Quantized Filter Analysis - Introduction to Digital Signal Processing and Filter Design - page 359

are available in a figure displayed under the SP Tool. For example, by clicking the
Edit button and then selecting either Figure Properties , Axis Properties ,
or Current Object Properties ,the Property Editor becomes active and
properties of these three objects can be modified.
Finally, we look at the first panel titled Current Filter Information .
This lists the structure, order, and number of sections of the filter that we have
designed. Below this information, it indicates whether the filter is stable and
points out whether the source is the designed filter (i.e., reference filter designed
with double precision) or the quantized filter with a finite wordlength. The default
structure for the IIR reference filter is a cascade connection of second-order
sections, and for the FIR filter, it is the direct form. When we have completed
the design of the reference filter with double precision, we verify whether it
meets the desired specification, and if we wish, we can convert the structure of
the reference filter to any one of the other types listed below. We click the Edit
button on the main menu and then the Convert Structure button. A dropdown
list shows the structures to which we can convert from the default structure or
the one that we have already converted.
For IIR filters, the structures are

1. Direct form I
2. Direct form II
3. Direct form I transposed
4. Direct form II transposed
5. Lattice ARMA
6. Lattice-coupled allpass
7. Lattice-coupled allpass—power complementary
8. State space

Items 6 and 7 in this list refer to structures of the two allpass networks in
parallel as described in Chapter 6, with transfer functions G(z)

1
2 [ A 1 (z)

= +

1
2 [ A 1 (z)

A 2 (z) ]and H(z) A 2 (z) ], respectively. The allpass filters A 1 (z) and

A 2 (z) are realized in the form of lattice allpass structures like the one shown
in Figure 6.19b. The MA and AR structures are considered special cases of the
lattice ARMA structure, which are also discussed in Chapter 6.
For FIR filters, the options for the structures are

= −

• Direct-form FIR
• Direct-form FIR transposed
• Direct-form symmetric FIR

When we have converted to a new structure, the information that can be
displayed in the Analysis area, like the coefficients of the filter, changes. We also
like to point out that any one of the lowpass, highpass, bandpass, and bandstop
filters that we have designed can be converted to any other type, by clicking