An emerging narrowband radio technology named narrowband Internet of Things (NB-IoT) based on cellular communications has been standardised by the 3rd Generation Partnership Project in release-13. It is specifically designed to provide low-power wide-area connectivity for the IoT. In this study, the authors derive an analytical signal model for Long Term Evolution (LTE)-based uplink NB-IoT systems. The problem of channel equalisation for the uplink NB-IoT systems having mismatched baseband processing and sampling rate between transmitter and receiver is addressed. A relation between the channel impulse response and the channel frequency-domain equalisation coefficients is derived under imbalanced baseband processing and sampling rate environment. Accordingly, a novel one-tap frequency-domain channel equalisation algorithm specific to NB-IoT uplink systems is proposed based on the resultant channel coefficients. Comprehensive link-level simulations are carried out to validate the potentiality of the proposed equalisation method, compared with other conventional techniques like zero forcing and minimum mean square error equalisers in terms of symbol error rate and throughput against signal-to-noise ratio. Simulation results indicate that the proposed equaliser outperforms the existing linear equalisers for all cases of evaluation.