Correction to "Symmetry constraints on two-dimensional half-plane digital transfer functions"
point arithmetic with the accuracy provided by the machine. A built-in program was used to generate white complex noise (with its real and imaginary parts being distributed uniformly between +l/fi) for feeding the two programs. A stable estimate of average NSR of each module was obtained for two different word lengths using the results of the two programs. v. RESULTS AND DISCUSSIONS For the purpose of calculation of the NSR, tl and t2 are assumed to be same. It is evident from Table I11 that the correlated model predicts the NSR much closer to the experimental results (for both 8 and 12 bits) than those predicted by the uncorrelated model. It is observed that the predicted output NSR falls short at most by 10.888 percent while those predicted by the uncorrelated model fall short by as much as 4 1.98 percent from the corresponding simulation results. While analyzing for the variances due to the coefficient quantization and rounding due to multiplication, the earlier authors [6] are not consistent in assuming the multiplying coefficients like +1 and ?j as noiseless. However, the present analysis considers these coefficients as noiseless for all the modules studied. The values of b and c thus obtained here are slightly different from those of Patterson and McClellan [ 61. Two truncation errors connected through more than one path, though correlated, have very small correlation coefficients. Since the analytical computation of such a correlation coefficient is more involved, it is neglected. The slight difference between simulation results and those of some correlated models could be due to such an assumption. Overscaling a module has been adopted to facilitate scaling procedure which, in turn, has introduced extra noise variance. Long-length GW DFT algorithms are derived using these shortlength DFT algorithms. Patterson and McClellan [6] have shown that the order in which the component algorithms are used affects the error performance. For minimum error performance, they should be used in such a way that the numbers (o;Ni)/(Ni - 1) are in increasing order. With respect to the output noise variance per unit, the modules are arranged in descending order as 7, 5, 9, 16, 3, 8, 4, and 2 which, according to the uncorrelated model, was 5, 7, 9, 3, 16, 8,4, and 2. Close agreement between theoretically predicted results and those of simulations justifies the validity of assumptions made in the analysis. The error performance of large-N GW algorithms under the assumption of correlation between truncation errors has been studied elsewhere [ 81.