In this paper, a novel digital self-interference canceller based on a Hammerstein adaptive filter is proposed and examined. The proposed system consists of a spline-interpolated lookup table to model the nonlinear power amplifier, followed by a linear filter accounting for the impulse response of the linear self-interference channel. The gradient descent based parameter learning algorithms are derived, which estimate the spline control points and the filter coefficients in a decoupled manner. The proposed digital canceller leads to a complexity reduction of 77% when compared to the existing state-of-the-art solutions. Performance evaluations using measured data from a complete inband full-duplex prototype system operating at 2.4 GHz ISM band show the effectiveness of the proposed technique, demonstrating that it obtains similar cancellation performance as the existing state-of-the-art canceller, regardless of its lower complexity. The measured digital self-interference cancellation values are 45 dB, 43 dB and 38 dB with 20 MHz, 40 MHz and 80 MHz channel bandwidths, respectively. These results indicate that the complexity-accuracy trade-off of the proposed decoupled spline-based cancellation approach is very favorable. Owing to the resulting decrease in the computational complexity, the proposed digital cancellation technique brings inband full-duplex transceivers one step closer to commercial deployments.