  System identification is an exceptionally expansive topic and of remarkable
significance in the discipline of signal processing and communication. Our goal
in this paper is to show how simple adaptive FIR and IIR filters can be used in
system modeling and demonstrating the application of adaptive system
identification. The main objective of our research is to study the LMS
algorithm and its improvement by the genetic search approach, namely, LMS-GA,
to search the multi-modal error surface of the IIR filter to avoid local minima
and finding the optimal weight vector when only measured or estimated data are
available. Convergence analysis of the LMS algorithm in the case of coloured
input signal, i.e., correlated input signal is demonstrated on adaptive FIR
filter via power spectral density of the input signals and Fourier transform of
the autocorrelation matrix of the input signal. Simulations have been carried
out on adaptive filtering of FIR and IIR filters and tested on white and
coloured input signals to validate the powerfulness of the genetic-based LMS
algorithm.
