On Thu, Mar 19, 2020 at 8:11 AM Dario Sanfilippo
wrote:
>
> I believe that the time complexity of FFT is O(nlog(n)); would you perhaps
> have a list or reference to a paper that shows the time complexity of
> common DSP systems such as a 1-pole filter?
>
The complexity depends on the topology. T
On Tue, Mar 10, 2020 at 1:05 PM Richard Dobson wrote:
>
> Our ICMC paper can be found here, along with a few beguiling sound
> examples:
>
> http://dream.cs.bath.ac.uk/SDFT/
So this is pretty cool stuff. I can't say I've digested the whole idea yet,
but I had a couple of obvious questions.
In
my github with
> audio if you want to hear whether or not there is quantization noise from
> this FFT EQ or not (from changing the coefficients, etc).
>
>
> cheers,
> Eric Z
> https://www.github.com/kardashevian
>
> On Fri, Mar 13, 2020 at 6:18 PM Ethan Duni wrote:
>
&g
On Thu, Mar 12, 2020 at 9:35 PM robert bristow-johnson <
r...@audioimagination.com> wrote:
> i am not always persuaded that the analysis window is preserved in the
> frequency-domain modification operation.
It definitely is *not* preserved under modification, generally.
The Perfect Reconstruct
Hi Robert
On Wed, Mar 11, 2020 at 4:19 PM robert bristow-johnson <
r...@audioimagination.com> wrote:
>
> i don't think it's too generic for "STFT processing". step #4 is pretty
> generic.
>
I think the part that chafes my intuition is more that the windows in steps
#2 and #6 should "match" in s
On Tue, Mar 10, 2020 at 8:36 AM Spencer Russell wrote:
>
> The point I'm making here is that overlap-add fast FIR is a special case
> of STFT-domain multiplication and resynthesis. I'm defining the standard
> STFT pipeline here as:
>
> 1. slice your signal into frames
> 2. pointwise-multiply an a
> On Mar 10, 2020, at 3:38 AM, Richard Dobson wrote:
>
> You can have windows when hop size is 1 sample (as used in the sliding phase
> vocoder (SPV) proposed by Andy Moorer exactly 20 years ago, and the focus of
> a research project I was part of around 2007). So long as the window is based
It is certainly possible to combine STFT with fast convolution in various ways.
But doing so imposes significant overhead costs and constrains the overall
design in strong ways.
For example, this approach:
> On Mar 9, 2020, at 7:16 AM, Spencer Russell wrote:
>
>
> if you have an KxN STFT (
On Sun, Mar 8, 2020 at 8:02 PM Spencer Russell wrote:
> In fact, the the standard STFT analysis/synthesis pipeline is the same
> thing as overlap-add "fast convolution" if you:
>
> 1. Use a rectangular window with a length equal to your hop size
> 2. zero-pad each input frame by the length of you
>
> If the system is suitably designed (e.g. correct window and overlap),
> you can filter using an FFT and get identical results to a time domain
> FIR filter (up-to rounding/precision limits, of course). The
> appropriate window and overlap process will cause all circular
> convolution artefact
hallmark of the MDCT or
> DCT type IV which is ubiquitous in audio codecs.
>
>> On Sun, Mar 8, 2020, 7:41 PM Ethan Duni wrote:
>> FFT filterbanks are time variant due to framing effects and the circular
>> convolution property. They exhibit “perfect reconstruction” if you
FFT filterbanks are time variant due to framing effects and the circular
convolution property. They exhibit “perfect reconstruction” if you design the
windows correctly, but this only applies if the FFT coefficients are not
altered between analysis and synthesis. If you alter the FFT coefficient
It is physically impossible to build a causal, zero-phase system with
non-trivial frequency response.
