In the last decade, Approximate Computing (AxC) has been extensively employed to improve the energy efficiency of computing systems, at different abstraction levels. The main AxC goal is reducing the energy budget used to execute errortolerant applications, at the cost of a controlled and intrinsicallytolerable quality degradation. An important amount of work has been done in proposing approximate versions of basic operations, using fewer resources. From a hardware standpoint, several approximate arithmetic operations have been proposed. Although effective, such approximate hardware operators are not tailored to a specific final application. Thus, their effectiveness will depend on the actual application using them. Taking into account the target application and the related input data distribution, the final energy efficiency can be pushed further. In this paper we showcase the advantage of considering the data distribution by designing an input-aware approximate multiplier specifically intended for a high pass FIR filter, where the input distribution pattern for one operand is not uniform. Experimental results show that we can significantly reduce the power consumption while keeping an error rate lower than state of the art approximate multipliers.