1. Pointwise convergence of Fourier series; Dirichlet criterion

2. Hilbert transform and the definition of the instantaneous frequency

3. The eigenvectors and eigenvalues of the unitary Fourier transform operator; Hermite functions

5. Generalized functions: definition, derivatives, and Fourier transform

6. Solution of vibrating chords

See the .pdf document.

Solutions of PDE's: see here.

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.