Re: [music-dsp] Compensate for interpolation high frequency signal loss
On 22/08/2015, Ethan Duni ethan.d...@gmail.com wrote: So your whole point is that it's not *exactly* sinc^2, but a slightly noisy version thereof? My point was that there are no effects of resampling visible in the graphs. And you're wrong - all those 88 alias images are effects of resampling... That has nothing to do with exactly how the graphs were generated, nor does insisting that the graphs are slightly noisy address the point. Well, it was *you* who insisted that it displays a graphed sinc^2 curve, and not a resampled signal... And you were wrong. Indeed, you've already conceded that the resampling effects are not visible in the graphs several posts back. Aren't all those 88 alias images effects of resampling? What are those, if not effects of resampling? You claimed no upsampling is involved, yet when I upsample noise, I get exactly that graph. So it seems you were wrong. It seems like you're just casting about for some other issue that you can tell yourself you won, and then call me names, to feed your fragile ego. Well, if you do not see that the curve is NOT a graphed sinc^2, but rather, a noisy curve seemingly from resampled noise, then you have some underlying problem. Honestly, it's a pretty sad spectacle and I'm embarrassed for you. I'm embarrassed for you. It really would be better for everyone - including you - if you could interact in a good-faith, mature manner. Please make an effort to start doing so, or you're pretty soon going to find that nobody here will interact with you any more. Yet - for some reason - you keep interacting with me for the past 22 mails you wrote. Maybe to feed your fragile ego and prove that you won... (?) By the way, there's no reason for any jaggedness to appear in the plots, given the lengths of data you were talking about. There *is* reason for jaggedness to appear in the plots. If you don't believe, try it yourself - take some white noise sampled at 500 Hz, and resample it to 44.1 kHz. The shorter the length, the more jagged the spectrum will look. Besides, we do not know how much data Olli processed, so you cannot say there's no reason for jaggedness in his graph - as you do not know how he derived his graph. So your argument is invalid again. Producing a very smooth graph from a long enough segment of data is straightforward, if you use appropriate techniques (not just one big FFT of the whole thing, that won't ever get rid of the noisiness no matter how much data you throw at it). Exactly. And that's what I used (spectral averaging over a long segment), yet it is STILL noisy, if the white noise segment is not very long. So your argument is wrong again... -P ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] unsubscribe
On 22/08/2015, Alen akoe...@rogers.com wrote: Indeed. This debate is getting tiresome. That's what happens when someone does not accept that he is wrong, despite overwhelming evidence. ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Compensate for interpolation high frequency signal loss
So you claim that the graph depicts a sinc^2 graph, and it shows the frequency response of a continuous time linearly interpolated signal, and involves no resampling. That is false. That is not how Olli created his graph. First, the continuous time signal (which, by the way, already contains an infinite amount of aliases of the original spectrum) exists only in your imagination - I'm almost 100% certain Olli made his graph by resampling noise. The telltale signs of this are: - the curves on the graph are jagged/noisy, typical of averaged white noise spectrum - if you watch closely, the same jaggedness repeats at a 2*PI frequency interval, showing that they are aliases of the original spectrum, which was noisy. Therefore, Ollis graph does *not* depict a continuous time signal, but rather, a noisy signal that was resampled to 44.1 kHz. Therefore, what you see on the graph, is the artifacts from the resampling. Therefore, all your arguments are invalid. -P ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Compensate for interpolation high frequency signal loss
So let me get this straight - you have an *imaginary* graph in your head, depicting the frequency response of a continuous time linearly interpolated signal, and you keep arguing about this *imaginary* graph (maybe to feed your fragile ego and to prove that you won). That is *not* what you see on Olli's graph, as been discussed in depth. So what you're arguing about, is not Olli's graph that was presented, but rather, an *imaginary* graph, that exists only in your head. -P ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Compensate for interpolation high frequency signal loss
And besides, no one ever said that Olli's graph depicts analyitical frequency responses of continuous time interpolators. The graphs come from a musicdsp.org code entry: http://musicdsp.org/archive.php?classid=5#49 There's no comment whatsover, just the code and the graphs. If you read his 65 page long paper on interpolators, he doesn't discuss analytical continuous time interpolator frequency responses whatsoever. He just shows their graphs, and tells where they have zeros in the response. No formulas for analytical frequency responses, at all - seemingly he is not interested in that. I just skimmed through his paper again, and the closest thing that he has in it, are polynomial approximations for frequency responses in the passband. About that's all, other than that, no frequency response formulas. -P ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Compensate for interpolation high frequency signal loss
