On matrix-valued wave packet frames in L2(Rd,Cs×r)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2({\mathbb {R}}^d, {\mathbb {C}}^{s\times r})$$\end{document}

In this paper, we study matrix-valued wave packet frames for the matrix-valued function space L2(Rd,Cs×r)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2({\mathbb {R}}^d, {\mathbb {C}}^{s\times r})$$\end{document}. An interplay between matrix-valued wave packet frames and its associated atomic wave packet frames is discussed. This is inspired by examples which show that frame properties cannot be carried from matrix-valued wave packet scaling functions to its associated atomic wave packet scaling functions and vice versa. Construction of matrix-valued wave packet frames for L2(Rd,Cs×r)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2({\mathbb {R}}^d, {\mathbb {C}}^{s\times r})$$\end{document} from corresponding atomic wave packet frames for L2(Rd)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2({\mathbb {R}}^d)$$\end{document} (and conversely) are given. Some special classes of matrix-valued scaling functions are given. A characterization of tight matrix-valued wave packet frames in terms of orthogonality of Bessel sequences has been obtained. Further, we provide a characterization of superframes which can generate matrix-valued frames. Finally, a Paley-Wiener type perturbation result with respect to matrix-valued wave packet scaling functions is given.