Construction of dual wavelet frame pairs and signal recovery. (English) Zbl 1440.42142
Summary: Signal processing is an enabling technology that helps us to denote any operation which modifies or analyzes the information contained in a signal. In this paper, we first decompose the original signal by a wavelet packet frame and analyze the coefficients. Then, by using dual wavelet frames, we reconstruct the original signal. In this reconstruction, the standard choice for duals which plays a key role is the canonical dual. Our aim is to develop new duals to obtain more accurate results. To this end, we consider wavelet frames which Fourier transform of generators form a partition of unity. Then we introduce several explicit duals for them and compare the advantage of these duals in signal processing. This indicates that we may obtain more reliable estimates by alternate duals.
MSC:
| 42C15 | General harmonic expansions, frames |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
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