Hence second-order difference equation (6) is a special case of (E).The results on asymptotic properties and oscillation of equations of type (6) can be found, i.e., in [23-26].

Rehak, "Asymptotic formulae for solutions of linear second-order difference equations," Journal of Difference Equations and Applications, vol.

SCLR chooses the second-order difference matrix as the analysis operator to enforce the approximate piecewise linear structure, and it takes use of [l.sub.1] norm and nuclear norm as a convex surrogate function for [l.sub.0] norm and rank function.

In Figure 1, we select chb01_31.edf which is used in our experiments as the test data and take the second-order difference matrix as the cosparse operator.

Consider the following second-order difference equation:

Next, we consider the following second-order difference equation:

Firstly, we introduce the resemblance coefficient (RC) of the first- and second-order difference sequences as an efficient feature to distinguish ES from MS.

Because most values of sequence {[d.sub.1]} for ES are near 0, we further calculate the second-order difference sequence:

Difference of adjacent points of the feature matrices denotes the change direction of the envelope curve and the

second-order difference denotes its change tendency.

Finally, substitution of (25), (26) into (24) gives the

second-order difference equation

Testing for CI between the second-order difference variables (i.e., [D.sup.2][y.sub.t] and [D.sup.2][x.sub.t)] fails to be accepted because the absolute value on the coefficient of [u.sub.t-1] exceeds unity (Row 3, Table 3).

(3.) [D.sup.2] is the second-order difference operator.