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554 Chapter 10 ROUND-OFF EFFECTS IN DIGITAL FILTERS
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(a) Two’s-complement Overflow
FIGURE 10.9 Overflow characteristics used in Qfix
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(b) Saturation
To simulate these two effects, we provide the function y = Qfix(x,B,
’Qmode’,’Omode’). This function performs a fixed-point two’scomplement
format quantization using (B+1)-bit representation so that
the resulting number y is between −1 ≤ y < 1. The quantization mode,
Qmode, iseither a rounding or a truncation operation. The overflow characteristic
is provided in Omode. Using this function, we can study both
types oflimit cycles.
function [y] = QFix(x,B,Qmode,Omode)
% Fixed-point Arithmetic using (B+1)-bit Representation
% -----------------------------------------------------
% [y] = QFix(x,B,Qmode,Omode)
% y: Decimal equivalent of quantized x with values in [-1,1)
% x: a real number array
% B: Number of fractional bits
% Qmode: Quantizer mode
% ’round’: two’s-complement rounding characteristics
% ’trunc’: Two’s complement truncation characteristics
% Omode: Overflow mode
% ’satur’: Saturation limiter
% ’twosc’: Two’s-complement overflow
% Quantization operation
if strcmp(lower(Qmode), ’round’);
y = round(x.*(2^B));
elseif strcmp(lower(Qmode), ’trunc’);
y = floor(x.*(2^B));
else
error(’Use Qmode = "round" or "trunc"’);
end;
y = y*(2^(-B)); % (B+1)-bit representation
% Overflow operation
if strcmp(lower(Omode), ’satur’);
y = min(y,1-2^(-B)); y = max(-1,y); % Saturation
elseif strcmp(lower(Omode), ’twosc’);
y = 2*(mod(y/2-0.5,1)-0.5); % Overflow
else error(’Use Omode = "satur" or "twosc"’);
end;
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