dbd wrote:
>
> The zero-stuffed H2 does not have the correct response for the single
> stage filter design scheme given.

Yes, but when convolved with H1, it does. Would you not agree that by a
Noble identity, the following are equivalent:

--> H1 --> v L1 --> H2 --> v L2 -->

--> H1 --> H2' --> v L1 --> v L2 -->

i.e. we can push H2 through the decimator, where formally H2'(z) = H2(z^L1).

If so, it is then a trivial step to then combine the two adjacent
filters by convolution, and also combine the two adjacent decimators
into one. The resulting system will be mathematically identical to the
original two-stage implementation. (In fact, what I've just written
mirrors precisely what Verictor has written in another reply.)


> Combining two filters as in the single stage scheme is not an
> efficient filter design method for comparison to a multistage design.
>
> You post enough to know how to query 'multistage decimation' to Google
> or search comp.dsp for a recommended text. There are a lot of
> explanations and examples available.

I'm aware that designing a single filter straight off is less efficient
than designing a separate filter for each stage, and I understand the
reason for this is the inverse relationship between normalised
transition bandwidth and filter length, and that normalised transition
bandwidth increases with the decimation ratio. In that respect, I've
done plenty of reading in the past.

The problem I face is why the example I've given would appear to
demonstrate otherwise!


--
Oli