Ethan
> On Mar 7, 2020, at 7:42 PM, Zhiguang Eric Zhang wrote:
>
>
> Not to threadjack from Alan Wolfe, but the FFT EQ was responsive written in C
> and running on a previous gen MacBook P
So as Nigel and Robert have already explained, in general you need to
separately handle the spectral shaping and pdf shaping. This dither
algorithm works by limiting to the particular case of triangular pdf with a
single pole at z=+/-1. For that case, the state of the spectral shaping
filter can be
Looks like they use the Viterbi algorithm to get the pitch tracks.
> On Mar 6, 2019, at 6:59 PM, Jay wrote:
>
>
> Looks like there's a link to a python implementation on this topics page,
> might provide some insights:
> https://github.com/topics/pitch-tracking
>
>
>
>
>
>
>
>
>> On W
Aren't Auto-Tune and similar built on LPC vocoders? I had the impression
that was publicly known (recalling magazine interviews/articles from the
late 90s). The secret sauce being all the stuff required for pitch
tracking, unvoiced segments, different tunings, vibrato, corner cases, etc.
But as fa
applications?
>
> The background is still that I want to use a higher resolution for
> ananlysis and
> a lower resolution for synthesis in a phase vocoder.
>
> Am 08.11.2018 um 21:45 schrieb Ethan Duni:
>
> Not sure can get the odd bins *easily*, but it is certainly possible
gt; For instance we should have:
>
> X1 = x0 + (r - r*i)*x1 - i*x2 + (-r - r*i)*x3 - x4 + (-r + r*i)*x5 + i*x6
> + (r + r*i)*x7
>
> where r=sqrt(1/2)
>
> Is it actually possible? It seems like the phase of the coefficients in
> the Y's and Z's advance too quickly t
You can combine consecutive DFTs. Intuitively, the basis functions are
periodic on the transform length. But it won't be as efficient as having
done the big FFT (as you say, the decimation in time approach interleaves
the inputs, so you gotta pay the piper to unwind that). Note that this is
for nak
Well you definitely want a monotonic, equal-amplitude crossfade, and
probably also time symmetry. So I think raised sinc is right out.
In terms of finer design considerations it depends on the time scale. For
longer crossfades (>100ms), steady-state considerations apply, and you can
design for fre
You should have a search for papers by Jean Laroche and Mark Dolson, such
as "About This Phasiness Business" for some good information on phase
vocoder processing. They address time scale modification mostly in that
specific paper, but many of the insights apply in general, and you will
find refere
Alex, it sounds like you are confusing algorithmic latency with framing
latency. At each frame, you take in 10ms (or whatever) of input, and then
provide 10ms of output. This (plus processing time to generate the output) is
the IO latency of the process. But the algorithm itself can add addition
rbj wrote:
>i, personally, would rather see a consistent method used throughout the
MIDI keyboard range
If you squint at it hard enough, you can maybe convince yourself that the
naive sawtooth generator is just a memory optimization for low-frequency
wavetable entries. I mean, it does a perfect jo
>The simple question that forced itself on me often, as I"m sure some can
relate,
>after having been used to all those early signal sources including a host
of analog
>synthesizers I had in the past, and a lot of music in various analog forms
from standard
>pop to G. Duke and Rose Royce to mention
Hi ben
You don't need to evaluate the asin() - it's piecewise monotonic and
symmetrical, so you can get the same comparison directly in the signal
domain.
Specifically, notice that x(n) = sin(2*pi*(1/4)*n) = [...0,1,0,-1,...]. So
you get the same result just by checking ( abs( x[n] - x[n-1] ) ==
agination.com> wrote:
>
>
> Original Message
> Subject: Re: [music-dsp] Sampling theory "best" explanation
> From: "Ethan Duni"
> Date: Wed, September 6, 2017 4:49 pm
> To: "rober
te.
>
> Sorry you misinterpreted it.
>
> On Sep 7, 2017, at 5:34 AM, Ethan Duni wrote:
>
> 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 imp
s far as DAC not using
> impulses, it's only because the shortcut is trivial. Like I said, audio
> sample rates are slow, not that hard to do a good enough job for
> demonstration with "close enough" impulses.
