Charles Henry escribió:
The hardest class I ever had was stochastic analysis (as recent as 4
years ago), where we solved problems like this. Fundamentally, it's
not too hard, but the details of the calculus are tricky. I'd prefer
to stay away unless there's a real good reason to do so :)
You're trying to restrict the analysis to a convenient (but reasonable)
class of signals, and to assume that the signal to be interpolated, x,
belongs to that class. Right?
Well, sort of. What works well as an interpolator for one signal may
not work well for another. The point I started
On Wed, Mar 31, 2010 at 5:12 PM, Matteo Sisti Sette
matteosistise...@gmail.com wrote:
It occurs to me that there exists one very obvious function for which
the squared error is minimized for a 4-point interpolator. 4-point
interpolator impulse functions have to be 0 outside the interval
Charles Henry escribió:
The error depends on x the signal. Here, I want to make the
*convenient* assumption that the spectrum of x is flat, since we want
some kind of generality and we want to minimize average error across
frequencies. This would make the problem equivalent to using just
I get what you're saying too, and I'm at least a little skeptical
myself. But as I think about it generally, my entire approach to
looking at these problems has been very similar.
I basically thought that when comparing interpolators, I could
disregard the signals involved and just look at the
Charles Henry escribió:
When it comes to the general class of functions with flat spectra, the
only difference is in phase, right?
But the error is the same in time domain as in frequency domain thanks
to the isometric property of the Fourier transform. Our interpolation
is the same as a
I don't know either. We have the formulas for each, so we can
calculate squared error vs. sinc(x), but there also appears to be
differences in which frequencies the distortion occurs and some could
be more audible.
It occurs to me that there exists one very obvious function for which
the
It occurs to me that there exists one very obvious function for which
the squared error is minimized for a 4-point interpolator. 4-point
interpolator impulse functions have to be 0 outside the interval
[-2,2].
So,
E=|f(x)-sinc(x)|^2 is minimized when
f(x)={sinc(x) -2x2 ,0 elsewhere
A workaround is to up-sample everybody by a factor of 2 - this
dramatically reduces error, usually by 24 dB.
Every upsampling is some kind of interpolation. So what you mean, is to
reduce the error of your interpolator by getting much of the job done by a
different interpolator instead ?
On Mon, 2010-03-29 at 21:06 -0400, Matt Barber wrote:
LONG, sorry.
Thanks again for your time and patience.
One really good way to think, then, is in terms of the continuous
frequency response of the interpolator. In that long, long discussion
a couple years ago, Chuck Henry made the
Is it really possible to express a cubic interpolator (such as Lagrange
or Hermite, i.e. such as tabread4 or tabread4c) in terms of impulse
response? Is it equivalent to a convolution? That is to ask: is it linear???
Or is that an approximation?
--
Matteo Sisti Sette
matteosistise...@gmail.com
So to me
it still remains unclear in what aspect [tabread4~] is superior
to [tabread4c~], from both a theoretical and from an empirical
perspective.
The answer may be here:
http://www.aes.org/e-lib/browse.cfm?elib=8151
Btw does anybody have access to that article?
The analysis reveals an
Now regarding Matt's words:
I have read that the Lagrange interpolators have better stopband
attenuation and Hermites have flatter passband response, but I'm not
sure this is true
Is it possible that it is exactly viceversa?
I think it probably is exactly vice-versa -- I was quoting
Yes, as far as I know it's identical -- when you do one of these
interpolations with four points, you can either think of it in terms
of a cubic polynomial formula involving those four points, or in terms
of the sum of four scaled basis functions - the latter seems to me
intuitively equivalent to
On Tue, 2010-03-30 at 14:15 +0200, Matteo Sisti Sette wrote:
However, even in presence of a tradeoff that makes some sense (i.e. each
of the two choices has advantages and disadvantages), it seems to me
that for audio applications the generated high-frequency noise due to
discontinuities
Roman Haefeli escribió:
On Tue, 2010-03-30 at 14:15 +0200, Matteo Sisti Sette wrote:
However, even in presence of a tradeoff that makes some sense (i.e. each
of the two choices has advantages and disadvantages), it seems to me
that for audio applications the generated high-frequency noise due
i think this pdf can add lot's of useful information to this thread :
http://www.student.oulu.fi/~oniemita/dsp/deip.pdf
cyrille
Matteo Sisti Sette a écrit :
Roman Haefeli escribió:
On Tue, 2010-03-30 at 14:15 +0200, Matteo Sisti Sette wrote:
However, even in presence of a tradeoff that
Matt Barber escribió:
Yes, as far as I know it's identical -- when you do one of these
interpolations with four points, you can either think of it in terms
of a cubic polynomial formula involving those four points, or in terms
of the sum of four scaled basis functions - the latter seems to me
On Mon, 29 Mar 2010, Matteo Sisti Sette wrote:
Mathieu Bouchard escribió:
both are truly cubic interpolations.
