TAILIEUCHUNG - Đề tài " Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order "

Digital signal processing has revolutionized the storage and transmission of audio and video signals as well as still images, in consumer electronics and in more scientific settings (such as medical imaging). The main advantage of digital signal processing is its robustness: although all the operations have to be implemented with, of necessity, not quite ideal hardware, the a priori knowledge that all correct outcomes must lie in a very restricted set of well-separated numbers makes it possible to recover them by rounding off appropriately. . | Annals of Mathematics Approximating a bandlimited function using very coarsely quantized data A family of stable sigma-delta modulators of arbitrary order By Ingrid Daubechies and Ron DeVore Annals of Mathematics 158 2003 679 710 Approximating a bandlimited function using very coarsely quantized data A family of stable sigma-delta modulators of arbitrary order By Ingrid Daubechies and Ron DeVgre 1. Introduction Digital signal processing has revolutionized the storage and transmission of audio and video signals as well as still images in consumer electronics and in more scientific settings such as medical imaging . The main advantage of digital signal processing is its robustness although all the operations have to be implemented with of necessity not quite ideal hardware the a priori knowledge that all correct outcomes must lie in a very restricted set of well-separated numbers makes it possible to recover them by rounding off appropriately. Bursty errors can compromise this scenario as is the case in many communication channels as well as in memory storage devices making the perfect data unrecoverable by rounding off. In this case knowledge of the type of expected contamination can be used to protect the data prior to transmission or storage by encoding them with error correcting codes this is done entirely in the digital domain. These advantages have contributed to the present widespread use of digital signal processing. Many signals however are not digital but analog in nature audio signals for instance correspond to functions f t modeling rapid pressure oscillations which depend on the continuous time t . t ranges over R or an interval in R and not over a discrete set and the range of f typically also fills an interval in R. For this reason the first step in any digital processing of such signals must consist in a conversion of the analog signal to the digital world usually abbreviated as A D conversion. For different types of signals different A D schemes .

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