Round-Off Errors and Limit Cycles in Digital Filters

Content Provider	Scilit
Author	Agathoklis, P. Tawfik, Ayman
Copyright Year	2020
Description	There are many different possibilities to implement digital filters depending on the speed and hardware requirements of the particular application. Such possibilities include software on a general-purpose computer, DSP chips either using fixed-point or floating-point arithmetic, or hardware implementations using VLSI and FPGAs. All these implementations use finite word lengths (FWL) which generate what is called FWL effects. The severity of these effects, however, can vary significantly. For applications which do not require high speeds, such as non-real-time applications, long word lengths can be used so that the resulting FWL effects are negligible. At the other end, applications where speed and/or hardware complexity are important factors, long word lengths are not always possible and the FWL effects need to be considered carefully. Between these two extremes there are many other cases where it is important to know that the filter implementation will perform as expected after implementation. Techniques to analyze and predict the performance of a digital filter implementation are therefore very useful. In a typical application, the filters to be implemented are obtained using design specifications implied from the particular application. Obviously, there are many different possible designs which satisfy these specifications, and these filters do not perform the same under FWL constraints. In fact, their performances can vary 228significantly even for medium (16 bits) word lengths. Such differences come from changes in the frequency response of the filter due to the finite word length of the parameters or from a decrease in the signal-to-noise ratio in the output due to noise generated from rounding or truncation during arithmetic operations. Further, there is the possibility that the output of the filter exhibits limit cycles due to overflow and becomes independent of the input signal. Book Name: CRC Handbook of ELECTRICAL FILTERS
Related Links	https://content.taylorfrancis.com/books/download?dac=C2006-0-01369-9&isbn=9781003069201&doi=10.1201/9781003069201-15&format=pdf
Ending Page	237
Page Count	11
Starting Page	227
DOI	10.1201/9781003069201-15
Language	English
Publisher	Informa UK Limited
Publisher Date	2020-11-12
Access Restriction	Open
Subject Keyword	Book Name: Crc Handbook of Electrical Filters Hardware and Architecturee Extremes Word Implementation Filter Hardware Speed Digital Arithmetic Possibilities Fwl
Content Type	Text
Resource Type	Chapter