Unlimited Sampling Theorem Based on Fractional Fourier Transform

Fractal and Fractional

article

Hui Zhao¹  Bing-Zhao Li¹ 

[1] School of Mathematics and Statistics, Beijing Institute of Technology;Beijing Key Laboratory on MCAACI, Beijing Institute of Technology

关键词: Fourier transform;    fractional Fourier transform;    unlimited sampling theorem;    nonlinear modulus mapping;   

DOI  :  10.3390/fractalfract7040338

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

The recovery of bandlimited signals with high dynamic range is a hot issue in sampling research. The unlimited sampling theory expands the recordable range of traditional analog-to-digital converters (ADCs) arbitrarily, and the signal is folded back into a low dynamic range measurement, avoiding the saturation problem. Since the non-bandlimited signal in the Fourier domain cannot be directly applied to its existing theory, the non-bandlimited signal in the Fourier domain may be bandlimited in the fractional Fourier domain. Therefore, this brief report studies the unlimited sampling problem of high dynamic non-bandlimited signals in the Fourier domain based on the fractional Fourier transform. Firstly, a mathematical signal model for unlimited sampling is proposed. Secondly, based on this mathematical model, the annihilation filtering method is used to estimate the arbitrary folding time. Finally, a novel fractional Fourier domain unlimited sampling theorem is obtained. The theory proves that, based on the folding characteristics of the self-reset ADC, the number of samples is not affected by the modulo threshold, and any folding time can be handled.

【 授权许可】

CC BY