Section I: The Transforms
Signal Processing I: Sampling of the Signal (The Sampling Theorem, The Convolution, The Correlation, Correlation is not Causation, Decomposition of the Signal on the Sphere)
Signal Processing II: The Fourier Transform (The DFT, The FFT, The Power Spectrum, The Phases, Discretization of the Signal on the Sphere)
The Information: Wavelets, PCA and EMD (Data compression, MP3, JPEG2000,JP3D)
Section II: The Signal and The Noise
The Noise: Noise Sources, Noise Types and Spectra, SNR maximization, Noise suppression
Data Restoring: Image reconstruction vs Scanning, Speckle Imaging, Blind Deconvolution
Data Analysis: Patterns in Data, Punctual Operatore and Filters, More Transforms, Morphological Operators and Descriptors
In the LAB:
Data Access: FITS + multiFITS
Datafication examples: H-R diagram, Kepler data and star periods
The Fourier Transform: Fourier spectrum, Digital Filters, Data manipulation (shifts, transform)
Data-cubes Analysis: Wavelet Spectra, EMD analysis
Data Compression: Image quality estimators, Image information estimators.
The aim of the course is to provide to the student a broad overview of the various methods and techniques of data analysis, with a deeper insight on those used in modern-time astrophysics. In particular, we will study the aspects of digital information access, handling, restoration, manipulation, compression and transformation into data.