You ask about getting the date part of a timestamp field, but what your question is actually about is filtering on the date of a timestamp field. There is a much simpler method of accomplishing that: you can use the knowledge that all the possible timestamps on a specific date won't have any timestamps for different dates between them.
select DATE
from TABLE
where DATE >= '30.12.2011' and DATE < '31.12.2011'
Your edit explains that you haven't got a timestamp field at all. Nevertheless, a similar approach may still work:
select DATE
from TABLE
where DATE LIKE '30.12.2011 %'
Or the Firebird-specific
select DATE
from TABLE
where DATE starting with '30.12.2011 '
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