time-causal limit kernel

The time-causal limit kernel is a temporal smoothing kernel that is (i) time-causal, (ii) time-recursive and (iii) obeys temporal scale covariance. This kernel constitutes the limit case of coupling an infinite number of truncated exponential kernels in cascade, with specifically chosen time constants to obtain temporal scale covariance. For practical purposes, the infinite convolution operation can often be well approximated by a moderate number (4-8) truncated exponential kernels coupled in cascade. The discrete implementation can, in turn, be performed by a set of first-order recursive filters coupled in cascade.