On external properties satisfied by the Io-sinh window

The Io-sinh window has been used extensively in signal processing applications. By the choice of one parameter, one can conveniently trade its desirable main lobe width (resolution) and side lobe rejection properties. The extremal property satisfied by the dissipative wave equation Green´s function is derived. The Io-sinh window is shown to be a special case of the Green´s function for the 1-D dissipative wave operator. As such, it satisfies the energy equality of the dissipative wave equation. As a natural extension, we also consider 2-D and 3-D Green´s function solutions as logical choices for higher order windows.