On Apr 2, 3:55 pm, jim <".sjedgingN0sp"@m...@mwt.net> wrote:
> Eric Jacobsen wrote:
>
>
...
>
> > Jeebuz, no wonder this conversation has been difficult.  You might
> > want to re-read the thread and see who's really said what.   You now
> > seem to be criticising me for being confused about points I made!
>
> I have no way of knowing whether you are confused or not. But you have
> said you are confused by the use of term anti-alias filter when
> downsampling. And you take my inability to do anything about that as a
> criticism. There is nothing I can do about that either.
>

i dunno if i should touch this again or not.  i'll say on the outset
here, that i think i'm with Eric, but just in case i am not sure, i
want to ask the group here; "what qualifies, semantically, as an
'alias'?"  to make the question more specific, is it or is it not an
alias when a signal bandlimited to 10 kHz (nothing in that "top
octave" - me being audio-centric), but sampled at 48 kHz; if that
signal is downsampled to 44.1 kHz and the specific equation used to
reconstuct the new samples is


    x2[n] = x(n*T2)

where

           K-1+N/2
    x(t) = SUM{ x(k*T1) * sinc(t/T1 - k) * w(t/T1 - k) }
           k=K-N/2

and w(t) is, say, a Hamming window (not a good choice, but i can
easily define it here):

    w(t) = (0.54*cos(pi*u/N) + 0.46)*rect(u/N).

now, it is clear here that this is "interpolation" in the sense that
the resulting samples are equal to the input samples if t = n*T2 =
k*T1 for integers n and k.  and if T1 < T2 (which it is, T1 = 1/48 and
T2 = 1/44.1), it's downsampling.  now, there are images of x(t) that
appear in copies of X(f) shifted to integer multiples of 1/T1.  now,
since N is finite (let's say 16, for shits and grins), it is clear
that it's not a perfect sinc function, and some of those images will
contribute to the new baseband spectrum, whatever is |f| < 1/(2*T2).
what do you call those frequency components?  if they didn't end up in
the new baseband, i would simply call them "images" and the word
"alias" would not apply.  but if they happened to land in the
baseband, what would they be?  are they not a frequency component in
the original spectrum that finds itself at another frequency, thereby
*masquarading* as a frequency component that is not what it originally
was?  is that not an alias?

Dale, Jim, i continue to assure you that i am not confused about this,
and that statement by Dale is simply incorrect.  at least, it is not
*always* true (which is essentially what i said about it from the very
beginning of my participation in this discussion).

r b-j