National Instruments Xmath G, -a, s() Gs() valuesvalues, b

Chapter 3 Multiplicative Error Reduction

The values of G(s), as shown in Figure3-2, along the jω-axis are

the same as the values of around a circle with diameter defined by

[a–j0,b–1 +j0] on the positive real axis.

Figure 3-2. Bilinear Mapping from G(s) to (Case 1)

Also, the values of , as shown in Figure 3-3, along the jω-axis are

the s ame as the values of G(s) around a circle with diameter defined by

[–b–1+j0, – a+j0].

Figure 3-3. Bilinear Mapping from G(s) to (Case 2)

We can implement an arbitrary bilinear transform using the subsys( )

function, which substitutes a given transfer function for the s- or z-domain

operator.

To implement use:

gtildesys=subsys(gsys,makep([-b,1]/makep([1,-a])

To implement use:

gsys=subsys(gtildesys,makep([b,1]/makep([1,a])

Note The systems substituted in the previous calls to subsys invert the function

specification because these functions use backward polynomial rotation.

˜s()

1–

˜s()

G˜s()Gs()valuesvalues-a

b1–

˜s()

˜s() Gsa–

bs–1+

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Gs() G

˜sa+

s1+

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