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Welcome to Week 4 of Digital Signal Processing.

By now we know what a signal is, what flavors it comes in, and how to proceed in order to take it apart to see what's inside. It's now time to learn how to manipulate signals, namely, we're going to start the "processing" part of Signal Processing.

This week and the following will be devoted to linear filters and by the end of next week we'll have covered Chapters 5 to 7 in the book; we will skip some of the dry technicalities but, with respect to the text, we'll talk about cool things such as real-time implementations and sound effects. This week we will start with the mandatory theoretical analysis but next week will be chock-full of neat applications. So stay tuned and remember that everything we do in this module you can implement in your numerical package of choice and apply it to your favorite signals!

Day 7

Video lectures:

• 5.1 - Linear Filters
• 5.2 - Filtering by example
• 5.3 - Filter stability

Lecture slides for Module 5: full version .

Signal of the day:

• Can one hear the shape of a room?

Practice homework:

• Practice Homework 7 (Solutions)

Homework (due November 23, 5:00pm CET):

• Homework 7
• Feedback 7

Day 8

Video lectures:

• 5.4 - Frequency response
• 5.5 - Ideal filters
• 5.6 - Filter design - Part 1: Approximation of ideal filters

Lecture slides for Module 5: full version .

Numerical example:

• Linear Time-Invariant Systems (Python), (access on GitHub)

Practice homework:

• Practice Homework 8 (Solutions)

Homework (due November 23, 5:00pm CET):

• Homework 8
• Feedback 8

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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