Series, Fourier and Z- Transforms (MATLC0022), 3 op

Perustiedot

Esitietovaatimukset

MATL0020 Basic Course of Mathematics, MATL0021 Integral Calculus and Laplace Transforms

Sisältö (ydinaines ja -osaaminen)

Arithmetic and geometric series, power series, application to the evaluation of functions. The concepts of difference equations, discrete functions and the z transform, application to simple problems like moving average. Block diagrams. Fourier series and Fourier transforms, using tables for the basic cases, the concepts of amplitude and phase spectrum.

Sisältö (täydentävä ja erityisosaaminen)

Taylor and Maclaurin series, error estimates. Integration and differential equations using series. Transfer functions of discrete systems, stability, digital filtering. Calculating Fourier series and transforms, discrete and continuous spectra. Power spectrum, Parseval?s theorem, filtering, Bode diagram. Fast Fourier transform. Convolution of discrete and continuous signals. Modulation.

Tiedolliset oppimistulokset (ydinaines ja -osaaminen)

After completion of this course the student understands the meaning of sequences and series and approximation of functions. The student understands the amplitude and phase spectra of discrete and continuous functions and simple filtering. The student has an idea of the connection between time domain and frequency domain.

Taidolliset oppimistulokset (ydinaines ja -osaaminen)

After completion of this course the student is able to evaluate functions using series. The student can solve simple difference equations and use them in the analysis of systems, for example simple filtering. He/she can use tables for Fourier series and Fourier transforms and sketch simple spectra.

Kirjallisuus ja muu materiaali

Croft ? Davison ? Hargreaves: Engineering Mathematics

Opetusmenetelmät

Lectures and
Laboratory assignments
Examinations
Homework and self-study

Opiskelijan kuormittavuus

Tentti - 6
Luennot ja tuntiharjoitukset - 42
Itseopiskelu - 38
Laboratoriotyöt - 14

Arvioinnin perusteet

Examinations (40 % of maximal points) and computer assignments

Koulutusohjelmakohtaiset kompetenssit

Teoreettinen perusta ja matemaattis-luonnontieteelliset valmiudet (T)