The most correct and accurate methods for calculating the fractional integral require a record of all previous history, and therefore would require a linear space complexity solution O(n), where n is the number of samples measured for the complete history.
The data table is initialized as all zeros, which represents a lack of activity for all previous time.
The convolution is solved by multiplying corresponding elements from the weight and data tables, and summing the resulting products.
This approximation has the desirable effect of removing the echo, while preserving the space complexity of the solution.
The negative effect of the approximation is that the phase character of the solution is lost as the system frequency approaches DC.