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582 Chapter 10 ROUND-OFF EFFECTS IN DIGITAL FILTERS
Solution
We will need the quantities ∑ |h(n)| 2 and ( ∑ |h(n)|) 2 . These quantities should
be computed using 12-bit quantization of the filter coefficients. These values
using the quantized numbers are ∑ |h(n)| 2 =0.2599 and ( ∑ |h(n)|) 2 =1.Using
(10.88), the output SNR is 65.42 dB for 5 multipliers and is 72.41 dB for 1
multiplier. The following MATLAB script evaluates these and other quantities.
% Example Parameters
B = 12;
% # of fractional bits
N = 100000;
% # of samples
xn = (2*rand(1,N)-1); % Input sequence - Uniform Distribution
h = [0.1,0.2,0.4,0.2,0.1]; % Filter parameters
M = length(h);
% Local variables
bM = 7; DbM = 2^bM; % bin parameter
BB = 2^B;
% useful factor in quantization
K = round(DbM/2); % Half number of bins
bins = [-K+0.5:1:K-0.5]; % Bin values from -K to K
Q = bins/DbM; % Normalized bins
YTN = 2^(-bM);
% Ytick marks interval
YLM = 4*YTN;
% Yaxis limit
% Quantize the input and the filter coefficients
h = QFix(h,B,’round’,’satur’); % h quantized to B bits
Xm = 1/sum(abs(h));
% Scaling factor
xn = QFix(Xm*xn,B,’round’,’satur’);% Scaled Input quant to B bits
% Filter output without multiplication quantization
yn = filter(h,1,xn); % output using filter routine
% Filter output with multi quant (5 multipliers)
x1 = [zeros(1,1),xn(1:N-1)]; x2 = [zeros(1,2),xn(1:N-2)];
x3 = [zeros(1,3),xn(1:N-3)]; x4 = [zeros(1,4),xn(1:N-4)];
h0x0 = QFix(h(1)*xn,B,’round’,’twosc’);
h1x1 = QFix(h(2)*x1,B,’round’,’twosc’);
h2x2 = QFix(h(3)*x2,B,’round’,’twosc’);
h3x3 = QFix(h(4)*x3,B,’round’,’twosc’);
h4x4 = QFix(h(5)*x4,B,’round’,’twosc’);
yq = h0x0+h1x1+h2x2+h3x3+h4x4;
yq = QFix(yq,B,’round’,’satur’);
% Output Error Analysis
qn = yn-yq;
varyn = var(yn); varqn = var(qn);
qqmax = max(qn); qqmin = min(qn);
qnmax = max(abs([qqmax,qqmin]));
qnavg = mean(qn); qnstd = std(qn);
% Outout error sequence
% Signal and noise power
% Maximun and minimum of the error
% Absolute maximum range of the error
% Mean and std dev of the error
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