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This paper introduces a blind channel estimation method for a block transmission system using fractional sampling at a receiver. In most digital communication systems, low-pass filters are placed at a transmitter to confine the transmitting waveform to an allocated bandwidth and at a receiver to improve the signal-to-noise (SNR) power ratio. Consequently, if the received waveform is sampled with sufficiently fast rate, the resulting discrete-time signal is band-limited and exhibits a smooth waveform. The method exploits this property for estimating the channel impulse response, via an interpolation formula. The method does not require knowledge of input statistics or the autocorrelation of the received signal. It is free of channel order estimation and thus robust against its overestimation. Moreover, the algorithm is quite efficient because it does not need to compute eigenvalues of a matrix.