Page 188 - DSP Integrated Circuits

4.21 Interpolation With an Integer Factor L 173

Figure 4.64 Spectrum of the input signal and the interleaved signal

It is favorable to use bireciprocal WDF lattice filters for interpolation with a
factor of two. The stopband requirement can easily be satisfied and the ripple in
the passband will, due to the symmetry, be very small when such filter structures
are used. Note that the filter designed in Example 4.12 meets this specification.

It is, of course, unnecessary to process input values that are zero. In Example
4.16 we will show that it is possible to modify the system of difference equations so
that the bireciprocal wave digital filter operates at the lower input sampling rate
[3, 29].

EXAMPLE 4.16
Show that the interpolation filter in Example 4.15 can be made to operate at the
lower (input) sampling rate.
The 2-transform of the interleaved input sequence is

The transfer function of the original filter is

Hence, the 2-transform of the output is

Note that the term H<£z*} X(z^) corresponds to a sequence that is zero for
every other sample. Alternatively, this sequence can be obtained by filtering the