Re: [music-dsp] Sampling theory "best" explanation

com> wrote: > > > Original Message ---- > Subject: Re: [music-dsp] Sampling theory "best" explanation > From: "Ethan Duni" <ethan.d...@gmail.com> > Date: Wed, September 6, 2017 4:49 pm > To

Re: [music-dsp] Sampling theory "best" explanation

So when is a "system", or better put, it's mathematical model, a linear system ? In a way the scalar high school definition suffices, when the inputs are added, the result must be the same as when the inputs are processed separately, and a mulitplied input gives a multiplied output. Simple

Re: [music-dsp] Sampling theory "best" explanation

It is a most fascinating thread. The more one looks into it, the more one has to marvel that the process works at all. Richard Dobson On 07/09/2017 07:16, Nigel Redmon wrote: Somehow, combining the term "rat's ass" with a clear and concise explanation of your viewpoint makes it especially

Re: [music-dsp] Sampling theory "best" explanation

- Original Message ---------------- > Subject: Re: [music-dsp] Sampling theory "best" explanation > From: "Ethan Duni" <ethan.d...@gmail.com> > Date: Wed, September 6, 2017 4:49 pm > To: "robert bristow-johnson" <r...@audioimagi

Re: [music-dsp] Sampling theory "best" explanation

Original Message Subject: Re: [music-dsp] Sampling theory "best" explanation From: "Ethan Duni" <ethan.d...@gmail.com> Date: Wed, September 6, 2017 4:49 pm To: "robert bristow-johnson" <r.

Re: [music-dsp] Sampling theory "best" explanation

Okay, no big deal. It's easy to come off the wrong way in complicated, fast moving email threads. Ethan D On Wed, Sep 6, 2017 at 6:37 PM, Nigel Redmon wrote: > Ethan, I wasn't taking a swipe at you, by any stretch. In fact, I wasn't > even addressing your ADC comment. It

Re: [music-dsp] Sampling theory "best" explanation

Of course I mean that we store a representation of an impulse. I've said many times that the sample values "represent" impulses. > On Sep 7, 2017, at 5:34 AM, Ethan Duni wrote: > > >For ADC, we effectively measure an instantaneous voltage and store it as an > >impulse. >

Re: [music-dsp] Sampling theory "best" explanation

Nigel Redmon wrote: >As an electrical engineer, we find great humor when people say we can't do impulses. I'm the electrical engineer who pointed out that impulses don't exist and are not found in actual ADCs. If you have some issue with anything I've posted, I'll thank you to address it to me

Re: [music-dsp] Sampling theory "best" explanation

sion-making purposes it clearly is, it seem you've defeated the purpose. > On Sep 5, 2017, at 11:57 PM, robert bristow-johnson > <r...@audioimagination.com> wrote: > > > > Original Message ------------ > Subject: Re: [music

Re: [music-dsp] Sampling theory "best" explanation

Original Message Subject: Re: [music-dsp] Sampling theory "best" explanation From: "Nigel Redmon" <earle...@earlevel.com> Date: Tue, September 5, 2017 4:05 am To: mu

Re: [music-dsp] Sampling theory "best" explanation

Original Message Subject: Re: [music-dsp] Sampling theory "best" explanation From: "Ethan Duni" <ethan.d...@gmail.com> Date: Tue, September 5, 2017 1:07 am To: "A discussion list fo

Re: [music-dsp] Sampling theory "best" explanation

> > If not, then the phrase "resampling is LTI" - without some kind of "ideal" > qualifier - seems misleading. If it's LTI then what are all these aliases > doing in my outputs? > Yeah, I think you had it right when you pointed out that the existence of aliasing shows that resampling is not LTI if

Re: [music-dsp] Sampling theory "best" explanation

As an electrical engineer, we find great humor when people say we can't do impulses. What constitutes an impulse depends on the context—nano seconds, milliseconds... For ADC, we effectively measure an instantaneous voltage and store it as an impulse. Arguing that we don't really do

Re: [music-dsp] Sampling theory "best" explanation

rbj wrote: >1. resampling is LTI **if**, for the TI portion, one appropriately scales time. Have we established that this holds for non-ideal resampling? It doesn't seem like it does, in general. If not, then the phrase "resampling is LTI" - without some kind of "ideal" qualifier - seems

Re: [music-dsp] Sampling theory "best" explanation

> The fact that 5,17,-12,2 at sample rate 1X and > 5,0,0,0,17,0,0,0,-12,0,0,0,2,0,0,0 at sample rate 4X are identical is obvious > only for samples representing impulses. > > I agree that the zero-stuff-then-lowpass technique is much more obvious when > we you consider the impulse train

Re: [music-dsp] Sampling theory "best" explanation

OTOH, just about everything we do with digital audio doesn’t exactly work. Start with sampling. Do we give up if we can’t ensure absolutely no signal at and above half the sample rate? Fortunately, our ears have limitations (whew!). ;-) Anyway, the aliasing occurred to me as I wrote that, but

Re: [music-dsp] Sampling theory "best" explanation

ASRC chip uses), that means (taking advantage of symmetry) 8K coefficients needed in a table, 64 MAC instructions, and one linear interpolation per output sample. �doesn't matter what the sample-rate conversion ratio is (as long as we don't worry about aliasing in downsampling). � bestest, r b-j � -

Re: [music-dsp] Sampling theory "best" explanation

> > First, I want to be clear that I don’t think people are crippled by > certain viewpoint—I’ve said this elsewhere before, maybe not it this thread > or the article so much. In that case I'd suggest some more editing is in order, since the article stated this pretty overtly at least a couple

Re: [music-dsp] Sampling theory "best" explanation

> > Time variance is a bit subtle in the multi-rate context. For integer > downsampling, as you point out, it might make more sense to replace the > classic n-shift-in/n-shift-out definition of time invariance with one that > works in terms of the common real time represented by the different >

Re: [music-dsp] Sampling theory "best" explanation

Hmm this is quite a few discussions of LTI with respect to resampling that have gone badly on the list over the years... Time variance is a bit subtle in the multi-rate context. For integer downsampling, as you point out, it might make more sense to replace the classic n-shift-in/n-shift-out

Re: [music-dsp] Sampling theory "best" explanation

Interesting comments, Ethan. Somewhat related to your points, I also had a situation on this board years ago where I said that sample rate conversion was LTI. It was a specific context, regarding downsampling, so a number of people, one by one, basically quoted back the reason I was wrong.

