Digital Signal Processing

About this course: Digital Signal Processing is the branch of engineering that, in the space of just a few decades, has enabled unprecedented levels of interpersonal communication and of on-demand entertainment. By reworking the principles of electronics, telecommunication and computer science into a unifying paradigm, DSP is a the heart of the digital revolution that brought us CDs, DVDs, MP3 players, mobile phones and countless other devices. The goal, for students of this course, will be to learn the fundamentals of Digital Signal Processing from the ground up. Starting from the basic definition of a discrete-time signal, we will work our way through Fourier analysis, filter design, sampling, interpolation and quantization to build a DSP toolset complete enough to analyze a practical communication system in detail. Hands-on examples and demonstration will be routinely used to close the gap between theory and practice. To make the best of this class, it is recommended that you are proficient in basic calculus and linear algebra; several programming examples will be provided in the form of Python notebooks but you can use your favorite programming language to test the algorithms described in the course.

Who is this class for: This course is primarily designed for STEM undergraduates who have already completed classes in calculus and linear algebra. It is also ideal as a Digital Signal Processing primer for students interested in a mathematically solid introduction to the subject. Note that this class is NOT a hands-on, applied DSP course. While many programming examples are provided, the focus is on the theory and not on the implementation.

Created by:  École Polytechnique Fédérale de Lausanne

• Taught by:  Paolo Prandoni, Lecturer

  School of Computer and Communication Science

• Taught by:  Martin Vetterli, Professor

  School of Computer and Communication Sciences

Level Intermediate Commitment 8-10 hours/week Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.7 stars Average User Rating 4.7See what learners said Coursework

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École Polytechnique Fédérale de Lausanne

Syllabus


WEEK 1


Module 1: Basics of Digital Signal Processing



7 videos, 7 readings expand

1. Video: Welcome to the DSP course
2. Reading: Introduction to Module 1
3. Reading: Introduction to Lecture 1.1
4. Video: 1.1.a Introduction to digital signal processing
5. Reading: Introduction to Lecture 1.2
6. Video: 1.2.a Discrete-time signals
7. Reading: Introduction to Lecture 1.3
8. Video: 1.3.a How your PC plays discrete-time sounds
9. Video: 1.3.b The Karplus-Strong algorithm
10. Video: Signal of the Day: Goethe's temperature measurement
11. Reading: Introduction to Lecture 1.4
12. Video: 1.4.a Complex exponentials
13. Reading: Notes and external resources
14. Notebook: Transoceanic Signal Transmission
15. Notebook: The Karplus-Strong Algorithm
16. Reading: Practice homework for Module 1

Graded: Homework for Module 1

WEEK 2


Module 2: Vector Spaces



6 videos, 7 readings expand

1. Reading: Introduction to Module 2
2. Reading: Introduction to Lecture 2.1
3. Video: 2.1.a Signal processing and vector spaces
4. Video: Signal of the Day: Exoplanet hunting
5. Reading: Introduction to Lesson 2.2
6. Video: 2.2.a Vector space
7. Video: 2.2.b Signal spaces
8. Reading: Introduction to Lecture 2.3
9. Video: 2.3.a Bases
10. Reading: Introduction to Lecture 2.4
11. Video: 2.4.a Subspace-based approximations
12. Reading: Notes and external resources
13. Notebook: Haar Bases for Image Compression
14. Reading: Practice homework for Module 2

Graded: Homework for Module 2

WEEK 3


Module 3: Part 1 - Basics of Fourier Analysis



14 videos, 11 readings expand

1. Reading: Introduction to Module 3
2. Reading: Introduction to Lesson 3.1
3. Video: 3.1.a The frequency domain
4. Video: 3.1.b The DFT as a change of basis
5. Reading: Summary of Lesson 3.1
6. Reading: Introduction to Lesson 3.2
7. Video: 3.2.a DFT definition
8. Video: 3.2.b Examples of DFT calculation
9. Video: 3.2.c Interpreting a DFT plot
10. Reading: Summary of Lesson 3.2
11. Reading: Introduction to Lesson 3.3
12. Video: 3.3.a DFT analysis
13. Video: 3.3.b DFT example - analysis of musical instruments
14. Video: 3.3.c DFT synthesis
15. Video: 3.3.d DFT example - tide prediction in Venice
16. Video: 3.3.e DFT example - MP3 compression
17. Video: Signal of the Day: The first man-made signal from outer space
18. Reading: Summary of Lesson 3.3
19. Reading: Real-valued Transforms
20. Reading: Introduction to Lesson 3.4
21. Video: 3.4.a The short-time Fourier transform
22. Video: 3.4.b The spectrogram
23. Video: 3.4.c Time-frequency tiling
24. Reading: Summary of Lesson 3.4
25. Notebook: How to Plot the DFT
26. Notebook: DFT and Numerical Precision
27. Notebook: Dial Tones
28. Reading: Practice homework for Module 3 Part 1

