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From: jim on 6 Jan 2010 19:38
glen herrmannsfeldt wrote:
> Tim Wescott <tim(a)seemywebsite.com> wrote:
> > Reconstruction filters can ring. Filters that ring,
> > when presented with inputs with sharp edges, can ring
> > strongly enough to exceed the bounds of the input.
> That is true, but there are also sampled values that, when
> reconstructed, result in a sine with amplitude greater
> than full scale of the D/A conversion. Easiest to see
> is the signal with period of four samples [ 1 1 -1 -1 ].
it didn't sound like he was asking about reconstruction. He asked about
interpolating without overshoot.
> If the source is analog data through an A/D conversion
> then that isn't so likely, though.
> -- glen
From: jim on 6 Jan 2010 19:41
> I just know there would be a lpf, not quite sure about the reconstruction
> I got an idea that the overshoot caused from the lpf, but the detail "how"
> is still not clear.
A low pass filter with only positive values and a DC gain of 1 will
guarantee no overshoot.
From: glen herrmannsfeldt on 6 Jan 2010 20:46
Laron <jason.piker(a)inbox.com> wrote:
(snip on overshoot and reconstruction)
> I just know there would be a lpf, not quite sure about the
> reconstruction process. I got an idea that the overshoot
> caused from the lpf, but the detail "how" is still not clear.
Because it is the right answer.
Another way to see it, take a square wave of amplitude one
and low pass filter it such that only the fundamental comes through.
The peak will be higher than 1.0. Mostly the third harmonic is
negative at the peak of the fundamental, so when you remove it the
result has a higher amplitude.
From: Jerry Avins on 6 Jan 2010 23:34
> it didn't sound like he was asking about reconstruction. He asked about
> interpolating without overshoot.
Interpolating is sort of partial reconstruction. If you interpolate the
signal 0, 1, 1, 0, -1, -1, ... by two, you get 0, .577, 1, 1.55, 1, 577,
0. -.577, -1, -1.55, -1, -.577, ....
Engineering is the art of making what you want from things you can get.
From: jim on 7 Jan 2010 07:32
Jerry Avins wrote:
> jim wrote:
> > it didn't sound like he was asking about reconstruction. He asked about
> > interpolating without overshoot.
> Interpolating is sort of partial reconstruction. If you interpolate the
> signal 0, 1, 1, 0, -1, -1, ... by two, you get 0, .577, 1, 1.55, 1, 577,
> 0. -.577, -1, -1.55, -1, -.577, ....
Surely you can't be claiming that is the only possible way to
interpolate that sequence.
What about linear interpolation? That would produce no overshoot. And
the reason is the filter [1/2 1/2] has unity gain at DC and no negative
terms. Any other filter that is also so constrained can be used for
interpolation without any overshoot.
> Engineering is the art of making what you want from things you can get.