Quadrature mirror filters, low crest factor arrays, functions achieving optimal uncertainty principle bounds, and complete orthonormal sequences – a unified approach. (English) Zbl 0802.42023
Summary: Quadrature mirror filters are used throughout image and speech analysis; low crest factor arrays play an important role in many problems in antenna design and communication; uncertainty principle bounds limit resolution in time-frequency analysis and other areas; and complete orthonormal sequences are crucial in essentially all applications of mathematics to science and engineering. We present a single construction which unifies these four concepts.
MSC:
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
| 94A11 | Application of orthogonal and other special functions |
| 42C10 | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
| 42C30 | Completeness of sets of functions in nontrigonometric harmonic analysis |
