In article , Mike Scott
wrote:
Jim Lesurf wrote:
In article , Rob
wrote:


That's really why I ask - I think. If there's more than one way to
downsample properly, I'm stuffed.

In principle 'downsampling' should be done 'properly' and will then
lead to a uniquely defined results - even if done in various
algorithmic ways.


That's not so.

Downsampling always involves a reduction in Nyquist frequency. It's
necessary therefore to filter the input to make sure frequencies above
this are sufficiently reduced.

Correct.

That filter can never be perfect, and there will be various tradeoffs,
involving extra loss of top-end, in-band ripple and 'wrap-around'
garbage from insufficient rejection of higher-than-Nyquist signal.

Also correct in practice. But you missed my "in principle" in what I wrote
above. (Which you have snipped away.) And presumbly then failed to
understand why I then went on to discuss how "in practice" will be
different - for reasons like the one you mention.

To remind you, what I wrote that you quoted above was immediately followed
by my saying:

But in practice any downsampling or resampling can produce its own
(needless in theory) alterations that vary with the method used.

Perhaps you failed to read that before leaping in. Pity, as understanding
it would have meant you'd have had no reason to write what you did. :-)

It's all down to what the person doing it thought would be best (by some
arbitrary criterion), and there is no unique or 'right' answer.

It is formally incorrect to say there is no "unique or right answer". The
formally correct and uniquely correct "answer" is to have all the in band
components preserved whilst losing all the out of band ones. This follows
from the sampling theorem, etc. That then represents the uniquely "correct"
answer in terms of information theory.

However, as my previous posting on this did point out (but you snipped and
ignored), in practice you tend to have to accept some level of
imperfection. Albeit very small if the resampling is well done.

Slainte,

Jim

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