>
>
>Jerry Avins wrote:
>>
>> jim wrote:
>> >
>> > robert bristow-johnson wrote:
>> >> On Mar 31, 4:10 am, dbd <d...@ieee.org> wrote:
>> >>> On Mar 30, 11:39 pm, robert bristow-johnson
>> >>>
>> >> ...
>> >>>> as far as interpolation is concerned (as opposed to the issue of
>> >>>> removing frequency components before sample rate reduction), this
is
>> >>>> necessary and sufficient:
>> >>>> +inf
>> >>>> x(t) = SUM{ x(nT)*sinc((t-nT)/T) }
>> >>>> n=-inf
>> >>>> but, like any practical implementation, you won't be adding up all
of
>> >>>> terms. likewise is the downsampling antialiasing. it's not
defining.
>> >> ...
>> >>> So you are another person who seems confused about "resampling to
an
>> >>> integer submultiple frequency where new values must be "calculated
on
>> >>> the curve" because anti-aliasing is required for samples that
still
>> >>> fall on the old sample times." I told Rick Lyons this was a problem
to
>> >>> discuss.
>> >> Dale, i'm not confused about anything regarding the subject.
>> >> certainly not anything stated in this thread. my participation
began
>> >> with my taking issue with your sweeping (at least unqualified) and
>> >> incorrect statement that "Resampling formulas -do_not- match the
old
>> >> samples when they include anti-alias filtering."
>> >
>> > How can that be "incorrect"? If you downsample and the new samples
are the
>> > same at the old sample points then your anti-alias filter did
absolutely
>> > nothing.
>>
>> It's all semantics, then. The alteration comes about not from the
>> downsampling, but from the filtering that precedes it.
>
>
>> When there is no
>> energy above the new Fs/2, there will be no change in the samples.
>
> The statement was when a anti-alias filter was "required". But even if
>you used one where it was not required there would be no change in
samples
>only if you know how to make an anti-alias filter that removes
absolutely
>no energy from below the new Fs/2.
>
>-jim
>
>
>
>>
>> Jerry
>> --
>> Engineering is the art of making what you want from things you can
*****************************
Hello Guys
This thread was started by my question on 'Interpolation'. And this
discussion has become more interesting and I have almost forgotten my
fundamentals!!!!!! But finally I solved my problem, thanks to Randy who
gave one nice link
http://ccrma.stanford.edu/~jos/pasp/Linear_Interpolation.html
This what I wanted to do. But in my case I was doing decimation as well as
Linear Interpolation together. May be it was my mistkae that I could not
explain my problem properly. Here I am writing what I have done so far:
I wanted to get proper symbol timing at receiver to sample the symbols.
Now what I did was at the i/p of decimator (sorry if I am making a mistake
again) I have got 4 samples per symbol and at the o/p of decimator I have 2
samples per symbol. Now for the first time I will decimate by factor of 2I
where I=1. But as I update the factor I lets sat I=1.001, so for the next
time I will do 'Linear Interpolation' first to find the new value between
two sample by using the formula given in the link and then I will
decimate. So by doing this my receiver works fine and my equaliser does
not have to work more.
Thanks to everybody who contributed to this thread. I am still at
beginners level and in future I will post my doubts so please try to help
me to solve my problems and increase my knowledge.
Thanks again.
Chintan P. Shah
Reply by jim●March 31, 20082008-03-31
Jerry Avins wrote:
>
> jim wrote:
> >
> > robert bristow-johnson wrote:
> >> On Mar 31, 4:10 am, dbd <d...@ieee.org> wrote:
> >>> On Mar 30, 11:39 pm, robert bristow-johnson
> >>>
> >> ...
> >>>> as far as interpolation is concerned (as opposed to the issue of
> >>>> removing frequency components before sample rate reduction), this is
> >>>> necessary and sufficient:
> >>>> +inf
> >>>> x(t) = SUM{ x(nT)*sinc((t-nT)/T) }
> >>>> n=-inf
> >>>> but, like any practical implementation, you won't be adding up all of
> >>>> terms. likewise is the downsampling antialiasing. it's not defining.
> >> ...