On 2015-08-18, Tom Duffy wrote: In order to reconstruct that sinusoid, you'll need a filter with an infinitely steep transition band. You've demonstrated that SR/2 aliases to 0Hz, i.e. DC. That digital stream of samples is not reconstructable. The conjugate sine to +1, -1, +1, -1, ... is 0, 0, 0, 0... Just phase shift the original sine at the Nyquist frequence. That'll show you that that precise signal cannot be reconstructed without resorting to complex continuation of the signal, on the Fourier plane. -- Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front +358-40-3255353, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2 ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] unsubscribe
On Fri, Aug 21, 2015 at 8:59 PM, b...@bobhuff.com wrote: To unsubscribe please see the list info page: https://lists.columbia.edu/mailman/listinfo/music-dsp best, douglas ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Compensate for interpolation high frequency signal loss
On 22/08/2015, Sampo Syreeni de...@iki.fi wrote: The conjugate sine to +1, -1, +1, -1, ... is 0, 0, 0, 0... Just phase shift the original sine at the Nyquist frequence. Let me ask what do you mean by conjugate sine ? If you mean complex conjugate, and assume the sine to be the real part of complex phasor rotating around the complex unit circle, then isn't the conjugate of that phasor also +1, -1, +1, -1,... ? The only difference is that the phasor is mirrored around the X axis (so the imaginary part +i becomes -i), so it rotates in the opposite direction (negative frequency). Since the frequency of that phasor is pi, the complex conjugate phasor rotating at the other direction is also +1, -1, +1, -1... Either direction, the phasor toggles between positions z=1 and z=-1. Maybe you meant quadrature sine ? That'll show you that that precise signal cannot be reconstructed without resorting to complex continuation of the signal, on the Fourier plane. Let me ask, what do you mean by Fourier plane? I never heard that term, and Google only gives me optics-related pages. Maybe you mean complex plane? ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] Compensate for interpolation high frequency signal loss
Okay, I'll risk exceeding my daily message limit. If the administrators think it is inappropriate, dealing with that is at their discretion. Here is another proof that the alias images in the spectrum are caused by the sampling/upsampling, not the interpolation: Let's replace linear interpolation with simply stuffing zeros between samples. So that means, we upsample the signal without applying interpolation or filtering. Let's try this on an ~50 Hz sine wave sampled at 44100/88 ~= 501 Hz, upsampled to 44.1 kHz by stuffing 87 zeros between each sample. The resulting waveform looks like individual impulses, spaced 88 samples apart: http://morpheus.spectralhead.com/img/sine_upsampled_waveform.png Here is the spectrum: http://morpheus.spectralhead.com/img/sine_upsampled_spectrum.png We can see the usual alias frequencies at 450 Hz, 550 Hz, 950 Hz, 1050 Hz, 1450 Hz, 1550 Hz, 1950 Hz, 2050 Hz, ... This is because the upsampling causes the original spectrum to repeated infinite times, causing these alias frequencies to appear in the resulting spectrum. Therefore, it is NOT the interpolation that is causing these alias images, but rather, the upsampling... More precisely, they're already present in the original signal sampled at 500 Hz, the upsampling just makes them visible. I used no interpolation at all, yet all this aliasing appeared on the spectrum. All the interpolation does, is it filters out some of this aliasing... Since the impulse response of linear interpolation is a triangle, applying linear interpolation is equivalent to convolving the resulting upsampled signal with a triangular kernel filter. Since the Fourier transform of a rectangle is a sinc function, and a triangular kernel is equivalent to convolving two rectangular kernels, the Fourier spectrum of a triangular kernel will look like a sinc^2 function. But that's not what causes the aliasing... it's there already after the upsampling, before you apply the interpolation/convolution. You can take a discretized version of a continuous triangular kernel sampled at the upsampled rate, and convolving the upsampled signal with that kernel will be equivalent to linear interpolation. You do not actually need a continuous time signal to be present, and the aliasing/imaging is there already before doing the triangular convolution at the upsampled rate. Several authors discuss the equivalence of linear interpolation and convolution with a triangular filter, examples: 1) linear interpolation can be expressed as convolving the sampled function with a triangle function[1] http://morpheus.spectralhead.com/img/linear_interpolation1.png 2) The first-order hold [= linear interpolation] corresponds to an impulse response for the reconstruction filter that is a triangle of duration equal to twice the sampling period.[2] http://morpheus.spectralhead.com/img/linear_interpolation2.png 3) http://morpheus.spectralhead.com/img/linear_interpolation3.png [1] Oliver Kreylos, Sampling Theory 101 http://idav.ucdavis.edu/~okreylos/PhDStudies/Winter2000/SamplingTheory.html [2] Alan V. Oppenheim, Signals and Systems, ch. 17. Interpolation http://ocw.mit.edu/resources/res-6-007-signals-and-systems-spring-2011/lecture-notes/MITRES_6_007S11_lec17.pdf [3] Ruye Wang, Sampling Theorem, Reconstruction of Signal by Interpolation http://fourier.eng.hmc.edu/e101/lectures/Sampling_theorem/node3.html -P ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
