Embedded Software and Motor Control Libraries for PXR40xx

Function GDFLIB_FilterIIR1_F32
main difference between DF-I and DF-II implementations of an IIR filter is in the number
of delay buffers and in the number of guard bits required to handle the potential overflow.
The DF-II implementation requires less delay buffers than DF-I, hence less data memory
is utilized. On the other hand, since the poles come first in the DF-II realization, the
signal entering the state delay-line typically requires a larger dynamic range than the
output signal y(k). Therefore, overflow can occur at the delay-line input of the DF-II
implementation, unlike in the DF-I implementation.
Because there are two delay buffers necessary for both DF-I and DF-II implementation of
the first order IIR filter, the DF-I implementation was chosen to be used in the
GDFLIB_FilterIIR1_F32 function.
Figure 4-1. Direct Form 1 first order IIR filter
The coefficients of the filter depicted in Figure 4-1 can be designed to meet the
requirements for the first order Low (LPF) or High Pass (HPF) filters. Filter coefficients
can be calculated using various tools, for example, the Matlab butter function. In order to
avoid overflow during the calculation of the GDFLIB_FilterIIR1_F32 function, filter
coefficients must be divided by eight. The coefficient quantization error due to finite
precision arithmetic can be neglected in the case of a first order filter. Therefore, the
calculation of coefficients can be done using Matlab as follows:
freq_cut = 100;
T_sampling = 100e-6;
[b,a]=butter(1,[freq_cut*T_sampling*2],'low');
sys=tf(b,a,T_sampling);
bode(sys)
f32B0 = b(1)/8;
f32B1 = b(2)/8;
f32A1 = a(2)/8;
disp('Coefficients for GDFLIB_FilterIIR1 function:');
disp(['f32B0 = FRAC32 (' num2str(f32B0) ')']);
disp(['f32B1 = FRAC32 (' num2str(f32B1) ')']);
disp(['f32A1 = FRAC32 (' num2str(f32A1) ')']);
Note
The filter delay line includes two delay buffers which should be
reset after filter initialization. This can be done by assigning to
the filter instance a GDFLIB_FILTER_IIR1_DEFAULT_F32
Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0
170 Freescale Semiconductor, Inc.