Forums

Interpolation

Started by cpshah99 March 25, 2008
Randy Yates wrote:

> You know, I don't give a damn what you people want to call it. I've > seen three extremely respectable and authoritative authors call it that > and that's good enough for me.
And I saw 20 saying differently, so what?
> If you want a pissing contest partner on this, look elsewhere.
My point is exactly this: this discussion is pointless. If people here are arguing about the definition, it means there is no definition, since many of this people (not myself) could be considered authoritative enough, in this field. Not to mention that the arguments used are meaningful. bye, -- piergiorgio
dbd <dbd@ieee.org> writes:

> On Mar 27, 6:06 pm, Randy Yates <ya...@ieee.org> wrote: > >> With just a little more reading (I'm embarrassed to admit it's in the >> very same paragraph), we find that Rick's definitions only hold for >> integer values of interpolation or decimation, not fractional values. >> >> However, your intimation that Rick would call downsampling by a >> fractional amount "interpolation" is not supported by anything I could >> find in this section. He does go into "combining decimation and >> interpolation" in section 10.3, which is of course what the OP requires. > > I cited p387 of section 10.2 titled "Interpolation" where, amazingly > enough, he defines interpolation with no reference to upsampling, > downsampling or decimation which was my point.
I guess if you want to take one sentence in isolation, then you'd be correct. However, in the very first sentence of the very first paragraph of that section on that same page, Rick states: As we said before, decimation is only part of the sample rate conversion story---now let's consider interpolation. He places interpolation in the context of sample rate conversion and in apposition to decimation. He is establishing it as another operation different than decimation. I'm sure he'll be around in a short while - why don't we ask Rick himself to clarify which "interpretation" is correct?
> "Decimation" and "interpolation" are not complementary sets spanning > sample rate changes and it is sloppy to use them that way.
So say you. You are entitled to an opinion, but that is exactly what it is and no more. Further, as far as I know, Dale B. Dalyrmple, has not written a textbook on DSP nor been recognized as an expert in the field. I'll stick with the usage and terminology that is established by the experts in the field who have written books on the matter. If you think that's sloppy, I can't imagine why.
> I made no representation of what Lyons would call "downsampling by a > fractional amount", I repeated his definition so everyone could make > their own interpretation.
Repeating select sentences out of context is every bit a distortion (if not more) than anything I've done here. Now, to actually address what I believe is the issue here, let me state that, in my opinion, the term "interpolation" has two definitions when used in the field of DSP: 1) as a process that increases the sample rate, and 2) as a process that determines the samples of a digital waveform at other points in time than the original samples. This second process can be accomplished either at the same sample rate, a higher sample rate, or a lower sample rate than the input sample rate. -- % Randy Yates % "She tells me that she likes me very much, %% Fuquay-Varina, NC % but when I try to touch, she makes it %%% 919-577-9882 % all too clear." %%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO http://www.digitalsignallabs.com
>dbd <dbd@ieee.org> writes: > >> On Mar 27, 6:06 pm, Randy Yates <ya...@ieee.org> wrote: >> >>> With just a little more reading (I'm embarrassed to admit it's in the >>> very same paragraph), we find that Rick's definitions only hold for >>> integer values of interpolation or decimation, not fractional values. >>> >>> However, your intimation that Rick would call downsampling by a >>> fractional amount "interpolation" is not supported by anything I
could
>>> find in this section. He does go into "combining decimation and >>> interpolation" in section 10.3, which is of course what the OP
requires.
>> >> I cited p387 of section 10.2 titled "Interpolation" where, amazingly >> enough, he defines interpolation with no reference to upsampling, >> downsampling or decimation which was my point. > >I guess if you want to take one sentence in isolation, then you'd >be correct. However, in the very first sentence of the very
****** Hello Guys... I am confused now.....now i have forgotten that what i m doing is decimation or interpolation..... do u want me to write my problem again???? and that to my interpolator or decimator is adaptive!!!!!!!! please help..... Chintan
>first paragraph of that section on that same page, Rick states: > > As we said before, decimation is only part of the sample rate > conversion story---now let's consider interpolation. > >He places interpolation in the context of sample rate conversion and in >apposition to decimation. He is establishing it as another operation >different than decimation. > >I'm sure he'll be around in a short while - why don't we ask Rick >himself to clarify which "interpretation" is correct? > >> "Decimation" and "interpolation" are not complementary sets spanning >> sample rate changes and it is sloppy to use them that way. > >So say you. You are entitled to an opinion, but that is exactly what it >is and no more. Further, as far as I know, Dale B. Dalyrmple, has >not written a textbook on DSP nor been recognized as an expert in the >field. > >I'll stick with the usage and terminology that is established by the >experts in the field who have written books on the matter. If you think >that's sloppy, I can't imagine why. > >> I made no representation of what Lyons would call "downsampling by a >> fractional amount", I repeated his definition so everyone could make >> their own interpretation. > >Repeating select sentences out of context is every bit a distortion >(if not more) than anything I've done here. > >Now, to actually address what I believe is the issue here, let me state >that, in my opinion, the term "interpolation" has two definitions when >used in the field of DSP: 1) as a process that increases the sample >rate, and 2) as a process that determines the samples of a digital >waveform at other points in time than the original samples. This second >process can be accomplished either at the same sample rate, a higher >sample rate, or a lower sample rate than the input sample rate. >-- >% Randy Yates % "She tells me that she likes me very
much,
>%% Fuquay-Varina, NC % but when I try to touch, she makes
it
>%%% 919-577-9882 % all too
clear."
>%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
>http://www.digitalsignallabs.com >
dbd <dbd@ieee.org> writes:

