On 8/18/15 3:44 PM, Ethan Duni wrote:
>Assume you have a Nyquist frequency square wave: 1, -1, 1, -1, 1, -1,
1, -1...
The sampling theorem requires that all frequencies be *below* the
Nyquist frequency. Sampling signals at exactly the Nyquist frequency
is an edge case that sort-of works in some limited special cases, but
there is no expectation that digital processing of such a signal is
going to work properly in general.
But even given that, the interpolator outputting the zero signal in
that case is exactly correct. That's what you would have gotten if
you'd sampled the same sine wave (*not* square wave - that would imply
frequencies above Nyquist) with a half-sample offset from the 1, -1,
1, -1, ... case. The incorrect behavior arises when you try to go in
the other direction (i.e., apply a second half-sample delay), and you
still get only DC.
But, again, that doesn't really say anything about interpolation. It
just says that you sampled the signal improperly in the first place,
and so digital processing can't be relied upon to work appropriately.
as suprizing as it may first appear, i think Peter S and me are totally
on the same page here.
regarding *linear* interpolation, *if* you use linear interpolation in a
precision delay (an LTI thingie, or at least quasi-time-invariant) and
you delay by some integer + 1/2 sample, the filter you get has
coefficients and transfer function
H(z) = (1/2)*(1 + z^-1)*z^-N
(where N is the integer part of the delay).
the gain of that filter, as you approach Nyquist, approaches -inf dB.
*my* point is that as the delay slowly slides from a integer number of
samples, where the transfer function is
H(z) = z^-N
to the integer + 1/2 sample (with gain above), this linear but
time-variant system is going to sound like there is a LPF getting segued in.
this, for me, is enough to decide never to use solely linear
interpolation for a modulateable delay widget. if i vary delay, i want
only the delay to change. and i would prefer if the delay was the same
for all frequencies, which makes the APF fractional delay thingie
problematic.
bestest,
r b-j
On Tue, Aug 18, 2015 at 1:40 AM, Peter S <peter.schoffhau...@gmail.com
<mailto:peter.schoffhau...@gmail.com>> wrote:
On 18/08/2015, Nigel Redmon <earle...@earlevel.com
<mailto:earle...@earlevel.com>> wrote:
>>
>> well, if it's linear interpolation and your fractional delay
slowly sweeps
>> from 0 to 1/2 sample, i think you may very well hear a LPF start
to kick
>> in. something like -7.8 dB at Nyquist. no, that's not right.
it's -inf
>> dB at Nyquist. pretty serious LPF to just slide into.
>
> Right the first time, -7.8 dB at the Nyquist frequency, -inf at
the sampling
> frequency. No?
-Inf at Nyquist when you're halfway between two samples.
Assume you have a Nyquist frequency square wave: 1, -1, 1, -1, 1,
-1, 1, -1...
After interpolating with fraction=0.5, it becomes a constant signal
0,0,0,0,0,0,0...
(because (-1+1)/2 = 0)
--
r b-j r...@audioimagination.com
"Imagination is more important than knowledge."
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