Signals, Information and Images

Aim

After passing the course, the student should be able to

• analyze a given passive electrical circuit with respect to direct current and alternating current properties.
• determine the output from both time-continuous and time-discrete stable LTI systems, given a description of the input and the system, in the time domain as well as in the frequency domain.
• understand and apply the sampling theorem.
• describe the fundamentalk limits for compression and transmission of signals and information, perform simple calculations related to these, and understand how these relate to the physical reality.
• describe and exhibit ingineering understanding of the basic principles for techniques for storing and transmission of information that are used in practice.
• describe 2D continuous and discrete signals in the spatial domain, sampling, convolution and the most common cores.
• interprete the result of a 2D Fourier transform fouriertransform of an image, such as understanding what a spatial frequency means / interpretation of the most common filters.
• describe fundamental geometrical image transformations and color models.
• account for the connection between different concepts in the course in a structured way using adequate terminology.

Content

Electrical circuits:

• Direct Current – Ohm’s law, Kirchhoff’s laws. Resistance, sources, power.
• Alternating Current – the j-omega method. Capacitance, inductance, power. dB.

Signals and Systems, in continuous time as well as in discrete time – the concept of LTI systems and their connection to difference and differential equations:

• Examples of signals in applications of electrical engineering.
• Analysis in the time domain – Unit impulses, impulse response, convolution.
• Analysis in the frequency domain – Fourier series and transforms. Also the cosine transform, used in JPG. The Sine-in-sine-out principle for stable LTI systems.
• Sampling and reconstruction using pulse-amplitude modulation. The sampling theorem.
• Quantization, noise.

Information:

• Entropy
• Data compression – Huffman codes
• Error correction – Hamming kodes – Fundamental limits.

Images:

• The JPG format – Compression of images using the JPG format.
• From 1D to 2D: Fourier transforms, DFT, sampling, and convolution.
• Linear operations on digital images.
• 2D geometry.
• Color models and histogram operations.