>
> Don't anyone get mad at me, please. Just sitting on
ristow-johnson <
r...@audioimagination.com> wrote:
>
>
> Original Message
> Subject: Re: [music-dsp] Sampling theory "best" explanation
> From: "E
that it's that partitions the space of input shifts, where if
>>> you restrict yourself to shifts from a given partition you will see time
>>> invariance (in a certain sense).
>>
>>
>> So this to me is a good example of how thinking of discrete time signals
he
> definition of LTI they were taught.
>
> On Sep 1, 2017, at 3:46 PM, Ethan Duni wrote:
>
> 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 arbitrar
place in radio
>> applications.
>
>
> 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.
>
> -Ethan F
>
>
> On Fri, Sep 1, 2017 at 5:30
>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 su
These PicoScopes look pretty cool :]
As it happens I am just now trying to free up some garage space to get an
electronics bench together. But it's coming up on 20 years since I last
soldered and it's a whole different world with scopes now. So thanks for
this thread!
Also if anybody knows good r
> how do you quadrature modulate without Hilbert filters?
>
Perhaps I'm using the wrong term - the operation in question is just the
multiplication of a signal by e^jwn. Or, equivalently, multiplying the real
part by cos(wn) and the imaginary part by sin(wn) - a pair of "quadrature
oscillators."
On Tue, Feb 7, 2017 at 6:49 AM, Ethan Fenn wrote:
> So I guess the general idea with these frequency shifters is something
> like:
>
> pre-filter -> generate Hilbert pair -> multiply by e^iwt -> take the real
> part
>
> Am I getting that right?
>
Exactly, this is a single sideband modulation tec
Ha this article made me chuckle. All the considerations about odd 8 bit
audio formats!
This method has his desired property that if all but one input is silent,
you get the non-silent one at output without attenuation or other
degradation. But the inclusion of the cross term makes it quite non-lin
mpute the impulse response and
truncate/window it to the desired length.
FFT domain is generally not a good place to design filters - you're only
controlling what happens at the bin centers, and all kinds of wild things
can happen in between them. And it's difficult to account for the
ci
I'm not sure I quite follow what the goal is here? If you already have lp
and p, then there aren't any additional calculations needed to obtain ap -
it's an IIR filter with numerator coefficients given by lp, and denominator
coefficients given by p. The pulse response is obtained by running the
fil
Right aren't monotonic signals the worst case here? Or maybe not, since
they're worst for one wedge, but best for the other?
Ethan D
On Fri, Sep 2, 2016 at 10:12 AM, Evan Balster wrote:
> Just a few clarifications:
>
> - Local maxima and first difference don't really matter. The maximum
> wedg
So like a cascade of allpass filters then?
Ethan D
On Fri, Jul 29, 2016 at 11:10 AM, gm wrote:
>
> I think what I am looking for would be the perfect reverb.
>
> So that's the question reformulated: how could you construct a perfectly
> flat short reverb?
>
> It's the same problem.
>
>
>
> Am 2
>okay, this PDF was more useful than the other. once i got down to slide
#31,
> i could see the essential definition of what a "unum" is.
>big deeel.
>first of all, if the word size is fixed and known (and how would you know
how far
>to go to get to the extra meta-data: inexact bit, num expone
Any noise other than white noise is correlated, by definition. That's what
"white noise" means - uncorrelated. Correlation in the time domain is
equivalent to non-constant shape in the frequency domain.
Ethan
On Thu, Apr 14, 2016 at 12:24 PM, Seth Nickell wrote:
> Maybe stupid question: Is pink
Supposing this is some griefer it seems reasonable to ignore them - but is
there a possibility that this is a symptom of some kind of server attack or
attempt to profile/track list members?
I've never received any unsub notices myself but it is a little
disconcerting that somebody persists at doin
Yeah zeroing out the state is going to lead to a transient, since the
filter has to ring up.
