6- https://doi.org/10.1142/s0219691305000853
ON COARSE QUANTIZATION OF TIGHT GABOR FRAME EXPANSIONS
- Jun 1, 2005
- International Journal of Wavelets, Multiresolution and Information Processing
- Özgür Yilmaz
Abstract
This paper presents a coarse quantization algorithm (TFΣΔ-II) for tight Gabor frame expansions of certain functions in L2(ℝ), an alternative to the TFΣΔ of Ref. 11. By using some a priori information about the function to be quantized and compromising the translation invariance of the TFΣΔ, TFΣΔ-II produces an approximation in L2(ℝ), as opposed to the weak type approximations of TFΣΔ. In particular, for a tight Gabor frame with frame bound A, we prove that the L2-approximation error corresponding to a kth-order TFΣΔ-II quantizer is of order O(A-k). Furthermore, motivated by TFΣΔ-II, we construct an algorithm to coarsely quantize the Fourier coefficients of certain compactly supported functions.
- # Tight Gabor Frame
- # Functions In L2
- # Approximation In L2
- # Tight Frame
- # Coarse Quantization
- # Weak Approximations
- # Frame Expansions
- # Gabor Frame
- # Quantization Algorithm
- # Weak Type
