6 papers
Representation theory and multilevel filters
Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
We present a general setting where wavelet filters and multiresolution decompositions can be defined, beyond the classical setting. This is done in a fr…
Discrete Wiener Algebra in the Bicomplex Setting, Spectral Factorization with Symmetry, and Superoscillations
Daniel Alpay, Izchak Lewkowicz, Mihaela Vajiac
In this paper we present parallel theories on constructing Wiener algebras in the bicomplex setting. With the appropriate symmetry condition, the bicomplex matrix valued case can b…
Characterizations of families of rectangular finite impulse response, para-unitary systems
Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
We here study Finite Impulse Response (FIR) rectangular, not necessarily causal, systems which are (para)-unitary on the unit circle (=the class ). First, we offer thr…
A new realization of rational functions, with applications to linear combination interpolation
Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz +1
We introduce the following linear combination interpolation problem (LCI): Given distinct numbers and complex numbers and , find all…
Realizations of infinite products, Ruelle operators and wavelet filters
Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
Using the notions and tools from realization in the sense of systems theory, we establish an explicit and new realization formula for families of infinite products of rational matr…
State space realization of even generalized positive and odd rational function. Applications to static output feedback
Daniel Alpay, Izchak Lewkowicz
We here specialize the well known Positive Real Lemma (also known as the Kalman-Yakubovich-Popov Lemma) to complex matrix-valued rational functions, (i) generalized positive even a…