Graded: Homework for Module 3 Part 1

WEEK 4


Module 3: Part 2 - Advanced Fourier Analysis



10 videos, 7 readings expand

1. Reading: Introduction to Lesson 3.5
2. Video: 3.5.a Discrete Fourier series
3. Video: 3.5.b Karplus-Strong revisited and DFS
4. Reading: Summary of Lesson 3.5
5. Reading: Introduction to Lesson 3.6
6. Video: 3.6.a Karplus-Strong revisited and the DTFT
7. Video: 3.6.b Existence and properties of the DTFT
8. Video: 3.6.c The DTFT as a change of basis
9. Reading: Summary of Lesson 3.6
10. Reading: Introduction to Lesson 3.7
11. Video: 3.7.a Sinusoidal modulation
12. Video: 3.7.b Tuning a guitar
13. Video: Signal of the Day: Tristan Chord
14. Reading: Notes and external ressources
15. Video: 3.8* Relationship between transforms
16. Video: 3.9* The fast Fourier transform
17. Notebook: Can You Hear the Phase of a Sound?
18. Notebook: Audio Frequency Beatings
19. Reading: Practice homework for Module 3 Part 2

Graded: Homework for Module 3 Part 2

WEEK 5


Module 4: Part 1 Introduction to Filtering



14 videos, 12 readings expand

1. Reading: Introduction to Module 4
2. Reading: Introduction to Lesson 4.1
3. Video: 4.1.a Linear time-invariant filters
4. Video: 4.1.b Convolution
5. Video: SOTD: Can one hear the shape of a room?
6. Reading: Summary of Lesson 4.1
7. Reading: Introduction to Lesson 4.2
8. Video: 4.2.a The moving average filter
9. Video: 4.2.b The leaky integrator
10. Reading: Summary of Lesson 4.2
11. Reading: Introduction to Lesson 4.3
12. Video: 4.3.a Filter classification in the time domain
13. Video: 4.3.b Filter stability
14. Reading: Summary of Lesson 4.3
15. Reading: Introduction to Lesson 4.4
16. Video: 4.4.a The convolution theorem
17. Video: 4.4.b Examples of frequency response
18. Reading: Summary of Lesson 4.4
19. Reading: Introduction to Lesson 4.5
20. Video: 4.5.a Filter classification in the frequency domain
21. Video: 4.5.b The ideal lowpass filter
22. Video: 4.5.c Ideal filters derived from the ideal lowpass filter
23. Video: 4.5.d Demodulation revisited
24. Reading: Summary to Lesson 4.5
25. Reading: Practice homework for Module 4 Part 1
26. Video: MP3 Encoder
27. Ungraded Programming: MP3 encoder - Spectrum estimation

Graded: Homework for Module 4 Part 1

WEEK 6


Module 4: Part 2 Filter Design



14 videos, 10 readings expand

1. Reading: Introduction to Lesson 4.6
2. Video: 4.6.a Impulse truncation and Gibbs phenomenon
3. Video: 4.6.b Window method
4. Video: 4.6.c Frequency sampling
5. Video: Signal of the Day: Resolution and Space Exploration
6. Reading: Summary of Lesson 4.6
7. Reading: Introduction to Lesson 4.7
8. Video: 4.7.a The z-transform
9. Video: 4.7.b Region of convergence and stability
10. Reading: Summary of Lesson 4.7
11. Reading: Introduction to Lesson 4.8
12. Video: 4.8.a Intuitive IIR designs
13. Reading: Summary of Lesson 4.8
14. Reading: Introduction to Lesson 4.9
15. Video: 4.9.a Filter specifications
16. Video: 4.9.b IIR design
17. Video: 4.9.c FIR design
18. Reading: Summary of Lesson 4.9
19. Reading: Module 4: Notes and external ressources
20. Video: 4.8.b* Fractional delay and Hilbert filter
21. Video: 4.10* Implementation of digital filters
22. Video: 4.11* Real-time processing
23. Video: 4.12* Dereverberation and echo cancellation
24. Notebook: Filtering Music
25. Notebook: FIR Implementation
26. Notebook: Parks-McClellan FIR Design Algorithm
27. Notebook: A Taste of Nonlinear Processing (courtesy of the Beatles)
28. Reading: Practice homework for Module 4 Part 2
29. Ungraded Programming: MP3 encoder - Prototype filter design

