System Design Flow and Fixed-point Arithmetic - Digital Design of Signal Processing Systems: A Practical Approach - page 123

sosMatrix: [4x6 double]
ScaleValues: [5x1 double]
ResetBeforeFiltering: 'on'
States: [2x4 embedded.fi]
NumSamplesProcessed: 0
CoeffWordLength: 16
CoeffAutoScale: true
Signed: true
InputWordLength: 16
InputFracLength: 15
StageInputWordLength: 16
StageInputAutoScale: true
StageOutputWordLength: 16
StageOutputAutoScale: true
OutputWordLength: 16
OutputMode: 'AvoidOverflow'
StateWordLength: 16
StateFracLength: 15
ProductMode: 'FullPrecision'
AccumMode: 'KeepMSB'
AccumWordLength: 40
CastBeforeSum: true
RoundMode: 'convergent'
OverflowMode: 'wrap'

While exploring different design options for optimal word length, any of the attributes of hd can
be changed using set directive.
Filter Design and Analysis Tool (FDATOOL) is a collection of tools for design, analysis,
conversion and code generation. The tool designs FIR and IIR digital filters in both floating-point
and fixed-point formats. The tool provides a great degree of control with a user-friendly interface.
Figure 3.28 shows two snapshots of the GUI depicting all the design options available to the designer
for designing, analyzing, fixed-point conversion and code generation. The elliptical filter can also be
conveniently designed by setting different options in FDATOOL.

3.8.3 Coefficient Quantization Analysis of a Second-order Section
Even in second-order section the quantization effects can be further mitigated. The conversion
in fixed-point format of the denominator coefficient as given in (3.14) creates a non-uniform
grid:

1

HðÞ¼ ð 3 : 14 Þ

1 þa 1 z 1 þa 2 z 2

The grid is shown in Figure 3.29 for a 1 and a 2 converted to Q3.3 and Q2.4 formats,
respectively. A filter design package, depending on the specifications, may place a double-
precision pole at any point inside the unit circle. The conversion of the coefficients to fixed-point