Course pages 2015–16
Digital Signal Processing
No. of lectures: 12
Suggested hours of supervisions: 3
Prerequisite courses: Mathematical Methods I-III, Mathematical Methods for Computer Science, LaTeX and MATLAB.
This course teaches the basic signal-processing principles necessary to understand many modern high-tech systems, with digital-communications examples. Students will gain practical experience from numerical experiments in MATLAB-based programming assignments.
- Signals and systems. Discrete sequences and systems, their types and properties. Linear time-invariant systems, convolution.
- Phasors. Eigen functions of linear time-invariant systems. Review of complex arithmetic. Some examples from electronics, optics and acoustics.
- Fourier transform. Phasors as orthogonal base functions. Forms and properties of the Fourier transform. Convolution theorem.
- Dirac’s delta function. Fourier representation of sine waves, impulse combs in the time and frequency domain.
- Discrete sequences and spectra. Periodic sampling of continuous signals, periodic signals, aliasing, interpolation, sampling and reconstruction of low-pass and band-pass signals, spectral inversion.
- Digital modulation. IQ representation of band-pass signals, in particular AM, FM, PSK, and QAM signals.
- Discrete Fourier transform. Continuous versus discrete Fourier transform, symmetry, linearity, review of the FFT, real-valued FFT.
- Spectral estimation. Leakage and scalloping phenomena, windowing, zero padding.
- Finite impulse-response filters. Properties of filters, implementation forms, window-based FIR design, use of frequency-inversion to obtain high-pass filters, use of modulation to obtain band-pass filters, FFT-based convolution.
- Infinite impulse-response filters. Sequences as polynomials, z-transform, zeros and poles, some analog IIR design techniques (Butterworth, Chebyshev I/II, elliptic filters).
- Random sequences and noise. Random variables, stationary processes, autocorrelation, crosscorrelation, deterministic crosscorrelation sequences, filtered random sequences, white noise, exponential averaging.
- Correlation coding. Random vectors, dependence versus correlation, covariance, decorrelation, matrix diagonalization, eigen decomposition, Karhunen-Loève transform, principal component analysis. Relation to orthogonal transform coding using fixed basis vectors, such as DCT.
By the end of the course students should be able to
- apply basic properties of time-invariant linear systems;
- understand sampling, aliasing, convolution, filtering, the pitfalls of spectral estimation;
- explain the above in time and frequency domain representations;
- use filter-design software;
- visualize and discuss digital filters in the z-domain;
- use the FFT for convolution, deconvolution, filtering;
- implement, apply and evaluate simple DSP applications in MATLAB;
- apply transforms that reduce correlation between several signal sources;
- explain the basic principles of some widely-used modulation and image-coding techniques.
* Lyons, R.G. (2010). Understanding digital signal processing. Prentice Hall (3rd ed.).
Oppenheim, A.V. & Schafer, R.W. (2007). Discrete-time digital signal processing. Prentice Hall (3rd ed.).