On finite word length effects of second order recursive digital filters
Abstract
Factors which improve digital performance include filter structure, usage of different types of adders and calculation of scale factor. Based on the state space eigenvalue sensitivity function, a low sensitivity realization of a second order IIR filter was determined. The low sensitivity, modularity and mutual compatibility of the implemented output coefficients make this structure a good candidate for filter realization. A closed form upper bound of the filter state was found and used to determine the proper scale factor. For the uniform grid structure, it is shown that if the poles of the filter lie within a specific region, the proposed bound is better than the existing bounds. An algorithm for computing the signal to round off noise power ratio for all minimum realization configurations, is presented. Large magnitude, selfsustained, zero input limit cycle oscillations exist in a two's complement filter of canonical form. The locations of poles and the initial conditions of the filter affect the oscillation. A number of interesting properties concerning this phenomenon are investigated.
 Publication:

Ph.D. Thesis
 Pub Date:
 1981
 Bibcode:
 1981PhDT........48L
 Keywords:

 Digital Filters;
 Eigenvalues;
 Recursive Functions;
 Scaling Laws;
 Algorithms;
 Fixed Points (Mathematics);
 Modularity;
 Signal To Noise Ratios;
 Electronics and Electrical Engineering