> On Mar 27, 3:10 pm, "cpshah99" <cpsha...@rediffmail.com> wrote: > >> >> Hello Guys >> >> Please help me to understand this concept because I feel it is nice where >> decimation is updated for every symbol as the weights of the DFE are >> updated but I am not getting how to do this because in my case the >> feedforward length is 32 tap (i.e. 32 samples) and feedback filter length >> is 15 tap (i.e 15 symbol) >> >> I have the books by Crochiere and Rabiner and Vaidyanathan. >> >> Thank you. >> >> Chintan > > I'm not sure I understand just what you are looking for, but... > > If you are interested in implementing a standalone adjustable > resampling function as one of your blocks, consider the Farrow > structure. You can find a description by fred harris here: > http://www.signumconcepts.com/download/paper018.pdf > > Altera provides a detailed description of an implementation here: > http://www.altera.com/literature/an/an347.pdf
In addition to these good references, Julius O. Smith describes a technique he calls "bandlimited interpolation" here: http://ccrma-www.stanford.edu/~jos/resample/ This is another way of accomplishing your goal. -- % Randy Yates % "Watching all the days go by... %% Fuquay-Varina, NC % Who are you and who am I?" %%% 919-577-9882 % 'Mission (A World Record)', %%%% <yates@ieee.org> % *A New World Record*, ELO http://www.digitalsignallabs.com
"cpshah99" <cpshah99@rediffmail.com> writes:
> [...] > Hello Guys... > > I am confused now.....now i have forgotten that what i m doing is > decimation or interpolation..... > > do u want me to write my problem again???? > > and that to my interpolator or decimator is adaptive!!!!!!!! > > please help..... > > Chintan
Chintan, Let me apologize. There are obviously some inconsistencies in the terminology, which the previous discussions have born out. I will back-pedal and say it's not wrong to call it interpolation, especially if the output sample rate is adaptive. If it were a fixed sample rate conversion (as I had originally thought) and the the output rate was less than the input rate, then I would call it decimation. I think the references Dale gave you yesterday regarding "Farrow filters" and the one I just now posted on Julius O. Smith's "bandlimited interpolation" are two specific ways to accomplish the interpolation function you seek. -- % Randy Yates % "I met someone who looks alot like you, %% Fuquay-Varina, NC % she does the things you do, %%% 919-577-9882 % but she is an IBM." %%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO http://www.digitalsignallabs.com
>"cpshah99" <cpshah99@rediffmail.com> writes: >> [...] >> Hello Guys... >> >> I am confused now.....now i have forgotten that what i m doing is >> decimation or interpolation..... >> >> do u want me to write my problem again???? >> >> and that to my interpolator or decimator is adaptive!!!!!!!! >> >> please help..... >> >> Chintan > >Chintan, > >Let me apologize. There are obviously some inconsistencies in the >terminology, which the previous discussions have born out. > >I will back-pedal and say it's not wrong to call it interpolation, >especially if the output sample rate is adaptive. If it were a fixed >sample rate conversion (as I had originally thought) and the the output >rate was less than the input rate, then I would call it decimation. > >I think the references Dale gave you yesterday regarding "Farrow >filters" and the one I just now posted on Julius O. Smith's "bandlimited >interpolation" are two specific ways to accomplish the interpolation >function you seek. >-- >% Randy Yates % "I met someone who looks alot like
you,
>%% Fuquay-Varina, NC % she does the things you do,
>%%% 919-577-9882 % but she is an
IBM."
>%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
>http://www.digitalsignallabs.com >
******** Hi Randy Thanks for this references. I will read this and will get my fundamentals clear again. Thanks to all. Chintan
On Mar 28, 6:57 am, Randy Yates <ya...@ieee.org> wrote:

