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Nonrecirculating filter, second form
Sometimes we will need a variant of the filter above, shown in Figure
8.10, called the
elementary nonrecirculating filter, second form.
Instead of multiplying the delay output by we multiply the direct signal
by its
complex conjugate
. If
is any complex number, its complex conjugate is defined as:
Graphically this reflects points of the complex plane up and down across the
real axis. The transfer function of the new filter is
This gives rise to the same frequency response as before since
Here we use the fact that
, for any unit complex
number , as can be verified by writing out in either
polar or rectangular form.
Although the two forms of the elementary nonrecirculating filter have the same
frequency response, their phase responses are different; this will
occasionally lead us to prefer the second form.
Figure 8.10:
The elementary nonrecirculating filter, second form.

Next: Elementary recirculating filter
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20061230