**Abstract.** An efficiency
of two blind signal extraction algorithms (gradient and
fixed point) based on the
maximization of absolute kurtosis is analyzed in the work. Algorithms allow to
extract a pulse signal on the background of impulse noise. The algorithms’ convergence
at null and nonzero initial conditions is proved. A lemma and two theorems which
allow to prove blind allocation signal and to determine the number of decisions
regarding the extracting signal are formulated. It is determined that the fixed
point algorithm based on maximizing the absolute kurtosis is more efficient. It
allows extracting the pulse desired signal having the signal-to–noise ratio 30
dB greater than the gradient algorithm with the same objective function.

**Key words:** blind signal extraction, fixed point algorithm, kurtosis, Hessian,
the rate of convergence.

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