Integral TransformsLaajuus (3 ECTS)

Objective

After completing the course, the student will know the basic concepts and techniques of integral transforms, and the basic properties of the transforms. The student will know the principles and restrictions of using the conversion tables. The student will know the basic properties of periodic functions and their representations as Fourier series together with the concept of the spectrum. The student will know the basic principles related to filtering.

After completing the course, the student will be able to use integral transforms to solve simple models, and make good use of the conversion tables. The student will be able to investigate the stability of the transfer function by the poles, and to define the step and impulse response. The student will be able to use MATLAB to solve problems related to integral transforms.

Content

1. Laplace transform
2. Fourier series, spectrum
3. Fourier transform

Qualifications

Differential Calculus and Integral Calculus

Assessment criteria, satisfactory (1)

1. Laplace transform
The student understands the concept of Laplace transform. He or she can calculate simple Laplace transforms using a transform table.

2. Fourier series, spectrum
The student understands the concept of Fourier series and spectrum. He or she can calculate the Fourier series of simple signals.

3. Fourier transform
The student understands the concept of Fourier transform. He or she can calculate the Fourier transform of simple signals.

Assessment criteria, good (3)

1. Laplace transform
The student is able to derive the Laplace transform of simple signals without using a transform table.

2. Fourier series, spectrum
The student understands and is able to calculate the Fourier series of more complex signals. He or she has a clear understanding of signal spectrum.

3. Fourier transform
The student is able to calculate the Fourier transform of more complex signals.

Assessment criteria, excellent (5)

1. Laplace transform
The student has a clear and intuitive understanding of Laplace transform. He or she is able to solve demanding problems involving the use of Laplace transform.

2. Fourier series, spectrum
The student has an excellent understanding of Fourier series and spectrum.

3. Fourier transform
The student is able to solve demanding problems involving the use of Fourier transform. He or she is able to calculate the Fourier transform of demanding signals. He or she is able to derive the Fourier transform of systems and signals.