that language. If you look for the page about AY 21-22, it's there.

Schedule, location and links

Last year end of course summary

Below is a table with links to the material screened in class during the past year; the progress made during the current year is reported further down

Topics slide video
Course Overview link 1
Signals and Systems link 1
Fourier series and signals space link 1, 2
Fourier transform and convolution link 1, 2, 3, 4
Sampling and digital signal processing link 1, 2, 3
Analog and numeric filters chapter 1, 2
Random signals, correlation, Wiener's theorem and signal statistics chapter 2
Information Theory chapter 2
Signal Processing over Graphs link 1, 2, 3, 4
Intermediate tests 1st, 2nd, 3rd

Study material

Consists mainly of the slides projected in class, to add to

  • my book in the original or translated version (please report errors!)
  • the material linked in the classroom pages
  • other material proposed from time to time in the classroom
  • during the new cycle of lessons I'm updating the slides, so make sure you read the latest version

Progress of individual lessons

In addition to summarizing the topics covered from time to time, references to the support material used in class are also provided

  • tue 7/3, fry 10/3 - Course Overview: After the illustration of the reference telematic tools for the course, we introduce ourselves. A brief introduction to the nature of signals and their processing follows, in order to provide an overview of the objects we will be dealing with. In accordance with what I have proposed to myself, some applicative aspects of signal processing and information theory in the biological, medical, genetic, microscopic and structural fields are then outlined, up to a mention of the most recent applications. But, really, don't be afraid of that, I just wanted to pique your curiosity to study signal processing, at least to understand anything you still don't understand about more advanced topics!
  • tue 14/3 - Signal and Systems: This series of slides covers the contents of chapter 1 in the Signal Basics book. After a brief introduction on the (co)domains of signals, on the family of Fourier analyzes and on the relationships between impulse response, convolution, frequency response and filtering, different classes of signals are defined, on the basis of their behavior over time and asymptotic, and some notes on common operations performed on signals, their combination and on graphs are provided. Then the more commonly used signals are illustrated.
  • fri 17/3 - Signal and Systems 2: a complex algebra review is provided and an in-depth analysis is undertaken on the role of the complex exponential in frequency analysis. Since signal processing is typically implemented as the transit of the signal itself through a linear operator, the characteristics of the latter are explained, and therefore the differences with respect to non-linear systems are highlighted.
    • Do you want to see the conformal map describing the result y=1/x? Follow the first link on this page and remember that 1/x = a/(a2+b2) - jb/(a2+b2)
    • Are you wondering what is so special about the number e that it is the only one that gives rise to Euler's formula? Here is a discussion on the subject
  • tue 21/3 - Fourier series and signal spaces: After an introduction to phasors notation, the representation of periodic signals as an ordered set of Fourier coefficients is given, together with their reconstruction formula known as Fourier series. Then the alternative representations for real signals are given, as well as the effects of using only a limited set of coefficients. This section closes with the proof of the Parseval's theorem which gives a typical effect of the exponentials orthogonality property. Then we deal with the concepts of vector algebra when applied to signal spaces and, as a way to motivate the Fourier series validity, beginning to talk about the basis of representation of a vector space and the norm of a vector
    • link to the 3rd slide set Fourier series and signal spaces
    • Go visualize the Fourier coefficients for some typical periodic waveforms, and experiment by changing the number of coefficients. Have you wondered why the Gibbs horns arise just around the discontinuity?
  • fry 24/3 - Fourier series and signal spaces 2: After deepening the concepts of dimension of a vector space and of linear independence for its basis of representation, the concept of norm of a vector is introduced, followed by that of scalar product, and of the norm that it induces, by virtue of the existence of the Schwartz inequality which allows to define an angle between vectors. Therefore, having an orthonormal basis, the scalar product between vectors can be calculated on the basis of the respective coefficients, as happens in a Euclidean space, obtaining an identical definition of distance. These concepts are then applied to the spaces of periodic, energy and power signals, after having defined for them the formula that evaluates the inner product, and showing how many of the properties valid for signals are correlated in a simple way with the particularities of metric spaces. Furthermore, its shown how any linear transformation or operator can be thought of as the result of evaluating an inner product, so that many signal processing results such as Fourier transform, convolution, signal correlation, fall into this case.