Adaptive Filters - Digital Signal Processing and Applications with the C6713 and C6416 DSK - page 275

Example 7.6: Adaptive FIR for System ID of Fixed IIR as an
Unknown System ( adaptIDIIR )

Figure 7.22 shows a listing of the program adaptIDIIR . c , which uses an adaptive
FIR filter to model or identify a system (fixed unknown IIR). See Example 5.1,
which implements an IIR filter, and Examples 7.4 and 7.5, which implement an adap-
tive FIR filter to model a fixed FIR filter.
To test the adaptive scheme, the unknown system to be identified is chosen as a
36th-order IIR bandpass filter with 18 second-order stages centered at 2 kHz. The
coefficients of this fixed IIR filter are in the file bp2000.cof , introduced in
Example 5.1. A 200-coefficient adaptive FIR filter is used to model the fixed
unknown IIR bandpass filter. A larger number of coefficients or weights than for
the adaptive FIR filter are necessary for a good model of the IIR filter.
A pseudorandom noise sequence is generated (see Example 2.16) and becomes
the input to both the fixed IIR filter and the adaptive FIR filter. The adaptation
process continues until the error signal is minimized. This feedback error signal is
the difference between the output of the fixed unknown IIR filter and the output
of the adaptive FIR filter.
Build and run this project as adaptIDIIR . Verify that the output of the adap-
tive filter ( adaptfir_out ) converges to (models) the IIR bandpass filter centered
at 2 kHz, as shown in Figure 7.23 (with the slider initially in position 1).Verify that
the output ( iir_out ) is the fixed IIR bandpass filter with the slider in position 2.
Include the coefficient file lp2000.cof in lieu of bp2000.cof. The coefficient
file lp2000.cof represents an eighth-order (four second-order stages) IIR
lowpass filter with a cutoff frequency of 2 kHz, introduced in Example 5.1. Verify
that the adaptive FIR filter now adapts to the IIR lowpass filter with a cutoff fre-
quency of 2 kHz.

Example 7.7: Adaptive Predictor for Cancellation of Narrowband
Interference Added to a Desired Wideband Signal ( adaptpredict )

The program adaptpredict.c , shown in Figure 7.24, implements an adaptive FIR
predictor for the cancellation of a narrowband interference in the presence of a
wideband signal. The desired wideband signal with an additive narrowband inter-
ference is delayed and becomes the input to a 60-coefficient adaptive FIR filter.
The desired wideband signal is generated with a MATLAB program wbsig-
nal . m , shown in Figure 7.25. This MATLAB program generates a 256-point lookup
table in the file wbsignal.h (on the CD). A random sequence {

1, 1} is generated,
scaled, and written into the file wbsignal.h . Since the random sequence is for
a length of 128 with a bit rate of 4 kHz, it is up-sampled to a 256-point sequence
with a bit rate of 8 kHz. The wideband random sequence generated (with the file
wbsignal.h ) represents the signal desired.
The narrowband interference is an external signal. The bandwidth of the inter-
ference is narrow compared with the bandwidth of the random sequence generated

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