7 Integer Filters

When digital filters must operate in a real-time environment, many filter designs become unsatisfactory due to the amount of required computation time. A considerable reduction in computation time is achieved by replacing floating-point coefficients with small integer coefficients in filter equations. This increases the speed at which the resulting filter program executes by replacing floating-point multiplication instructions with integer bit-shift and add instructions. These instructions require fewer clock cycles than floating-point calculations. Integer filters are a special class of digital filters that have only integer coefficients in their defining equations. This characteristic leads to some design constraints that can often make it difficult to achieve features such as a sharp cutoff frequency. Since integer filters can operate at higher speeds than traditional designs, they are often the best type of filter for high sampling rates or when using a slow microprocessor. This chapter discusses basic design concepts of integer filters. It also reviews why these filters display certain characteristics, such as linear phase, and how to derive the transfer functions. Next this theory is extended to show how to design low-pass, high-pass, bandpass, and band-reject integer filters by appropriate selection of pole and zero locations. Then a discussion shows how certain aspects of filter performance can be improved by cascading together integer filters. Next a recent design method is summarized which is more complicated but adds flexibility to the design constraints. Finally, a lab provides hands-on experience in the design and use of integer filters. 7.1 BASIC DESIGN CONCEPT Lynn (1977) presented the best known techniques for integer filter design used today by showing a methodology to design low-pass, high-pass, bandpass, and bandreject filters with integer coefficients. This method is summarized in several steps. First place a number of evenly spaced zeros around the unit circle. These zeros completely attenuate the frequencies corresponding to their locations. Next choos