Embedded Software and Motor Control Libraries for PXR40xx

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_F16 function.
Figure 4-2. Direct Form 1 first order IIR filter
The coefficients of the filter depicted in Figure 4-2 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. 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)
f16B0 = b(1);
f16B1 = b(2);
f16A1 = a(2);
disp('Coefficients for GDFLIB_FilterIIR1 function:');
disp(['f16B0 = FRAC16 (' num2str(f16B0) ')']);
disp(['f16B1 = FRAC16 (' num2str(f16B1) ')']);
disp(['f16A1 = FRAC16 (' num2str(f16A1) ')']);
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_F16
macro during instance declaration or by calling the
GDFLIB_FilterIIR1Init_F16 function.
Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0
Chapter 4 API References
Freescale Semiconductor, Inc. 175