Pseudo Clifford Bandpass Prolates

Jeffrey Andrew Hogan, Joseph D Lakey

Abstract: We introduce operators which generalise the classical modulation and translation operators, now acting on functions defined on ${\mathbb R}^m$ and taking values in the associated Clifford algebra ${\mathbb C}_m$. The modulation operators are used to map orthonormal bases for Paley-Wiener spaces associated with balls in ${\mathbb R}^m$ to incomplete orthonormal sets in Paley-Wiener spaces $PW_A$ associated with annuli $A$ in ${\mathbb R}^m$. The complementary spaces are characterised and an orthonormal basis for them is given. These bases are used to construct an orthonormal basis for $PW_A$ composed of pseudo bandpass prolates.

Submission Type: Full Paper