IIRC, one kind of cubic interpolation is designed to go through all four
points, and the other kind is designed to be pieced with other cubic
interpolations, and Miller confused the
On Tue, Mar 30, 2010 at 9:52 AM, Matteo Sisti Sette
matteosistise...@gmail.com wrote:
Matt Barber escribió:
Yes, as far as I know it's identical -- when you do one of these
interpolations with four points, you can either think of it in terms
of a cubic polynomial formula involving those four
Hi,
Well, if you use [tabread4~] or any of the many other Pd objects
that use the same broken interpolation algorithm
(copy/paste programming),
Broken? What's wrong in the tabread4~ interpolation? (note this is not a
sarchastical question implying there's nothing wrong in it, it's a
On Mon, 2010-03-29 at 13:49 +0200, Matteo Sisti Sette wrote:
Claude wrote:
If you use [tabread4] to interpolate graphical
parameters for animations, the discontinuities in the derivatives are
really obvious.
[]
But IMHO if you're doing piecewise cubic interpolation, it's a bit
Roman Haefeli escribió:
Check this thread:
http://lists.puredata.info/pipermail/pd-list/2008-06/062878.html
I checked it out (not read the _whole_ thread to the end) but,
In what way can the current tabread4~ interpolation, which is
discontinuous even in its 1st derivative, be superior to
By the way tabread4c~ is not in Pd Extended, is it?
Roman Haefeli escribió:
On Mon, 2010-03-29 at 13:49 +0200, Matteo Sisti Sette wrote:
Claude wrote:
If you use [tabread4] to interpolate graphical
parameters for animations, the discontinuities in the derivatives are
really obvious.
Hi all-
I haven't looked at Cyrille's interpolator but... tabread4~ uses true cubic
interpolation (which perhaps Cyrille's object also does in some other way).
The tabread4~ algorithm is to put a cubic through the 4 points surrounding
the input point. However, this cubic curve does not
Matteo Sisti Sette a écrit :
By the way tabread4c~ is not in Pd Extended, is it?
no.
it is there :
http://www.chnry.net/ch/?083-Nusmuk-audio
c
Roman Haefeli escribió:
On Mon, 2010-03-29 at 13:49 +0200, Matteo Sisti Sette wrote:
Claude wrote:
If you use [tabread4] to interpolate
cyrille henry escribió:
Matteo Sisti Sette a écrit :
By the way tabread4c~ is not in Pd Extended, is it?
no. it is there : http://www.chnry.net/ch/?083-Nusmuk-audio
Hi,
I downloaded the zip file but Windows tells me he can't open it.
Is it something different than a normal .zip file?
(it
Miller Puckette escribió:
The tabread4~ algorithm is to put a cubic through the 4 points surrounding
the input point. However, this cubic curve does not necessarily match the
next curve over in first derivative.
Oh I see! I thought it did. I confuded that technique with natural cubic
The link works and extracts fine here in WinXP SP3. I used the built-in
compressed (zipped) folders tool in the explorer shell.
On Mon, Mar 29, 2010 at 11:38 AM, Matteo Sisti Sette
matteosistise...@gmail.com wrote:
cyrille henry escribió:
Matteo Sisti Sette a écrit :
By the way
I checked it out (not read the _whole_ thread to the end) but, In what
way can the current tabread4~ interpolation, which is discontinuous even
in its 1st derivative, be superior to true cubic interpolation? Even at
transpositions near to zero, I can't see what's the advantage, nor what
it
John Harrison escribió:
The link works and extracts fine here in WinXP SP3. I used the built-in
compressed (zipped) folders tool in the explorer shell.
Crazy.
Internet Explorer breaks downloaded files whenever it takes you more
than a few seconds to select the folder to download in. I
Mathieu Bouchard escribió:
both are truly cubic interpolations.
IIRC, one kind of cubic interpolation is designed to go through all four
points, and the other kind is designed to be pieced with other cubic
interpolations, and Miller confused the two and left the bug there.
According to his
I checked it out (not read the _whole_ thread to the end) but, In what
way can the current tabread4~ interpolation, which is discontinuous even
in its 1st derivative, be superior to true cubic interpolation? Even at
transpositions near to zero, I can't see what's the advantage, nor what
it
Hi Matt
Thanks for the detailed explanation. I still have troubles getting the
idea of the Lagrange interpolator in the context of [tabread4~]. You
say, that it finds the cubic polynomial which hits all four points. But
what is the advantage of that? As I understand [tabread4~], if the index
is
LONG, sorry.
On Mon, Mar 29, 2010 at 7:03 PM, Roman Haefeli reduzie...@yahoo.de wrote:
Hi Matt
Thanks for the detailed explanation. I still have troubles getting the
idea of the Lagrange interpolator in the context of [tabread4~]. You
say, that it finds the cubic polynomial which hits all
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