Objectives:
· To
know how to identify a system using Adaptive filtering
·
To investigate
the “Adaptive filter for equalization”
Equipment and tools:
·
A
computer having code composedly studio and Matlab.
·
A
6713dsk toolkit.
·
A
picoscope.
Theory:
System identification an be accomplished by using the adaptive
filter be connecting both the unknown system and the adaptive filter in
parallel as shown in Figure
3. A random test signal is applied as an input for both
the unknown system and the adaptive filter.
The error signal is the difference between
the response of the unknown system and the response of the
adaptive filter . This error signal is fed back to the adaptive filter and is used
to update the adaptive filter’s coefficients until the overall output .When this happens, the adaptation process is finished, and
approaches zero. If the
unknown system is linear and not timevarying, then after the adaptation is
complete, the filter’s characteristics no longer change. In this scheme, the
adaptive filter models the unknown system.
1.
Adaptive
predictor. Figure
4 shows an adaptive predictor structure that can provide
an estimate of an input. This structure is illustrated later with a programming example.
Experimental procedures
An extra memory location is used in each of the two delay sample
buffers (fixedand adaptive FIR). This is used to update the delay samples (see
method B inExample 4.8in Rulphchassing).
1.
Design
an FIR band pass filter with a center frequency of , bandwidth of 400 Hz. Use 55 coefficients in
designing the filter. Export the filter coefficients to a file called bp55.cof
2.
Use
the following header file required for the random noise generation in your
project directory
//Noise_gen.h header file for pseudorandom noise
sequence
typedefstruct BITVAL //register bits to be packed as integer
{
unsigned int
b0:1, b1:1, b2:1, b3:1, b4:1, b5:1, b6:1;
unsigned int
b7:1, b8:1, b9:1, b10:1, b11:1, b12:1,b13:1;
unsigned int
dweebie:2; //Fills the 2 bit hole  bits 1415
} bitval;
typedef union SHIFT_REG
{
unsigned
intregval;
bitvalbt;
} shift_reg;

3.
Build
and run this project as adaptIDFIR. Verify that the output (adaptfir_out) of
the adaptive FIR filter converges to a bandpass filter centered at 2kHz(with
the slider in position 1 by default).
4.
With
the slider in position 2, verify the output (fir_out) of the fixed FIR bandpass
filter centered at 2 kHz and represented by the coefficient file bp55.cof. It
can be observed that this output is practically identical to the adaptive
filter’s output.
#include "DSK6713_AIC23.h" //codecDSK
support file
Uint32 fs=DSK6713_AIC23_FREQ_8KHZ; //set sampling
rate
#include "bp55.cof" //fixed FIR filter
coefficients
#include "noise_gen.h" //support noise
generation file
#define beta 1E14 //rate of convergence
#define WLENGTH 60 //# of coefffor adaptive FIR
float w[WLENGTH+1]; //buffer coeff for adaptive FIR
intdly_adapt[WLENGTH+1]; //buffer samples of
adaptive FIR
intdly_fix[N+1]; //buffer samples of fixed FIR
short out_type = 1; //output for adaptive/fixed FIR
intfb; //feedback variable
shift_regsreg; //shift register
intprand(void) //pseudorandom sequence {1,1}
{
intprnseq;
if(sreg.bt.b0) prnseq = 8000; //scaled negative
noise level
else prnseq = 8000; //scaled positive noise level
fb =(sreg.bt.b0)^(sreg.bt.b1); //XOR bits 0,1
fb^=(sreg.bt.b11)^(sreg.bt.b13); //with bits 11,13
>fb
sreg.regval<<=1;
sreg.bt.b0=fb; //close feedback path
return prnseq; //return noise sequence
}
interrupt void c_int11() //ISR
{
int i;
intfir_out = 0; //init output of fixed FIR
intadaptfir_out = 0; //init output of adapt FIR
float E; //error=diff of fixed/adapt out
dly_fix[0] = prand(); //input noise to fixed FIR
dly_adapt[0]=dly_fix[0]; //as well as to adaptive
FIR
for (i = N1; i>= 0; i)
{
fir_out +=(h[i]*dly_fix[i]); //fixed FIR filter
output
dly_fix[i+1] = dly_fix[i]; //update samples of
fixed FIR
}
for (i = 0; i < WLENGTH; i++)
adaptfir_out +=(w[i]*dly_adapt[i]); //adaptive FIR
filter output
E = fir_out  adaptfir_out; //error signal
for (i = WLENGTH1; i >= 0; i)
{
w[i] = w[i]+(beta*E*dly_adapt[i]); //update weights
of adaptive FIR
dly_adapt[i+1] = dly_adapt[i]; //update samples of
adaptive FIR
}
if (out_type == 1) //slider position for adapt FIR
output_sample((short)adaptfir_out); //output of
adaptive FIR filter
else if (out_type == 2) //slider position for fixed
FIR
output_sample((short)fir_out); //output of fixed
FIR filter
return;
}
void main()
{
int T=0, i=0;
for (i = 0; i < WLENGTH; i++)
{
w[i] = 0.0; //initcoeff for adaptive FIR
dly_adapt[i] = 0; //init buffer for adaptive FIR
}
for (T = 0; T < N; T++)
dly_fix[T] = 0; //init buffer for fixed FIR
sreg.regval=0xFFFF; //initial seed value
fb = 1; //initial feedback value
comm_intr(); //init DSK, codec, McBSP
while (1); //infinite loop
}

·
Here
we can see that the adaptive filter has identified the unknown system which is
the band pass filter we generated in step 1 using fdatool.
Conclusion
·
The
adaptive filter can be used to identify any system using the block diagram
shown in figure 1.
·
Adaptive
equalizer is used to compensate for the distortion caused by the transmission
medium (channel).
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