> >>> So you are another person who seems confused about "resampling to an
> >>> integer submultiple frequency where new values must be "calculated on
> >>> the curve" because anti-aliasing is required for samples that still
> >>> fall on the old sample times." I told Rick Lyons this was a problem to
> >>> discuss.
> >> Dale, i'm not confused about anything regarding the subject.
> >> certainly not anything stated in this thread. my participation began
> >> with my taking issue with your sweeping (at least unqualified) and
> >> incorrect statement that "Resampling formulas -do_not- match the old
> >> samples when they include anti-alias filtering."
> >
> > How can that be "incorrect"? If you downsample and the new samples are the
> > same at the old sample points then your anti-alias filter did absolutely
> > nothing.
>
> It's all semantics, then. The alteration comes about not from the
> downsampling, but from the filtering that precedes it.
> When there is no
> energy above the new Fs/2, there will be no change in the samples.
The statement was when a anti-alias filter was "required". But even if
you used one where it was not required there would be no change in samples
only if you know how to make an anti-alias filter that removes absolutely
no energy from below the new Fs/2.
-jim
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> �����������������������������������������������������������������������
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Reply by Jerry Avins●March 31, 20082008-03-31
jim wrote:
>
> robert bristow-johnson wrote:
>> On Mar 31, 4:10 am, dbd <d...@ieee.org> wrote:
>>> On Mar 30, 11:39 pm, robert bristow-johnson
>>>
>> ...
>>>> as far as interpolation is concerned (as opposed to the issue of
>>>> removing frequency components before sample rate reduction), this is
>>>> necessary and sufficient:
>>>> +inf
>>>> x(t) = SUM{ x(nT)*sinc((t-nT)/T) }
>>>> n=-inf
>>>> but, like any practical implementation, you won't be adding up all of
>>>> terms. likewise is the downsampling antialiasing. it's not defining.
>> ...
>>> So you are another person who seems confused about "resampling to an
>>> integer submultiple frequency where new values must be "calculated on
>>> the curve" because anti-aliasing is required for samples that still
>>> fall on the old sample times." I told Rick Lyons this was a problem to
>>> discuss.
>> Dale, i'm not confused about anything regarding the subject.
>> certainly not anything stated in this thread. my participation began
>> with my taking issue with your sweeping (at least unqualified) and
>> incorrect statement that "Resampling formulas -do_not- match the old
>> samples when they include anti-alias filtering."
>
> How can that be "incorrect"? If you downsample and the new samples are the
> same at the old sample points then your anti-alias filter did absolutely
> nothing.
It's all semantics, then. The alteration comes about not from the
downsampling, but from the filtering that precedes it. When there is no
energy above the new Fs/2, there will be no change in the samples.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Jerry Avins●March 31, 20082008-03-31
jim wrote:
>
> robert bristow-johnson wrote:
>> On Mar 31, 4:10 am, dbd <d...@ieee.org> wrote:
>>> On Mar 30, 11:39 pm, robert bristow-johnson
>>>
>> ...
>>>> as far as interpolation is concerned (as opposed to the issue of
>>>> removing frequency components before sample rate reduction), this is
>>>> necessary and sufficient:
>>>> +inf
>>>> x(t) = SUM{ x(nT)*sinc((t-nT)/T) }
>>>> n=-inf
>>>> but, like any practical implementation, you won't be adding up all of
>>>> terms. likewise is the downsampling antialiasing. it's not defining.
>> ...
>>> So you are another person who seems confused about "resampling to an
>>> integer submultiple frequency where new values must be "calculated on
>>> the curve" because anti-aliasing is required for samples that still
>>> fall on the old sample times." I told Rick Lyons this was a problem to
>>> discuss.
>> Dale, i'm not confused about anything regarding the subject.
>> certainly not anything stated in this thread. my participation began
>> with my taking issue with your sweeping (at least unqualified) and
>> incorrect statement that "Resampling formulas -do_not- match the old
>> samples when they include anti-alias filtering."
>
> How can that be "incorrect"? If you downsample and the new samples are the
> same at the old sample points then your anti-alias filter did absolutely
> nothing.
