Page 174 - DSP Integrated Circuits

4.18 Lattice Wave Digital Filters 159

A theoretical filter order of N mi n = 5.8707 is required in order to meet the
specification. We select N = 7, since only lowpass niters of odd orders are possible.
The increase in filter order results in the design margin which can be distributed
between the passband and stopband as well as between the cutoff and stopband
edges. The design margin will later be used for rounding the filter coefficients to
simple values. Normally, the cutoff edge is kept unchanged, but the stopband edge
is reduced somewhat. The program computes the minimum stopband (frequency)
edge. The stopband edge must be selected according to

If we select f s = f smi n the whole design margin is used, while if we select f s =
fsreq none of the margin is used, in which case the whole margin is left for the pass-
band and stopband ripples. We select

Next, the program determines the range of the ripple factor for the passband:

If we select £p = e pmi n the whole design margin is used up, while if we select £ p =
e preq none of the margin is used. The whole margin is left for the stopband. Since
the lattice filter has very low sensitivity in the passband and very high sensitivity
in the stopband, it is reasonable to allocate the major part of the design margin to
the latter. We therefore select the passband ripple to

which corresponds to

Hence, A max «A maxreq = 0.01 dB.
The sensitivity of lattice wave digital filters is very large in the stopband and
very small in the passband. Errors that occur when the ideal adaptor coefficients
are quantized to binary values of finite precision affect the stopband much more
than the passband. It may therefore be better to select a slightly larger ripple fac-
tor for the passband so that a larger part of the design margin is left for the stop-
band. The sensitivity in the passband will thereby increase slightly, but will still
remain very low, since the ripple in the passband is extremely small.
The program determines the stopband attenuation as

The lattice filter will have two parallel branches which consist of a third- and a
fourth-order allpass filter. The allpass filters can be realized by using circula-
tors, of the type shown in Figure 4.48. The resulting wave-flow graph is shown in
Figure 4.49. Note the order of the sections in the upper branch has been changed
compared with Figure 4.48.