Course overview
This course introduces the mathematical theory used in the study of deterministic and random signals in engineering, including transform methods (Fourier, Laplace, and z-transform), and probability theory. Theory of Fourier series: orthogonal and orthonormal systems; exponential, sine and cosine series. Theory of integral transforms: the Fourier and Laplace transforms and their inverses, properties and formulae; partial fraction expansion of inverses. The z-transform, its properties and its inverse. Applications to the modelling of engineering systems (electrical circuits, oscillatory systems, discrete and digital systems). Probability : discrete and continuous random variables, expectation , estimators. Random signals: autocovariance, ergodicity, power spectral analysis.
Course learning outcomes
- Apply Fourier Series methods to the decomposition of periodic signals.
- Use Fourier and Laplace transforms and their inverses to solve a range of engineering related problems.
- Apply transform and probability techniques to random signal analysis.