If you want to go that route, one possibility is to use two filters in
parallel: one that keeps the old state/coeffs but gets zero input, and
another that has zero state and gets the new input/coeffs. You
Theo wrote:
>I get there are certain statistical ideas involved. I wonder
>however where those ideas in practice lead to, because
>of a number of assumptions, like the "statistical variance"
>of a signal. I get that a self correlation of a signal in some
>normal definition gives an idea of the powe
>Lastly, it's important to note that differentiation and
semi-differentiation
>filters are always approximate for sampled signals, and will tend to
>exhibit poor behavior for very high frequencies and (for
semi-differentiation)
>very low ones.
I'm not sure there's necessarily a problem at low freq
Not a purely time-domain approach, but you can consider comparing sparsity
in the time and Fourier domains. The idea is that periodic/tonal type
signals may be non-sparse in the time domain, but look sparse in the
frequency domain (because all of the energy is on/around harmonics).
Similarly, trans
7;d put
it out there...
E
On Thu, Feb 18, 2016 at 5:27 PM, robert bristow-johnson <
r...@audioimagination.com> wrote:
>
>
> From: "Ethan Duni"
> Date: Thu, February 18, 2016 4:48 pm
> -
eption that you know
> what you're doing. Because it will be a long time before the perceptual
> properties of any brightness metric can be clearly understood, I'll stick
> to formulas whose mathematical properties are transparent -- these lend
> themselves infinitely better t
ute
> higher moments with the differential brightness estimator.
>
> – Evan Balster
> creator of imitone <http://imitone.com>
>
> On Thu, Feb 18, 2016 at 1:00 AM, Ethan Duni wrote:
>
>> >normalized to fundamental frequency or not
>> >normalized (so th
ion.com> wrote:
>
>
> Original Message
> Subject: Re: [music-dsp] Cheap spectral centroid recipe
> From: "Ethan Duni"
> Date: Wed, February 17, 2016 11:21 pm
> To: "A discussion list fo
>It's essentially computing a frequency median,
>rather than a frequency mean as is the case
>with the derivative-power technique described
> in my original approach.
So I'm wondering, is there any consensus on what is the best measure of
central tendency for a music signal spectrum? There's the m
>given the same order N for the polynomials, whether your basis set are
> the Tchebyshevs, T_n(x), or the basis is just set of x^n, if you come up
>with a min/max optimal fit to your data, how can the two polynomials be
>different?
Right, if you do that you'll end up with equivalent answers (to wi
>> [..] the autocorrelation is
>>
>> = (1/3)*(1-P)^|k|
>>
>> (I checked that with a little MC code before posting.) So the power
>> spectrum is (1/3)/(1 + (1-P)z^-1)
The FT of (1/3)*(1-P)^|k| is (1/3)*(1-Q^2)/(1-2Qcos(w) + Q^2), where Q =
(1-P).
Looks like you were thinking of the expression for
- Original Message ----
> Subject: Re: [music-dsp] how to derive spectrum of random sample-and-hold
> noise?
> From: "Ethan Duni"
> Date: Wed, November 11, 2015 7:36 pm
> To: "robert bristow-johnson"
> "A discussion list for
-- Original Message
> Subject: Re: [music-dsp] how to derive spectrum of random sample-and-hold
> noise?
> From: "Ethan Duni"
> Date: Wed, November 11, 2015 5:57 pm
> To: "robert bristow-johnson"
> "A discussion list
mption come from?
E
On Tue, Nov 10, 2015 at 6:33 PM, robert bristow-johnson <
r...@audioimagination.com> wrote:
>
>
> Original Message
> Subject: Re: [music-dsp] how to derive spectrum of random sample-and-hold
> noise?
>(Semi-)stationarity, I'd say. Ergodicity is a weaker condition, true,
>but it doesn't then really capture how your usual L^2 correlative
>measures truly work.
