Fourier Analysis, L and Z Transforms (SEFI)Laajuus (6 ECTS)

Objective

The objective is that the student builds a foundation for later studies in professional subjects and learns to see mathematics as a natural part of his or her professional skills and is ready to use mathematical concepts and methods.

Content

The Fourier series and the Fourier transformation: The spectra of a periodical function. The discrete Fourier transformation. Continuous spectra. The properties of the Fourier transformation. Convolution. The Fourier-transformation of the derivative and the integral. The Parseval theorem. The step function and the impulse function. Applications.

The Laplace transform: The properties of the Laplace transformation. The Laplace -transformation of the derivative and the integral. The Laplace -transformation of a periodical function. Convolution. The solution of a linear differential equation by the Laplace -transformation. The transfer function, stability. Impulse response. Applications.

The z-transformation. The properties of The z-transformation. The solution of a linear difference equation by the z-transformation. The transfer function, stability. Impulse response. Applications.

Statistics: Sample. Maximum likelihood estimation. Confidence interval. Hypotesis testing of mean value and variance. Comparing distributions. Regression. The linear correlation. Applications.

Qualifications

Differentiaali- ja integraalilaskennan, sarjojen, kompleksilukujen ja todennäköisyyslaskennan keskeisten käsitteiden ja niihin liittyvien tulosten ymmärtäminen ja soveltamisen taito.