Fourier Series

Lecture Description

Measure, fourier series, and fourier transforms

Course Description

This course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451, is offered in the spring.

Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication.

Course Index

1. Introduction to digital communication
2. Discrete source encoding
3. Memory-less sources
4. Entropy and asymptotic equipartition property
5. Markov sources and Lempel-Ziv universal codes
6. Quantization
7. High rate quantizers and waveform encoding
8. Fourier Series
9. Discrete-time fourier transforms
10. Degrees of freedom
11. Signal space
12. Nyquist theory
13. Random processes
14. Gaussian random vectors white Gaussian noise (WGN)
15. Linear functionals and filtering of random processes
16. Introduction to detection
17. Detection for random vectors and processes
18. Theorem of irrelevance
19. Baseband detection and complex Gaussian processes
20. Introduction of wireless communication
21. Doppler spread
22. Discrete-time baseband models for wireless channels
23. Rrayleigh fading and incoherent channels
24. Code division multiple access (CDMA)