I think we need both conditions, no?
>Something like that, yes, except that you have to factor in aliasing.
What aliasing? Isn't this pr
alking about power per linear or angular frequency. And
>>> there could be others I'm not thinking of maybe someone else can
>>> shed more light here.
>>>
>>
>> I multiplied the psd by 1/3 and as you can see from the graph it looks as
>> though the F
nd scaling, but
that's the basic idea.
https://en.wikipedia.org/wiki/Spectral_density_estimation
E
On Thu, Nov 5, 2015 at 2:00 AM, Ross Bencina
wrote:
> Thanks Ethan(s),
>
> I was able to follow your derivation. A few questions:
>
> On 4/11/2015 7:07 PM, Ethan Duni w
Yep that's the same approach I just posted :]
E
On Tue, Nov 3, 2015 at 11:48 PM, Ethan Fenn wrote:
> How about this:
>
> For a lag of t, the probability that no new samples have been accepted is
> (1-P)^|t|.
>
> So the autocorrelation should be:
>
> AF(t) = E[x(n)x(n+t)] = (1-P)^|t| * E[x(n)^2]
inite)
x[n] = (r[n]
wrote:
> On 4/11/2015 5:26 AM, Ethan Duni wrote:
>
>> Do you mean the literal Fourier spectrum of some realization of this
>> process, or the power spectral density? I don't think you're going to
>> get a closed-form expression for the for
Wait, just realized I wrote that last part backwards. It should be:
So in broad strokes, what you should see is a lowpass spectrum
parameterized by P - for P very small, you approach a DC spectrum, and for
P close to 1 you approach a spectrum that's flat.
On Tue, Nov 3, 2015 at 10:26 AM,
Do you mean the literal Fourier spectrum of some realization of this
process, or the power spectral density? I don't think you're going to get a
closed-form expression for the former (it has a random component). For the
latter what you need to do is work out an expression for the
autocorrelation fu
>the reason why it's merely convention is that if the minus sign was
swapped
>between the forward and inverse Fourier transform in all of the literature
and
>practice, all of the theorems would work the same as they do now.
Note that in some other areas they do actually use other conventions. It's
I don't have a dog in any JUCE fight, but excluding the sample rate from an
AudioSampleBuffer type object seems like good design to me. The reason is
that system parameters that depend on the sample rate tend to be things
like buffer sizes, and so changing them is typically not real-time thread
saf
ic on the lengths of
the filters as a function of oversampling ratio.
>i think we're on the same page. ain't we?
Yeah, I was unclear on which scenario(s) the aliasing analysis was supposed
to apply to.
E
On Wed, Aug 26, 2015 at 12:53 PM, robert bristow-johnson <
r...@audioimaginati
response. All I would add is that the general
rate-change case has to contend with both aliasing suppression and
imperfect fractional delay response, so I would expect a
fractional-delay-only system to have looser requirements since the signal
aliasing issue has been removed.
E
On Mon, Aug 24, 2015
Sounds good Douglass, I'm glad to see you taking the initiative on this
matter. The list has generally been an oasis of pleasant, respectful
behavior and informative discussions, and it's tragic that it has become so
toxic lately.
Thanks
E
On Sat, Aug 22, 2015 at 8:21 AM, Douglas Repetto wrote:
ne big FFT of
the whole thing, that won't ever get rid of the noisiness no matter how
much data you throw at it).
E
On Fri, Aug 21, 2015 at 5:47 PM, Peter S
wrote:
> On 22/08/2015, Ethan Duni wrote:
> >
> > We've been over this repeatedly, including in the very post yo
>1) Olli Niemiatalo's graph *is* equivalent of the spectrum of
>upsampled white noise.
We've been over this repeatedly, including in the very post you are
responding to. The fact that there are many ways to produce a graph of the
interpolation spectrum is not in dispute, nor is it germaine to my p
t of time creating various
>demonstrations and FFT graphs showing my point.
