Implementing an equation involving integrals as a filter

This is a question that possibly borders on the intersection of the general usage of MATLAB and/or signal processing. Thought I would first ask the question in a MATLAB forum before trying signal processing.



So our lecturer read out his notes/paper and said the equation







could be implemented as a filter.



At first, it seemed difficult to follow the idea but when realizing that integration is same as finding areas under the curve which seems similar to applying a low pass filter so that only the portion of the signal under the threshold is allowed to pass through, it made a bit of sense. But how - meaning to say which function - can I use to implement the above equation? Do I need three filters or can I use just one? How do I use the terms preceding the integrals in the filter?



Thanks in advance