It's all semantics, then. The alteration comes about not from the
downsampling, but from the filtering that precedes it. When there is no
energy above the new Fs/2, there will be no change in the samples.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Jerry Avins●March 31, 20082008-03-31
jim wrote:
>
> robert bristow-johnson wrote:
>> On Mar 31, 4:10 am, dbd <d...@ieee.org> wrote:
>>> On Mar 30, 11:39 pm, robert bristow-johnson
>>>
>> ...
>>>> as far as interpolation is concerned (as opposed to the issue of
>>>> removing frequency components before sample rate reduction), this is
>>>> necessary and sufficient:
>>>> +inf
>>>> x(t) = SUM{ x(nT)*sinc((t-nT)/T) }
>>>> n=-inf
>>>> but, like any practical implementation, you won't be adding up all of
>>>> terms. likewise is the downsampling antialiasing. it's not defining.
>> ...
>>> So you are another person who seems confused about "resampling to an
>>> integer submultiple frequency where new values must be "calculated on
>>> the curve" because anti-aliasing is required for samples that still
>>> fall on the old sample times." I told Rick Lyons this was a problem to
>>> discuss.
>> Dale, i'm not confused about anything regarding the subject.
>> certainly not anything stated in this thread. my participation began
>> with my taking issue with your sweeping (at least unqualified) and
>> incorrect statement that "Resampling formulas -do_not- match the old
>> samples when they include anti-alias filtering."
>
> How can that be "incorrect"? If you downsample and the new samples are the
> same at the old sample points then your anti-alias filter did absolutely
> nothing.
It's all semantics, then. The alteration comes about not from the
downsampling, but from the filtering that precedes it. When there is no
energy above the new Fs/2, there will be no change in the samples.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Jerry Avins●March 31, 20082008-03-31
jim wrote:
>
> robert bristow-johnson wrote:
>> On Mar 31, 4:10 am, dbd <d...@ieee.org> wrote:
>>> On Mar 30, 11:39 pm, robert bristow-johnson
>>>
>> ...
>>>> as far as interpolation is concerned (as opposed to the issue of
>>>> removing frequency components before sample rate reduction), this is
>>>> necessary and sufficient:
>>>> +inf
>>>> x(t) = SUM{ x(nT)*sinc((t-nT)/T) }
>>>> n=-inf
>>>> but, like any practical implementation, you won't be adding up all of
>>>> terms. likewise is the downsampling antialiasing. it's not defining.
>> ...
>>> So you are another person who seems confused about "resampling to an
>>> integer submultiple frequency where new values must be "calculated on
>>> the curve" because anti-aliasing is required for samples that still
>>> fall on the old sample times." I told Rick Lyons this was a problem to
>>> discuss.
>> Dale, i'm not confused about anything regarding the subject.
>> certainly not anything stated in this thread. my participation began
>> with my taking issue with your sweeping (at least unqualified) and
>> incorrect statement that "Resampling formulas -do_not- match the old
>> samples when they include anti-alias filtering."
>
> How can that be "incorrect"? If you downsample and the new samples are the
> same at the old sample points then your anti-alias filter did absolutely
> nothing.
It's all semantics, then. The alteration comes about not from the
downsampling, but from the filtering that precedes it. When there is no
energy above the new Fs/2, there will be no change in the samples.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by jim●March 31, 20082008-03-31
robert bristow-johnson wrote:
>
> On Mar 31, 4:10 am, dbd <d...@ieee.org> wrote:
> > On Mar 30, 11:39 pm, robert bristow-johnson
> >
> ...
> > > as far as interpolation is concerned (as opposed to the issue of
> > > removing frequency components before sample rate reduction), this is
> > > necessary and sufficient:
> >
> > > +inf
> > > x(t) = SUM{ x(nT)*sinc((t-nT)/T) }
> > > n=-inf
> >
> > > but, like any practical implementation, you won't be adding up all of
> > > terms. likewise is the downsampling antialiasing. it's not defining.
> >
> ...
> >
> > So you are another person who seems confused about "resampling to an
> > integer submultiple frequency where new values must be "calculated on
> > the curve" because anti-aliasing is required for samples that still
> > fall on the old sample times." I told Rick Lyons this was a problem to
> > discuss.
>
> Dale, i'm not confused about anything regarding the subject.
