IGLOO2 FPGA Adaptive FIR Filter Demo
6
Revision 2
Theory of Operation
Adaptive filters are mainly categorized into four basic architectures:
•
System identification
•
Noise cancellation
•
Linear prediction
•
Inverse modeling
In this demo, linear prediction architecture is used to implement adaptive filter. The LMS algorithm uses a
gradient search technique to determine the filter coefficients that minimize the mean square prediction
error. The estimate of the gradient is based on the sample values of the tap-input vector and the error
signal. The algorithm iterates over each coefficient in the filter, moving it in the direction of the
approximated gradient. After reaching the optimal filter coefficients, the error signal e(n) consists of the
Wideband signal.
Figure 2
shows the linear prediction based adaptive filter architecture.
The input signal x(n) consists of wideband signals along with the narrow band signals that are not
required, refer to
Figure 3 on page 8
. In a linear prediction architecture, the desired signal d(n) is same
as the input signal x(n) and a delayed input x(n-
) is fed to the adaptive filter as shown in
Figure 2
. The
delay factor
(delta) de-correlates the wide band component and correlates the narrow band component
of the desired signal d(n) with the delayed input signal x(n-
).
The adaptive filter tries to estimate the narrow-band component y(n), and forms an equivalent transfer
function, which is similar to that of narrow-band filters centered at the frequencies of the narrow-band
components of the input signal. At the summing junction, the filtered input signal subtracting with delayed
input signal produces an error signal. The error signal is used by the LMS algorithm to adjust the filter
coefficients. After some iterations, the Error signal converges to a wide band component The following
equations describe computing the coefficients using the LMS algorithm.
Figure 2 •
Linear Prediction Adaptive Filter Architecture
Adaptive FIR Filter
LMS Algorithm
z^ -∆
x(n-∆)
+
-
e(n)
y(n)
d(n)
x(n)
Superseded
