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Series, Fourier and Z- Transforms (MATLC0022), 3 op
Basic information
| Course name: | Series, Fourier and Z- Transforms Series, Fourier and Z- Transforms |
| Course Winha code: | MATLC0022 |
| Kurre acronym: | SeriesFz |
| Credits: | 3 |
| Type and level of course: | Basic studies |
| Year of study, semester or study period: | 2.year |
| Implementation: | Autumn semester, 3.period, 4.period |
| Semester: | 0708 |
| Language of tuition: | English |
| Teacher: | Seppo Uusitalo |
| Final assessment: | Grading scale (0-5) |
Descriptions
Prerequisites
MATL0020 Basic Course of Mathematics, MATL0021 Integral Calculus and Laplace Transforms
Course contents (core content level)
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.
Course contents (additional)
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.
Core content level learning outcomes (knowledge and understanding)
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.
Core content level learning outcomes (skills)
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.
Recommended reading
Croft ? Davison ? Hargreaves: Engineering Mathematics
Teaching and learning strategies
Lectures and assignments
Laboratory assignments
Examinations
Homework and self-study
Teaching methods and student workload
Exam
Lectures and assignments
Self-study
Laboratory assignments
Assessment weighting and grading
Examinations (40 % of maximal points) and computer assignments