We shall define the Heaviside unit step function, u, as that function which is equal to 1 for every positive value of t and equal to 0 for every negative value of t. This function could equally well have been defined in terms of a specific formula; for example (2.5)ut=121+tt. Figure...
, by viewing the time-varying signum function of It can reflect the characteristic property of each earthquake through and the second component of f, where is a time-sampling record of the acceleration of a ground motion. The barcode is formed by plotting ...
The sign function has the values ±1 when f = 0 and sign(0) = 0. Note that Eq. (5) has the following constant solutions: f = 0, ±1. Let us now briefly discuss essential mathematical aspects of Eq. (5). First, it is clear that f has to satisfy the condition f ′ (0)...