# Question about the convergence of Fast Affine projection Algorithm

Started by April 30, 2009
Hello,
I'm programming the Fast Affine Projection for echo cancellation,I see this article "Steven.L. Gay,
and S. Tavathia, “Fast affine projection algorithm,” in Proc. of the ICASSP,
vol. V, pp. 3023-3026,1995"to do it.
for the white noise (as input signal), it
converges but for the speech signal it does not, the answer is in
paragraph below but I did not understand exactly what to do.

5. NUMERICAL CONSIDERATIONS

FAP uses the sliding window technique to update and
downdate data in its implicit regularized sample correlation matrix
and cross correlation vector. Errors introduced by finite arithmetic
in practical implementations of the algorithm therefore cause the
correlation matrix and cross correlation vector to take random
walks with respect to their infinite precision counterparts. A
stablized sliding windowed FRLS algorithm[11] has been
introduced, with complexity 14N multiplications per sample period
(rather than 10N for non-stablized versions). However, even this
algorithm is stable only for stationary signals, a class of signals
which certainly does not include speech. Another approach, which
is very straightforward and rather elegant for FAP, is to
periodically start a new sliding window in parallel with the old
sliding window, and when the data is the same in both processes,
replace the old sliding window based parameters with the new
ones. Although this increases the sliding window based parameter
calculations by about 50% on average (assuming the restarting is
done every L+N sample periods), the overall cost is small since
only those parameters with computational complexity proportional
to N are affected. The overall complexity is only 2L+21N for FAP
without relaxation and 2L+30N for FAP with relaxation. Since
this approach is basically a periodic restart, it is numerically stable
for all signals.

Thank You
in advance and I wait for your response,

Best
regards,

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