> ... > I guess if you want to take one sentence in isolation, then you'd > be correct. However, in the very first sentence of the very > first paragraph of that section on that same page, Rick states: > > As we said before, decimation is only part of the sample rate > conversion story---now let's consider interpolation. > ...
Isn't that a single sentence in isolation? :) I think most of the difference here comes from an assumption that because they are in the same sentence or same section title, the two terms are not just different but must be taken as complementary. The elevation of this assumption to the level of a definition is what I disagree with. I haven't disagreed with Lyons. (although I reserve the right to). He provides a perfectly reasonable description of interpolation which you choose to ignore. I disagree with your narrow interpretation of a simple English sentence. An interpretation that is inconsistent with the definition of interpolation in the previous section titled "Interpolation". The only one disagreeing with Lyons here is you.
> % Randy Yates
Dale B. Dalrymple
On Mar 27, 5:59 am, Randy Yates <ya...@ieee.org> wrote:
> First of all, you use the proper terminology. If the output > sample rate (2/T) is less than the input sample rate (2.5/T), > then the block is called a *decimator*,
This block naming is in common usage.
> not an interpolator.
Many common usages of the term "interpolator" are not strictly disjoint from decimation, depending perhaps on the exact process and/or rate used by the decimator. The two terms are not always mutually exclusive. Therefore I disagree with Randy's use of the word "not", as opposed to a fuzzier term regarding his preferred shorthand nomenclature, and not how all other practitioners might label this process for all possible descriptive purposes. To the OP, I suggest drawing an XY graph, with the X axis labeled in time in Seconds (not just the sample index). Mark some actual sample points on the graph, and then mark which time points at which you desire sample values. For some of the points, doesn't this look like an old-fashioned interpolation problem? If computational efficiency is not a concern, and the signal is reasonably close to bandlimited, one can compute each desired point, in any order, and completely without regard to whether the total number of points is larger, smaller, the same, or to be decided tomorrow, compared to the original sample vector length. IMHO. YMMV. -- rhn A.T nicholson d.0.t C-o-M
"Ron N." <rhnlogic@yahoo.com> writes:

