Adaptive Filtering

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Adaptive Filtering

by: Thomas Drumright
Spring 1998

Digital signal processing (DSP) has been a major player in the current technical advancements
such as noise filtering, system identification, and voice prediction. Standard DSP techniques,
however, are not enough to solve these problems quickly and obtain acceptable results.
Adaptive filtering techniques must be implemented to promote accurate solutions and a timely
convergence to that solution.

Adaptive Filtering System Configurations
There are four major types of adaptive filtering configurations; adaptive system identification,
adaptive noise cancellation, adaptive linear prediction, and adaptive inverse system. All of the
above systems are similar in the implementation of the algorithm, but different in system
configuration. All 4 systems have the same general parts; an input x(n), a desired result d(n), an
output y(n), an adaptive transfer function w(n), and an error signal e(n) which is the difference
between the desired output u(n) and the actual output y(n). In addition to these parts, the system
identification and the inverse system configurations have an unknown linear system u(n) that can
receive an input and give a linear output to the given input.
Adaptive System Identification Configuration
The adaptive system identification is primarily responsible for determining a discrete estimation
of the transfer function for an unknown digital or analog system. The same input x(n) is applied
to both the adaptive filter and the unknown system from which the outputs are compared (see
figure 1). The output of the adaptive filter y(n) is subtracted from the output of the unknown


system resulting in a desired signal d(n). The resulting difference is an error signal e(n) used to
manipulate the filter coefficients of the adaptive system trending towards an error signal of zero.

After a number of iterations of this process are performed, and if the system is designed
correctly, the adaptive filter’s transfer function will converge to, or near to, the unknown
system’s transfer function. For this configuration, the error signal does not have to go to zero,
although convergence to zero is the ideal situation, to closely approximate the given system.
There will, however, be a difference between adaptive filter transfer function and the unknown
system transfer function if the error is nonzero and the magnitude of that difference will be
directly related to the magnitude of the error signal.
Adaptive Filtering
by: Thomas Drumright
Spring 1998
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