- 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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