Others have pretty much answered your question I guess.
If its local DD (I mean DD to be encashed within the country), the process could be a lot simpler; as there is NO correspondent bank involved. Bank might be able to tell you with out any dependency on other financial institutions.
If its a foreign DD, where some correspondent bank is involved, your bank might be dependent on the correspondent bank to pass the info; hence might take little longer. What I mean is that your bank might get to know about the date of encashment, a week after the actual date of encashment.
Hope it helps.
Cheers boltz