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Welcome to Week 5 of Digital Signal Processing.

This week we will continue (and conclude) the module on linear filters. We will start by introducing a tool that will enormously simplify our life when it comes to filter design and filter analysis: the $z$-transform. With that, we will start analyzing how to implement a filter in practice and we will explore a gallery of commonly used filters.

By now there are enough gadgets in our toolbox that we can start doing some pretty cool things with signal processing; and so this week we will provide you with a souped-up numerical example: a C++ framework that will allow you to easily implement some real-time audio effects. You'll be able to connect your guitar (or a microphone) to your PC and use the provided effects or write new ones!

All in all, these modules should be a lot of fun and you should start reaping the benefits of all the theory we had to slog through so far. And, last but not least, just a single homework set this week; this is to encourage you to play with the examples a bit more.

Day 9

Video lectures:

• 5.7 - Realizable filters
• 5.8 - Implementation of digital filters  (here are some additional notes on the module)
• 5.9 - Filter design - Part 2: Intuitive filters

Lecture slides for Module 5: full version .

Signal of the Day:

• Exoplanet Hunting

Practice Homework:

• Practice Homework 9 (Solutions)

Homework (due November 30, 5:00pm CET):

• Homework 9
• Feedback 9

Programming assignments (due December 28, 5:00pm CET):

• Programming assignment 1

Day 10

Video lectures:

• 5.10 - Filter design - Part 3: Design from specs
• 5.11 - Real-time processing
• 5.12 - Dereverberation and echo cancelation

Lecture slides for Module 5: full version .

Numerical example:

• Real-time audio processing

Homework (due November 30, 5:00pm CET):

• Feedback 10

Notes and external resources

Filter design is a vast (to say the least) domain, with inescapable ties to analog circuits and discrete electronics. At the same time, the fundamentals have been codified quite some time ago, so that there are some cornerstone references that one can turn to with confidence. A couple of textbooks that have passed the test of time with flying colors are:

• Discrete-Time Signal Processing by A. V. Oppenheim and R. W. Schafer
• Theory and Application of Digital Signal Processing by Rabiner and Gold

For a high-level review more in tune with the concepts and language used in this class, please download the free textbook "Foundations of Signal Processing" by M.Vetterli, J.Kovacevic and V.K.Goyal. Section 6.2.6 is particularly relevant.

Alternatively, a quick search on the internet will lead you to countless pages dedicated to filtering examples and filter design. Try it out but don't come back complaining if you end up spending too much time browsing all those cute examples!

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