Your time would be better spent figuring out a point that is relevant to
what I'm saying in the first place. It is indeed a waste of your time to
invent equivalent ways to generate graphs, since that is not the point
The details of how the graphs were generated don't really matter. The point
is that the only effect shown is the spectrum of the continuous-time
polynomial interpolator. The additional spectral effects of delaying and
resampling that continuous-time signal (to get fractional delay, for
example) are
just
highlights your insecurity.
E
On Fri, Aug 21, 2015 at 1:24 PM, Peter S
wrote:
> On 21/08/2015, Ethan Duni wrote:
> >>It shows *exactly* the aliasing
> >
> > It shows the aliasing left by linear interpolation into the continuous
> time
> > domain. It do
trum of the continuous time signal.
E
On Fri, Aug 21, 2015 at 10:51 AM, Peter S
wrote:
> On 21/08/2015, Ethan Duni wrote:
> >>Creating a 22000 Hz signal from a 250 Hz signal by interpolation, is
> >>*exactly* upsampling
> >
> > That is not what is shown in that gra
me signal, not a
discrete time signal of whatever sampling rate.
E
On Fri, Aug 21, 2015 at 2:09 AM, Peter S
wrote:
> On 21/08/2015, Ethan Duni wrote:
> >>In this graph, the signal frequency seems to be 250 Hz, so this graph
> >>shows the equivalent of about 22000/250 = 88x
>In this graph, the signal frequency seems to be 250 Hz, so this graph
>shows the equivalent of about 22000/250 = 88x oversampling.
That graph just shows the frequency responses of various interpolation
polynomials. It's not related to oversampling.
E
On Thu, Aug 20, 2015 at 5:40 PM, Peter S
wr
>If all you're trying to do is mitigate the rolloff of linear interp
That's one concern, and by itself it implies that you need to oversample by
at least some margin to avoid having a zero at the top of your audio band
(along with a transition band below that).
But the larger concern is the overa
s the tightest use of resources (for whatever constraints).
Typically those are the arcane ones that take a ton of debugging and
optimization :P
E
On Wed, Aug 19, 2015 at 1:00 PM, robert bristow-johnson <
r...@audioimagination.com> wrote:
> On 8/19/15 1:43 PM, Peter S wrote:
>
>>
Ugh, I suppose this is what I get for attempting to engage with Peter S
again. Not sure what I was thinking...
E
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targets. Memory tends to be at a
premium on those platforms.
E
On Wed, Aug 19, 2015 at 3:55 PM, Peter S
wrote:
> On 20/08/2015, Ethan Duni wrote:
> >
> > I don't dispute that linear fractional interpolation is the right choice
> if
> > you're going to over
t should also be noted that the linear interpolation can be used for
>the upsampling itself as well, reducing the cost of your oversampling,
Again, that would add up to a very low quality upsampler.
E
On Wed, Aug 19, 2015 at 2:06 PM, Peter S
wrote:
> On 19/08/2015, Ethan Duni wrote:
>
ples needed to drive the final fractional interpolator is
well-taken, but I think I need to see a more detailed accounting of that to
be convinced.
E
On Wed, Aug 19, 2015 at 1:00 PM, robert bristow-johnson <
r...@audioimagination.com> wrote:
> On 8/19/15 1:43 PM, Peter S wrote:
>
>
constraint forcing you to use a first-order interpolator.
>quite familiar with it.
Yeah that was more for the list in general, to keep this discussion
(semi-)grounded.
E
On Wed, Aug 19, 2015 at 9:15 AM, robert bristow-johnson <
r...@audioimagination.com> wrote:
> On 8/18/15 11:46 P
> for linear interpolation, if you are a delayed by 3.5 samples and you
keep that delay constant, the transfer function is
>
> H(z) = (1/2)*(1 + z^-1)*z^-3
>
>that filter goes to -inf dB as omega gets closer to pi.
