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| Detailed information |
| Original study plan |
Master's programme Computational Mathematics 2026W |
| Learning Outcomes |
Competences |
- Analytical Competency: Extract and interpret time-frequency information from signals (e.g., for pattern recognition or noise reduction).
- Modeling Competency: Select and justify appropriate transformation methods (Fourier vs. wavelet) for specific applications.
- Technical Competency: Implement and optimize algorithms for signal and image compression.
- Critical Evaluation: Assess the advantages and limitations of wavelet transforms compared to other methods (e.g., Fourier).
- Problem-Solving Competency: Solve real-world problems (e.g., in image processing or data analysis) using wavelet-based methods.
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| Skills |
Knowledge |
- Perform transformations: Apply Fourier, windowed Fourier, and wavelet transforms to a given function or sequence.
- Decomposition and reconstruction: Decompose a function with respect to a frame or orthogonal wavelet basis.
- Reconstruct the original function from transformation coefficients.
- Compression applications: Compress signal and image data using the discrete wavelet transform. Adjust compression parameters (e.g., quantization steps) and analyze their effects.
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- Definitions and properties of the Fourier transform, windowed Fourier transform, and wavelet transform.
- Fundamentals of frames and orthogonal wavelet bases (e.g., Haar wavelets, Daubechies wavelets).
- Principles of time-frequency analysis and multiresolution analysis.
- Mathematical foundations of signal and image compression (e.g., sparsity, quantization).
- Differences between continuous and discrete wavelet transforms.
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| Criteria for evaluation |
Oral exam
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| Methods |
Blackbord presentation
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| Language |
English |
| Changing subject? |
No |
| Further information |
- Lecture notes;
- Ten Lectures on Wavelets by Ingrid Daubechies;
- Wavelets by Louis, Maass, Rieder.
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| Earlier variants |
They also cover the requirements of the curriculum (from - to)
403MMIEWFAV22: VL Wavelets – Functional Analytical Basics (2022W-2023S)
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