MATH 464: List of Projects - Spring 2011
1. Pointwise convergence of Fourier series; Dirichlet criterion
2. Hilbert transform and the definition of the instantaneous frequency
3. Haar orthonormal wavelet basis
4. The eigenvectors and eigenvalues of the unitary Fourier transform operator; Hermite functions
5. Wavelets: Multiresolution analysis (MRA)
See the .pdf document.
Solutions of PDE's: see here.
III. Signal Processing
1. Implement the DCT transform and test it for image compression.
2. Implement the windowed Fourier transform and test it for audio signal compression.
3. Implement an orthonormal wavelet transform and test it for audio signal compression.
4. Implement an algorithm that computes the instantaneous frequency of an audio signal, using the Hilbert transform.