> certainly not anything stated in this thread. my participation began
> with my taking issue with your sweeping (at least unqualified) and
> incorrect statement that "Resampling formulas -do_not- match the old
> samples when they include anti-alias filtering."
How can that be "incorrect"? If you downsample and the new samples are the
same at the old sample points then your anti-alias filter did absolutely
nothing.
-jim
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Reply by jim●March 31, 20082008-03-31
robert bristow-johnson wrote:
>
> On Mar 31, 4:10 am, dbd <d...@ieee.org> wrote:
> > On Mar 30, 11:39 pm, robert bristow-johnson
> >
> ...
> > > as far as interpolation is concerned (as opposed to the issue of
> > > removing frequency components before sample rate reduction), this is
> > > necessary and sufficient:
> >
> > > +inf
> > > x(t) = SUM{ x(nT)*sinc((t-nT)/T) }
> > > n=-inf
> >
> > > but, like any practical implementation, you won't be adding up all of
> > > terms. likewise is the downsampling antialiasing. it's not defining.
> >
> ...
> >
> > So you are another person who seems confused about "resampling to an
> > integer submultiple frequency where new values must be "calculated on
> > the curve" because anti-aliasing is required for samples that still
> > fall on the old sample times." I told Rick Lyons this was a problem to
> > discuss.
>
> Dale, i'm not confused about anything regarding the subject.
> certainly not anything stated in this thread. my participation began
> with my taking issue with your sweeping (at least unqualified) and
> incorrect statement that "Resampling formulas -do_not- match the old
> samples when they include anti-alias filtering."
How can that be "incorrect"? If you downsample and the new samples are the
same at the old sample points then your anti-alias filter did absolutely
nothing.
-jim
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Reply by dbd●March 31, 20082008-03-31
On Mar 31, 10:27 am, robert bristow-johnson
<r...@audioimagination.com> wrote:
> ...
>
> > So you are another person who seems confused about "resampling to an
> > integer submultiple frequency where new values must be "calculated on
> > the curve" because anti-aliasing is required for samples that still
> > fall on the old sample times." I told Rick Lyons this was a problem to
> > discuss.
>
> Dale, i'm not confused about anything regarding the subject.
> certainly not anything stated in this thread. my participation began
> with my taking issue with your sweeping (at least unqualified) and
> incorrect statement that "Resampling formulas -do_not- match the old
> samples when they include anti-alias filtering." that statement
> implies the meaning *all* resampling formulae, and to that extent, it
> simply is erroneous. it's wrong (or more precisely, that it's not
> always true). i said so, i said why and i continue to stand by it.
>
> r b-j
The practices of "resampling to an integer submultiple frequency" do
not constitute "*all* resampling formulae". You have quoted the
qualification. It goes all the way back to my post to Rick Lyons.It is
the statement I referred to I my response to Gordon Sande's post. And
it is that response that you began by quoting.
Dale B. Dalrymple
Reply by glen herrmannsfeldt●March 31, 20082008-03-31
Jerry Avins wrote:
> robert bristow-johnson wrote:
(snip)
>> Dale, i'm not confused about anything regarding the subject.
>> certainly not anything stated in this thread. my participation began
>> with my taking issue with your sweeping (at least unqualified) and
>> incorrect statement that "Resampling formulas -do_not- match the old
>> samples when they include anti-alias filtering." that statement
>> implies the meaning *all* resampling formulae, and to that extent, it
>> simply is erroneous. it's wrong (or more precisely, that it's not
>> always true). i said so, i said why and i continue to stand by it.
It is often said that a band limited signal can be sampled and then
reproduced exactly. That is more theoretical than practical, though.
> Could the confusion be that even if the resampling doesn't alter the
> original samples, necessary low-pass filtering _before_ resampling
> probably will?
In real cases, yes. As I was following this thread I wanted to comment
on the word 'interpolation' which I usually consider an approximation
to the exact value. (Especially linear interpolation on non-linear
function.)
Given perfect samples of a band limited function theoretically
you can compute the exact values of the function at points in
between the samples. I would say that those should not be called
interpolation. Without the ability to make a perfect bandpass
filter they will be approximate, and so interpolations,
including the values at the original sample points.
-- glen