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Estimating central aortic blood pressure is important for cardiovascular health and risk prediction purposes. Cardiovascular system is a multi-channel dynamical system that yields multiple blood pressures at various body sites in response to central aortic blood pressure. This paper concerns the development and analysis of an observer-based approach to de-convolution of unknown input in a class of coprime multi-channel systems applicable to non-invasive estimation of central aortic blood pressure. A multi-channel system yields multiple outputs in response to a common input. Hence, the relationship between any pair of two outputs constitutes a hypothetical input-output system with unknown input embedded as a state. The central idea underlying our approach is to derive the unknown input by designing an observer for the hypothetical input-output system. In this paper, we developed an unknown input observer (UIO) for input de-convolution in coprime multi-channel systems. We provide a universal design algorithm as well as meaningful physical insights and inherent performance limitations associated with the algorithm. The validity and potential of our approach was illustrated using a case study of estimating central aortic blood pressure waveform from two non-invasively acquired peripheral arterial pulse waveforms. The UIO could reduce the root-mean-squared error associated with the central aortic blood pressure by up to 27.5% and 28.8% against conventional inverse filtering and peripheral arterial pulse scaling techniques.