Before revision:  This paper formulates a detection problem for distinguishing sustained signals from transient ones.
After revision:  It has been shown that the coherent type-1 feedforward loop with an AND logic at the output (or C1-FFL for short) can be used to discriminate a persistent input signal from a transient one. This has been done by modelling the C1-FFL, and then use the model to show that persistent and transient input signals give, respectively, a non-zero and zero output. Instead of assuming the structure of C1-FFL, this paper shows that it is possible to deduce the C1-FFL model from the requirement of discriminating a persistent signal. We do this by first formulating a statistical detection problem of distinguishing persistent signals from transient ones.