Description of the course:
Introduction to the basics of signal processing, with special emphasis on practice and applications. The theoretical results are illustrated by practical examples. The signal processing algorithms are implemented by the students in Matlab.
Syllabus:
Basics of signal processing.
· Discrete time systems
· Linear time invariant systems
· Discrete time systems
· Time and frequency domain
· Fourier Transform, DFT, FFT. The z-transform
Sampling in time domain
· Modelling of sampling
· Sampling theorems. Reconstruction of band-limited signals
· Sub-sampling and over-sampling. Application: equivalent sampling
Sampling in amplitude domain
· A/D converters
· Quantization error and its characterization
· D/A converters
· Delta-sigma modulation and its applications
Digital filters
· FIR and IIR filters
· Digital filter structures
· FIR filter design: windowing, sampling in frequency domain, equiripple filter design
· IIR filter design: analog filter design and transformation to digital domain
Discrete Fourier transform and its applications
· Properties of DFT
· Windowing and its application
· The FFT
· Circular and linear convolution
· Spectrogram and periodogram
Adaptive filters
· Optimal linear filtering: the Wiener filter. The Wiener-Hopf equation
· The LMS algorithm and its variants. Applications of the LMS algorithm.
· A Kalman filter and its applications
Literature:
Oppenheim, AV, Shafer, RW: Discrete Time Signal Processing. Pearson, Upper Saddle River, 2010
Ingle, VK, Proakis JG: Disgital Signal Processing Using Matlab V.4. PWS Publishing Company, Boston, 1997
Widrow, B, Stearns, SD: Adaptive Signal Processing. Prentice Hall, 1985
Grewal, MS, Andrews, AP: Kalman Filtering: Theory and Practice with MATLAB, 4th Edition. John Wiley & Sons, Inc., Hoboken, New Jersey, 2015
Mandic, DP; Kanna, S; Constantinides, AG: On the Intrinsic Relationship Between the Least Mean Square and Kalman Filters," Signal Processing Magazine, IEEE, vol.32, no.6, pp.117-122, Nov. 2015