After successful completion of the course, the student is expected to be able to:
represent time series with linear functions, polynomials or splines,
analyse time series for deterministic or statistical behaviour,
transform time series to spectra with Fourier transformation,
understand the processes leading to aliasing and spectral leakage and design filters to prevent aliasing and leakage,
compare the performance of different filters in time and frequency domain.
Least-squares approximations: linear functions, polynomial functions, splines. Deterministic and statistical time series. Fourier expansion: sampling theorem; finite record length, leakage and windowing. Practical estimation of spectra: discrete and Fast Fourier transform; convolution, covariance and correlation; covariance of power spectral estimates. Time and frequency filtering: convolution and deconvolution; shaping filters; spiking filters; matched filters; prediction filters. Z- transform, wavelets and applications as filters.
Lectures, homework, problem solving and computer exercises.
Take-home examination (3 credits) and homework assignments (2 credits).