Digital signal processing (3rd ed.): principles, algorithms, and applications
Digital signal processing (3rd ed.): principles, algorithms, and applications
Numerical computing with IEEE floating point arithmetic
Numerical computing with IEEE floating point arithmetic
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Formal Aspects of Correctness and Optimality of Interval Computations
Formal Aspects of Computing
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In this article, we use the interval mathematics and targeted rounding by specific functions to establish a framework for interval quantization. The function approximation F Id, that maps x to an interval [x 1, x 2] such that x 1 is the largest floating point number less than or equal to x and x 2 is the smallest floating point number greater than or equal to x, is used to establish the sampling interval and the levels of interval quantization. We show that the interval quantization levels (N j) represent the specific quantization levels (n j), that are comparable, according to Kulisch- Miranker order and are disjoint two by two. If an interval signal X[n] intercepts a quantization interval level N j, then the quantized signal will be X q[n] = N j. Moreover, for the interval quantization error (E[n] = X q[n] − X[n]) an estimate is shown due to the quantization step and the number of levels. It is also presented the definition of interval coding, in which the number of required bits depends on the amount of quantization levels. Finally, in an example can be seen that the the interval quantization level represent the classical quantization levels and the interval error represents the classical quantization error. (This work was partially supported by the Brazilian funding agency CAPES and by the Federal Institute for Education, Science and Technology of Rio Grande do Norte.)