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Nonlinear distortion of bandlimited signals results in spectral spreading. This paper develops a blind nonlinear compensation method for bandlimited signals by suppressing the spectral content of the distorted signal above the original signal bandwidth by means of adaptive nonlinear filtering. The nonlinear compensator is constructed using a power series filter with adaptive coefficients. The adaptive coefficients are identified blindly by applying a least-squares criterion to the out-of-band spectral content of the nonlinear compensator output. The extraction of the out-of-band signal is efficiently performed by the discrete cosine transform. The effectiveness of the blind nonlinear compensation method is demonstrated by way of simulation examples involving periodic, colored noise, and bandlimited speech signals.