Note that this holds for symmetric fractional delay filter of any odd order
(i.
frequency sinusoids has no bearing on the frequency
response of fractional interpolators. I'd suggest dropping this whole
derail, if you are no longer hung up on this point.
E
On Tue, Aug 18, 2015 at 2:08 PM, Peter S
wrote:
> On 18/08/2015, Ethan Duni wrote:
> >
> > That c
f simple arithmetic, the aliasing issue
works like this: I add two numbers together, and find that the answer is X.
I tell you X, and then ask you to determine what the two numbers were. Can
you do it?
E
On Tue, Aug 18, 2015 at 2:13 PM, Peter S
wrote:
> On 18/08/2015, Ethan Duni wrote:
>
>In order to reconstruct that sinusoid, you'll need a filter with
>an infinitely steep transition band.
No, even an ideal reconstruction filter won't do it. You've got your
+Nyquist component sitting right on top of your -Nyquist component. Hence
the aliasing. The information has been lost in the
>> well Peter, here again is where you overreach. assuming, without loss
>> of generality that the sampling period is 1, the continuous-time signals
>>
>> x(t) = 1/cos(theta) * cos(pi*t + theta)
>>
>> are all aliases for the signal described above (and incorrectly as
>> "contain[ing] no alia
eproduce a nyquist frequency
sinusoid when you run it through a DAC.
E
On Tue, Aug 18, 2015 at 1:28 PM, Peter S
wrote:
> On 18/08/2015, Ethan Duni wrote:
> >>Assume you have a Nyquist frequency square wave: 1, -1, 1, -1, 1, -1, 1,
> > -1...
> >
> > The sampling th
; wrote:
> On 8/18/15 3:44 PM, Ethan Duni wrote:
>
>> >Assume you have a Nyquist frequency square wave: 1, -1, 1, -1, 1, -1, 1,
>> -1...
>>
>> The sampling theorem requires that all frequencies be *below* the Nyquist
>> frequency. Sampling signals at exactl
>Assume you have a Nyquist frequency square wave: 1, -1, 1, -1, 1, -1, 1,
-1...
The sampling theorem requires that all frequencies be *below* the Nyquist
frequency. Sampling signals at exactly the Nyquist frequency is an edge
case that sort-of works in some limited special cases, but there is no
e
Yeah I am also curious. It's not obvious to me where it would make sense to
spend resources compensating for interpolation rather than just juicing up
the interpolation scheme in the first place.
E
On Mon, Aug 17, 2015 at 11:39 AM, Nigel Redmon
wrote:
> Since compensation filtering has been men
https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect
E
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address the source of your hostility, and also that you gain more insight
into Information Theory.
My apologies to the list for encouraging this unfortunate tangent.
E
On Thu, Jul 16, 2015 at 8:38 PM, Peter S
wrote:
> On 17/07/2015, Ethan Duni wrote:
> > What are these better estim
ropy of the residual. The average rate produced by some actual coding
system is an *upper bound* on the entropy rate of the random process in
question.
Again, I encourage you to slow the pace of your replies and instead try to
write fewer, more concise posts with greater emphasis on clarity and
prec
imation approach, not in the numerical
implementation thereof.
E
On Thu, Jul 16, 2015 at 7:07 AM, Peter S
wrote:
> On 15/07/2015, Ethan Duni wrote:
> > Right, this is an artifact of the approximation you're doing. The model
> > doesn't explicitly understand periodicity
>This algorithm gives an entropy rate estimate approaching zero for any
>periodic waveform, irregardless of the shape (assuming the analysis
>window is large enough).
But, it seems that it does *not* approach zero. If you fed an arbitrarily
long periodic waveform into this estimator, you won't see
>I wondered a few times what a higher "entropy" estimate for a higher
>frequency would mean according to this - I think it means that a
>higher frequency signal needs a higher bandwidth channel to transmit,
>as you need a transmission rate of 2*F to transmit a periodic square
>wave of frequency F.
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