  In general, one often encounters the systems that have sparse impulse
response, with time varying system sparsity. Conventional adaptive filters
which perform well for identification of non-sparse systems fail to exploit the
system sparsity for improving the performance as the sparsity level increases.
This paper presents a new approach that uses an adaptive convex combination of
Affine Projection Algorithm (APA) and Zero-attracting Affine Projection
Algorithm (ZA-APA)algorithms for identifying the sparse systems, which adapts
dynamically to the sparsity of the system. Thus works well in both sparse and
non-sparse environments and also the usage of affine projection makes it robust
against colored input. It is shown that, for non-sparse systems, the proposed
combination always converges to the APA algorithm, while for semi-sparse
systems, it converges to a solution that produces lesser steady state EMSE than
produced by either of the component filters. For highly sparse systems,
depending on the value of the proportionality constant ($\rho$) in ZA-APA
algorithm, the proposed combined filter may either converge to the ZA-APA based
filter or produce a solution similar to the semi-sparse case i.e.,
outerperforms both the constituent filters.
