Signal Theory

Aim

After completing the course the students should

• with own words clearly define central concepts regarding the specific topics listed under "course contents".
• with some reliability be able to solve problems that demand integration of knowledge from different parts of the course, i.e. analysis of LTI-filtering, modulation, sampling and non-linear filtering of stochastic processes, both one-dimensional and multi-dimensional.
• be able to, in a structured manner, and using adequate language and terminology, write a report about computer laboratory work.

Content

• Time continuous and time discrete, real as well as complex, stochastic processes: Probability distribution, probability density, expectation, ensemble expectation, auto correlation function, power spectral density, cross correlation function, cross spectral density, stationarity, ergodicity. Especially Gaussian processes and white processes. Multidimensional processes.
• LTI filtering of stochastic processes: Relations between statistical properties of the input process and the output process. Especially matched filters and white Gaussian noise as input.
• Amplitude and angle modulation of stochastic processes: Relations between statistical properties of the input process and the output process. Especially Gaussian processes as input. Noise analysis of those modulation forms, primarily with white Gaussian noise as disturbance.
• Non-linear momentary systems: Quantization and monomial non-linearities. Relations between statistical properties of the input process and the output process. Especially Gaussian processes as input. Properties of quantization noise.
• Transformation between time continuous and time discrete stochastic processes: Sampling and pulse amplitude modulation, the sampling theorem, reconstruction and reconstruction error.
• Case study: Reconstruction in CD players.
• Estimation of expectations, auto correlation function and power spectral density.