Other Features

Another facility provided by 47 is the plotting of signals and transforms. For discrete-time signals, time-domain plots are displayed in the conventional ``lollipop'' style [Oppenheim and Schafer 1989]. Continuous-time signals are plotted using built-in routines, augmented by new routines that display Dirac delta functions as arrows. Finally, pole-zero diagrams, root maps, and plots of magnitude and phase responses are available via the functions 48 and 49.

Other support routines provide drivers for multidimensional transforms. The multidimensional drivers simply call a one-dimensional rule base for each dimension of the transform and properly combine the region of convergence information obtained from each call. The end result of these drivers is a transform object. However, if a call to a transform rule base produces an incomplete transform, the multidimensional drivers exits immediately. In the digital and analog signal processing packages, these drivers are incorporated into the forward and inverse z- and Laplace-transform packages.

The last set of support routines, listed in Table 3, is needed in order to implement transform properties, because transform properties alter the transform function and the region of convergence. For all of these objects, the first argument is the name of a routine that returns true

`AddT`	`ConjT`	`ConvolveT`
`DerivativeT`	`IntegrateT`	`LineImpulsemDT`
`MultT`	`ScaleT`	`SubT`
	`SubstituteForT`

when its argument is a valid transform (<#220#>LForm<#220#> for the Laplace transform and <#221#>ZForm<#221#> for the z-transform). The second argument is a transform or transform code to be evaluated. When the second argument is a valid transform, the routine implements the property on it. Other arguments vary with the object. This convention allows a nesting or cascading of properties.