> On Mar 27, 5:59 am, Randy Yates <ya...@ieee.org> wrote: >> First of all, you use the proper terminology. If the output >> sample rate (2/T) is less than the input sample rate (2.5/T), >> then the block is called a *decimator*, > > This block naming is in common usage. > >> not an interpolator. > > Many common usages of the term "interpolator" are not > strictly disjoint from decimation, depending perhaps on the > exact process and/or rate used by the decimator. The two > terms are not always mutually exclusive. > > Therefore I disagree with Randy's use of the word "not", as > opposed to a fuzzier term regarding his preferred shorthand > nomenclature, and not how all other practitioners might > label this process for all possible descriptive purposes.
I agree with you, Ron, if it's ok that I disagree with myself... I agree that I came down a bit too hard - to state that I "prefer" the term decimation would've been more appropriate. -- % Randy Yates % "How's life on earth? %% Fuquay-Varina, NC % ... What is it worth?" %%% 919-577-9882 % 'Mission (A World Record)', %%%% <yates@ieee.org> % *A New World Record*, ELO http://www.digitalsignallabs.com
On Thu, 27 Mar 2008 13:45:25 -0700 (PDT), dbd <dbd@ieee.org> wrote:

>On Mar 27, 1:02 pm, Randy Yates <ya...@ieee.org> wrote:
(Snipped by Lyons)
> >Randy > >I only have your first reference at hand right now. > >A scan of the titles in the contents page supports your argument. >However, on page 387 of the 2004 version, Lyons says that >"Conceptually interpolation comprises the generation" of a >"continuous ... curve passing through our ... sampled values ... >followed by sampling that curve at a new sample rate". The title of >the section is "Interpolation" but Lyons uses "Sample rate increase by >interpolation" within the first paragraph. It may be common for book >editing to induce technical sloppiness in the course of a search for >conciseness and eye-pleasing page layout. That is not justification to >suggest the enforcement of such sloppiness here. > >Dale B. Dalrymple
Hi Dale, I'm not rightly sure that I understand the exact meaning of your post. But if you have any suggestions for me to help me minimize what you think is "sloppiness" in my writing, I'd sure be willing to hear your opinions. This thread's examination of the language of 'sample rate change' (SRC) is fascinating to me because in recent years I've also run into trouble reading the literature because there seems to be no standard definitions for words like "decimation", "interpolation", "expander", "upsampling", "downsampling", "compressor", etc. (And, I confess, my writing has not helped this situation, but I hope to correct that.) I'm gonna try to convince my Publisher to publish a 3rd edition of my book in the next year or two and, as such, I have totally re-written my current Chapter 10, "Sample Rate Conversion". In fact, I've written a short section in my new Chapter 10 material describing what I think is all the various, and sometimes ambiguous, terminology in the literature of sample rate change (SRC) processing. That new material of mine is meant to warn my readers to be both flexible and careful when they read the *words* authors use to describe SRC techniques. By the way, my current thinking (beyond what I wrote ten years) is that the term "interpolation" should be used for *ANY* sample rate change that is NOT decimation by an integer factor. Stated in different words, I now believe the phrase "interpolation" should be used, for example, to describe a sample rate decrease by a factor of 3/4. Ya' know what's interesting? In the early 1970's, when DSP was becoming more and more popular, a group of DSP experts/pioneers/gurus joined together and published the paper: L. Rabiner et al., "Terminology in Digital Signal Processing," IEEE Trans. on Audio and Electroacoustics., Vol. AU-20, No. 5, December 1972, pp. 322-337. In that paper, which makes for *VERY* useful reading for anyone in the field of DSP, the authors literally compiled a list of "recommended DSP terminology" for all future DSP-related papers, articles, and textbooks. They hoped to establish a self-consistent, unambiguous, language for DSP. For example, they clearly defined the difference between the terms "recursive filter" and "IIR filter". It might be interesting to write a paper titled: "Terminology in Sample Rate Change Systems" in the hope of reducing the confusion that now exists in the language of SRC as described in the literature. Any takers? See Ya', [-Rick-]