Many diagnostic datasets suffer from the adverse effects of spikes that are embedded in data and noise. For example, this is true for electrical power system data where the switches, relays, and inverters are major contributors to these effects. Spikes are mostly harmful to the analysis of data in that they throw off real-time detection of abnormal conditions, and classification of faults. Since noise and spikes are mixed together and embedded within the data, removal of the unwanted signals from the data is not always easy and may result in losing the integrity of the information carried by the data. Additionally, in some applications noise and spikes need to be filtered independently. The proposed algorithm is a multi-resolution filtering approach based on Haar wavelets that is capable of removing spikes while incurring insignificant damage to other data. In particular, noise in the data, which is a useful indicator that a sensor is healthy and not stuck, can be preserved using our approach. Presented here is the theoretical background with some examples from a realistic testbed.