Re: [music-dsp] Sampling theory "best" explanation

Ethan F wrote: >I see your nitpick and raise you. :o) Surely there are uncountably many such functions, >as the power at any apparent frequency can be distributed arbitrarily among the bands. Ah, good point. Uncountable it is! Nigel R wrote: >But I think there are good reasons to understand the

Re: [music-dsp] Sampling theory "best" explanation

Hi Ethan, Good comments and questions…I’m going to have to skip the questions for now (I’m in a race against time the next few days, then will been off the grid, relatively speaking, for a couple of weeks—but I didn’t want to seem like I was ignoring your reply; I think any quick answers to

Re: [music-dsp] Sampling theory "best" explanation

> > This needs an additional qualifier, something about the bandlimited > function with the lowest possible bandwidth, or containing DC, or > "baseband," or such. Yes, by bandlimited here I mean bandlimited to [-Nyquist, Nyquist]. Otherwise, there are a countably infinite number of bandlimited

Re: [music-dsp] Sampling theory "best" explanation

>I'm one of those people who prefer to think of a discrete-time signal as >representing the unique bandlimited function interpolating its samples. This needs an additional qualifier, something about the bandlimited function with the lowest possible bandwidth, or containing DC, or "baseband," or

Re: [music-dsp] Sampling theory "best" explanation

Thanks for posting this! It's always interesting to get such a good glimpse at someone else's mental model. I'm one of those people who prefer to think of a discrete-time signal as representing the unique bandlimited function interpolating its samples. And I don't think this point of view has

Re: [music-dsp] Sampling theory "best" explanation

Hi Remy, > On Aug 28, 2017, at 2:16 AM, Remy Muller wrote: > > I second Sampo about giving some more hints about Hilbert spaces, > shift-invariance, Riesz representation theorem… etc I think you’ve hit upon precisely what my blog isn’t, and why it exists at all. ;-) >

Re: [music-dsp] Sampling theory "best" explanation

Nigel Redmon wrote: Well, it’s quiet here, why not… Right, a good reiteration never hurts! I quickly read through and find your explanation fine, it's not right to expect everybody to be theoretically sound and solid up to the level of mathematical proof, but I'm a strong proponent of

Re: [music-dsp] Sampling theory "best" explanation

I second Sampo about giving some more hints about Hilbert spaces, shift-invariance, Riesz representation theorem... etc Correct me if you said it somewhere and I didn't saw it, but an important /implicit/ assumption in your explanation is that you are talking about "uniform bandlimited

Re: [music-dsp] Sampling theory "best" explanation

> > r b-j > > > > Original Message > Subject: Re: [music-dsp] Sampling theory "best" explanation > From: "Sampo Syreeni" <de...@iki.fi> > Date: Sun, August 27, 2017 2:20 am > To: &quo

Re: [music-dsp] Sampling theory "best" explanation

Sampo, the purpose was to convince people that samples are impulses, and why that means the spectrum represented by a series of samples is the intended spectrum plus aliased images, forever. in the simplest, most intuitive way I could think of. That’s why I put those points up front, before

Re: [music-dsp] Sampling theory "best" explanation

Well, it’s a DSP blog. The intended audience is whoever reads it, I’m not judgmental. So, the question is probably more like “who can benefit from it”. At the novice end, I’d say they can probably benefit at least from the revelation that it comes from solving issues in analog communication,

Re: [music-dsp] Sampling theory "best" explanation

Le 2017-08-26 03:21, Nigel Redmon a écrit : http://www.earlevel.com/main/tag/sampling-theory-series/?order=asc Hi Nigel, For me the best sampling theory explanation I ever saw is probably also one of the oldest (1980!) This explanation can be found in the second chapter of the 2920

Re: [music-dsp] Sampling theory "best" explanation

On 2017-08-25, Nigel Redmon wrote: http://www.earlevel.com/main/tag/sampling-theory-series/?order=asc Personally I'd make it much simpler at the top. Just tell them sampling is what it is: taking an instantaneous value of a signal at regular intervals. Then tell them that is all it takes to

Re: [music-dsp] Sampling theory "best" explanation

Please check out my new series on sampling theory, and feel free to comment here or there. The goal was to be brief, but thorough, and avoid abstract mathematical explanations. In other words, accurate enough that you can deduce correct calculations from it, but intuitive enough for the math-shy.

Re: [music-dsp] Sampling theory "best" explanation

thank you very much ! 2017-08-26 4:21 GMT+03:00 Nigel Redmon : > Well, it’s quiet here, why not… > > Please check out my new series on sampling theory, and feel free to > comment here or there. The goal was to be brief, but thorough, and > avoid abstract mathematical

Re: [music-dsp] Sampling theory "best" explanation

This is neat, thanks for sharing Nigel On Aug 25, 2017 6:22 PM, "Nigel Redmon" wrote: > Well, it’s quiet here, why not… > > Please check out my new series on sampling theory, and feel free to > comment here or there. The goal was to be brief, but thorough, and > avoid