On Using Gaussian filter for Spiky Signals: Effect on Resolution

In many signal processing applications, signals have characteristics like sparseness (i.e., a spike train, etc.). The original space charge signal of a dielectric specimen is one of the examples, having spikes at the specimen interface. For such signals, de-noising using a gaussian filter is preferred. However, de-noising using the above filter may affect the resolution of the output signal, which is not desirable in a space charge signal. As a result, the author presented analytical insights on the resolution of the estimated charge signal using a gaussian filter. Based on these insights, the author proposed an analytical solution to estimate the critical cut-off frequency, which had not previously been addressed. By using the proposed formula, the computational part is reduced considerably. In this study, a known impulse signal with white additive gaussian noise is considered.