A voltage measuring module measures first and second voltages at first and second electrical connectors of a fuel injector of an engine. A first summer module determines a first sum of (i) a difference between the first and second voltages and (ii) N previous values of the difference between the first and second voltages, wherein N is an integer greater than or equal to one. A second summer module determines a second sum of (i) the first sum and (ii) M previous values of the first sum, wherein M is an integer greater than or equal to one. A first difference module determines a first difference based on the second sum. A second difference module determines a second difference between (i) the first difference and (ii) a previous value of the first difference. An injector driver module selectively applies power to the fuel injector based on the second difference.