[music-dsp] [admin] list etiquette
Hi everyone, Douglas the list admin here. I've been away and haven't really been monitoring the list recently. It's been full of bad feelings, unpleasant interactions, and macho posturing. Really not much that I find interesting. I just want to reiterate a few things about the list. I'm loathe to make or enforce rules. But the list has been pretty much useless for the majority of subscribers for the last year or so. I know this because many of them have written to complain. It's certainly not useful to me. I've also had several reports of people trying to unsubscribe other people and other childish behavior. Come on. So: * Please limit yourself to two well-considered posts per day. Take it off list if you need more than that. * No personal attacks. I'm just going to unsub people who are insulting. Sorry. * Please stop making macho comments about first year EE students know this and blahblahblah. This list is for anyone with an interest in sound and dsp. No topic is too basic, and complete beginners are welcome. I will happily unsubscribe people who find they can't consistently follow these guidelines. The current list climate is hostile and self-aggrandizing. No beginner, gentle coder, or friendly hobbyist is going to post to such a list. If you can't help make the list friendly to everyone, please leave. This isn't the list for you. douglas ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] [admin] list etiquette
Thank you, Douglas. Regards, Mike - Michael Gogins Irreducible Productions http://michaelgogins.tumblr.com Michael dot Gogins at gmail dot com On Sat, Aug 22, 2015 at 11:21 AM, Douglas Repetto doug...@music.columbia.edu wrote: Hi everyone, Douglas the list admin here. I've been away and haven't really been monitoring the list recently. It's been full of bad feelings, unpleasant interactions, and macho posturing. Really not much that I find interesting. I just want to reiterate a few things about the list. I'm loathe to make or enforce rules. But the list has been pretty much useless for the majority of subscribers for the last year or so. I know this because many of them have written to complain. It's certainly not useful to me. I've also had several reports of people trying to unsubscribe other people and other childish behavior. Come on. So: * Please limit yourself to two well-considered posts per day. Take it off list if you need more than that. * No personal attacks. I'm just going to unsub people who are insulting. Sorry. * Please stop making macho comments about first year EE students know this and blahblahblah. This list is for anyone with an interest in sound and dsp. No topic is too basic, and complete beginners are welcome. I will happily unsubscribe people who find they can't consistently follow these guidelines. The current list climate is hostile and self-aggrandizing. No beginner, gentle coder, or friendly hobbyist is going to post to such a list. If you can't help make the list friendly to everyone, please leave. This isn't the list for you. douglas ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] [admin] list etiquette
On 08/22/2015 08:59 AM, Peter S wrote: Second, why take something off-list if it's related to the discussion? I agree, as long as one can present a professional attitude ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] [admin] list etiquette
Ditto! Richard Dobson On 22/08/2015 16:50, Michael Gogins wrote: Thank you, Douglas. Regards, Mike ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] [admin] list etiquette
I think this might be a bit too restrictive; there have been many highly informative exchanges here over the years, all well-considered, that have exceeded this limit. The key is surely well-considered - and the absence of egoic chest-beating! Richard Dobson On 22/08/2015 16:21, Douglas Repetto wrote: * Please limit yourself to two well-considered posts per day. Take it off list if you need more than that. ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] [admin] list etiquette
Perhaps the knowledge that you might risk exceeding your limit (which I'm sure would not be pedantically enforced) would make you to consider for yourself how much the given message is contributing to the discussion. Thank you Douglas, for clarifying the etiquette and audience. It was needed and I fully agree with the policy. Stefan On Sat, Aug 22, 2015, 18:35 Richard Dobson richarddob...@blueyonder.co.uk wrote: I think this might be a bit too restrictive; there have been many highly informative exchanges here over the years, all well-considered, that have exceeded this limit. The key is surely well-considered - and the absence of egoic chest-beating! Richard Dobson On 22/08/2015 16:21, Douglas Repetto wrote: * Please limit yourself to two well-considered posts per day. Take it off list if you need more than that. ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp ___ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
