Monotonicity Constraint

We can constrain the positive-time part of the window to be monotonically decreasing:

$$\Delta h_{i}=h\left(i+1\right)-h\left(i\right)\leq 0\qquad i=1,\ldots ,L-1$$ (4.77)

In matrix form,

$$\left[\begin{array}{ccccc} -1 & 1 & & & 0\\ & -1 & 1 & & \\ & & \ddots & \ddots & \\ 0 & & & -1 & 1\end{array}\right]h \le 0,$$

or,

$$\zbox {\mathbf{D}\,h \le 0.}$$ (4.78)

See Fig.3.38.

Figure 3.38: Monotonic Chebyshev Window