Week 3 Help Center
Welcome to Week 3 of Digital Signal Processing.
As announced last week, the next two days' worth of lectures will be once again devoted to Fourier Analysis. Last week we explored the different flavors of Fourier transform available for the various classes of discrete-time signals we introduced in the course. This week we will explore the relationships between these different tools and we will illustrate many practical ways to put Fourier Analysis to use; we also include a last module (4.x) devoted exclusively to real-world applications of the DFT: we will glide over most of the technical details and concentrate on giving you an idea of the far-reaching power of Fourier analysis.
In Day 6 you will find two modules devoted to algorithmic issues. We will start with the Short-Time Fourier Transform, a practical way to use the DFT to analyze long and time-varying signals such as speech or music. To conclude, we will briefly explain the algorithmic techniques behind an implementation of the DFT which goes under the name of Fast Fourier Transform. The efficiency of the FFT is what makes Fourier Analysis computationally possible in practice and it's no understatement that the FFT is the tool that really ushered the digital revolution; this algorithm has a long and fascinating story, dating back to Gauss, and will be the subject of Module 4.9.
Day 5
Video lectures:
Signal of the day:
Practice homework:
Homework (due November 16, 5:00pm CET):
Day 6
Video lectures:
- 4.8 - The Short-Time Fourier Transform
- 4.9 - The Fast Fourier Transform: history and algorithms
- 4.x - Why the DFT is useful: A few examples
Practice homework:
Homework (due November 16, 5:00pm CET):
Notes and external resources
Please see last week's reference for additional material on Fourier Analysis.
For some interesting reads on the algorithmic side of the Fourier Transform you can check the following:
Last Modified Fri 30 Oct 2015 4:28 PM CET