Signals and Images

Aim

After passing the course, the student is supposed to be able to

• analyze DC and AC circuits.
• analyze and perform calculations on signals and systems using convolutions, Fourier series and Fourier transforms, in both continuous and discrete time, including transformations between continuous and discrete time.
• account for parts of the basic theory for digital images (two-dimensional signals), e.g. 2D Fourier transform, 2D discrete convolution, resampling, interpolation, the JPG format, and some classical image analysis. The student is supposed to be able to perform related calculations.
• perform experiments on simple electrical circuits and perform calculations on time-varying signals and still-images using a high-level language, such as Python and/or Matlab.

Content

Electric 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. The Sine-in-sine-out principle for stable LTI systems.
• Sampling and reconstruction using pulse-amplitude modulation. The sampling theorem.
• Quantization, noise.

Image Processing:

• From 1D to 2D: Fourier transforms, DFT, sampling, and convolution.
• Linear operations on digital images. Filtering and correlation.
• 2D geometric operations. Interpolation and resampling.
• Histograms and thresholding. Simple morphological operations. Distance maps.
• The JPG format – Compression of images using the JPG format. The cosine transform. The color models RGB and YCbCr.