In this module, Shannon's classical sampling theory is compared to digital to analog signal reconstruction using spline interpolation. In the spline method, the signal is reconstructed using sample-weighted cardinal splines as opposed to sample-weighted s
In this module, the reader will be introduced to the scaling function spline factorization theorem by M. Unser and T. Blu. This factorization allows many key wavelet properties to be derived in a relatively straightforward manner.
On well-known property of valid scaling functions in wavelet analysis is that the scaling functions can perfectly reproduce a polynomial of degree no more than the wavelet smoothness. This property can be easily derived using the Unser-Blu Scaling Function / Spline Factorization Theorem.
Subject:
Mathematics and Statistics, Science and Technology
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