Graded: Homework for Module 4 Part 2

WEEK 7


Module 5: Sampling and Quantization



22 videos, 13 readings expand

1. Reading: Introduction to Module 5
2. Reading: Introduction to Lesson 5.1
3. Video: 5.1.a The continuous-time paradigm
4. Video: 5.1.b Continuous-time signal processing
5. Reading: Summary of Lesson 5.1
6. Reading: Introduction to Lesson 5.2
7. Video: 5.2.a Polynomial interpolation
8. Video: 5.2.b Local interpolation
9. Video: Signal of the Day: Fukushima
10. Reading: Summary of Lesson 5.2
11. Reading: Introduction to Lesson 5.3
12. Video: 5.3.a The spectrum of interpolated signals
13. Video: 5.3.b The space of bandlimited functions
14. Video: 5.3.c The sampling theorem
15. Reading: Summary of Lesson 5.3
16. Reading: Introduction to Lesson 5.4
17. Video: 5.4.a Raw sampling
18. Video: 5.4.b Sinusoidal aliasing
19. Video: 5.4.c Aliasing for arbitrary spectra
20. Video: 5.4.d Sampling strategies
21. Reading: Summary of Lesson 5.4
22. Reading: Introduction to Lesson 5.5
23. Video: 5.5.a Stochastic signal processing
24. Video: 5.5.b Quantization
25. Video: Signal of the Day: Lehman Brothers
26. Reading: Summary of Lesson 5.5
27. Reading: Module 5: Notes and external ressources
28. Video: 5.5.c* Clipping, saturation and conpanding
29. Video: 5.6* Practical sampling and interpolation
30. Video: 5.7* Bandpass sampling
31. Video: 5.8* Multirate signal processing
32. Video: 5.9* FIR-based sampling rate conversion
33. Video: 5.10* Analog-to-digital and digital-to-analog converters
34. Video: 5.11* Oversampling
35. Notebook: One-Bit Music
36. Notebook: The Fukushima Disaster and Banlimited Interpolation
37. Reading: Practice homework for Module 5
38. Ungraded Programming: MP3 encoder - Subband filtering

Graded: Homework for Module 5

WEEK 8


Module 6: Digital Communication Systems - Module 7: Image Processing



21 videos, 15 readings expand

1. Reading: Introduction to Module 6
2. Reading: Introduction to Lesson 6.1
3. Video: 6.1.a The success factors for digital communications
4. Video: 6.1.b The analog channel constraints
5. Video: 6.1.c The design problem
6. Video: Signal of the Day: Moire Patterns
7. Reading: Summary of Lesson 6.1
8. Reading: Introduction to Lesson 6.2
9. Video: 6.2.a Upsampling
10. Video: 6.2.b Fitting the transmitter spectrum
11. Reading: Summary of Lesson 6.2
12. Reading: Introduction to Lesson 6.3
13. Video: 6.3.a Noise and probability of error
14. Video: 6.3.b PAM and QAM
15. Reading: Summary of Lesson 6.3
16. Reading: Introduction to Lesson 6.4
17. Video: 6.4.a Modulation and demodulation
18. Video: 6.4.b Design example
19. Reading: Summary of Lesson 6.4
20. Reading: Introduction to Lesson 6.5
21. Video: 6.5.a Receiver design
22. Video: 6.5.b Delay compensation
23. Video: 6.5.c Adaptive equalization
24. Reading: Summary of Lesson 6.5
25. Reading: Introduction to Lesson 6.6
26. Video: 6.6.a ADSL design
27. Video: 6.6.b Discrete multitone modulation
28. Reading: Summary of Lesson 6.6
29. Reading: Module 6: Notes and external ressources
30. Notebook: The Telephone Channel
31. Notebook: Simple Data Transmission
32. Reading: Practice homework for Module 6
33. Ungraded Programming: MP3 encoder - Quantization
34. Video: 7.1* Introduction to image processing
35. Video: 7.2* Image manipulations
36. Video: 7.3* Frequency analysis
37. Video: 7.4* Image filtering
38. Video: 7.5* Image compression
39. Video: 7.6* The JPEG compression algorithm

Graded: Homework for Module 6