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Envelope Time Curve - ETC - Impulse Dynamics Plugins
Old 30th December 2010
  #31
Gear Guru
One Speaker

One speaker certainly for this work, can't be said often enough it appears.
Time measurements will make a lot more sense and you may eliminate some variables (USB) by using the Loop Back Correction. You shouldn't need to mess with the sliders if you use that.
When you think you have a significant reflection, i.e. louder than 15-20dB below the direct within 20mS or so, prove it. Block the path of the suspect, if the spike goes you were right. I use a fabric wrapped sheet of FRK 703 fabric wrapped for this. Light and handy. Crude but sure.
Frequencies may be interesting, here's a calculator http://www.jhbrandt.net/pubs.html, but will they make any difference to what you actually do about it? 10cm panels with a 10cm airgap are a good shot. Try an angle to get the reflection down farthest. Remember there are width modes and maybe even SBIR also, so thick side designs a la johnlsayers.com are worth considering.

The desk or work surface can be used to block the floor reflection, by careful positioning and size. Maybe even some absorption underneath to prevent any extra bouncing around down there.
The reflection from the top surface can be redirected away from the ear/mic by angling it down a little towards you. More comfortable too.


DD

Last edited by DanDan; 30th December 2010 at 04:22 AM.. Reason: Desk Extra
Old 30th December 2010
  #32
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Quote:
Originally Posted by DanDan View Post
One speaker certainly for this work, can't be said often enough it appears.

DD
I think I forgot to mention, but, both of the graphs are from my Left Speaker.
I will try a few more things tomorrow then.

Thanks
Old 30th December 2010
  #33
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Quote:
Originally Posted by DanDan View Post
One speaker certainly for this work, can't be said often enough it appears.
Time measurements will make a lot more sense and you may eliminate some variables (USB) by using the Loop Back Correction. You shouldn't need to mess with the sliders if you use that.


DD
Yes, you are right, I use the FM Loop Back Correction feature.

I use the sliders to get the frequency of the peak (it shows the time on the right)
Yet I cant seem to understand the changes on the graphs by moving the slider, I mean, its like for every position on the ETC graph a new TFR graph appears, is that intentional? what does it mean if so? I read the manual of FM and i couldnt find any explanation.

Thanks
Old 30th December 2010
  #34
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Sixfeet: there is no such thing as "instantaneous frequency". You can not check the frequency response at specific points in time, you have to look at an area in time. The more area in time, the better the resolution in frequency, and vice versa. If you try to look at a very short period of time, you'll have very low frequency resolution. It's known as Heisenberg uncertainty principle in English, although the German original is "unsharpening principle" which is a bit more explanatory. For such small time periods as milliseconds, frequency resolution is very very low.

The window times set the start/stop points for the frequency response graph. At 2ms, it's starting ahead of the first impulse, so you see the frequency response as it's seen from 2 to 377 milliseconds. When it starts at 4.77, you see the response from there to 377ms. In this case, excluding the direct sound. The important thing to notice is the end point at 377ms. You're observing a rather long range, most of which have nothing to do with the early reflections.

The start/stop times set the bounds of the observation window. The window shape is also important. In the graph you posted, it's set to rectangular. This means you are doing an infinitely fast unmute/mute edit at the start/stop points. The effect is the same as a bad edit in a wave editor. It gives a plopping explosion of extraneous energy. This energy does not exist as such, it's only seen in the frequency response graph. It's the result of manipulating the data through the use of a specific observation window. Using a softer window shape will avoid the problems of too sharp edits, at the expense of introducing modulation effects from the window shape itself.

All in all: it's probably not worth bothering trying to read "instantaneous frequency response". You can get some good ideas that way, or you can easily get many bad ideas. Depending on your proficiency at discriminating real data from the impulse response and the bogus data generated by the observation technique itself.
Old 30th December 2010
  #35
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Quote:
Originally Posted by Lupo View Post
there is no such thing as "instantaneous frequency". You can not check the frequency response at specific points in time, you have to look at an area in time. The more area in time, the better the resolution in frequency, and vice versa. If you try to look at a very short period of time, you'll have very low frequency resolution. It's known as Heisenberg uncertainty principle in English, although the German original is "unsharpening principle" which is a bit more explanatory. For such small time periods as milliseconds, frequency resolution is very very low.
Well on a technical point, there is indeed such a thing as instantaneous frequency, it is the derivative of instantaneous phase, which is in turn the arg of the imag and real components of the signal. In the context of an ETC the original impulse response provides the real component and the Hilbert transform of the impulse response provides the imaginary component.

On another technical point () the time-frequency uncertainty in Fourier analysis is a limitation of the analysis method and not an expression of any fundamental limitation in signal analysis. The difference between this and the situation described by Heisenberg is that Heisenberg's uncertainty principle applies to the simultaneous independent measurement of a pair of properties, typically position and velocity. In Fourier analysis there are no independent measurements, just an analysis of the results of a single measurement. If the signal being measured was a sine wave, for example, then just two points would be sufficient to use a parametric analysis to establish its frequency to an accuracy limited only by measurement noise. The basic limitation is the signal's information content, if a signal consists of K frequency components then, in the absence of noise, 2K measurement points are the minimum required to determine their frequencies, amplitudes and phases precisely.
Old 30th December 2010
  #36
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While intuitively it doesn't make sense that sine sweeps can be used to identify impulse data, it does make mathematical sense.

For a linear system (and we have to assume for now that sound pressure level in a room is linear), the frequency response and impulse response have a unique mapping, and given one you can calculate the other.

The swept response model can give you better S/N than the impulse response model....but it takes longer to get the data. With a sweep, you can tailor the sweep rate to dwell on areas where you need more data, whereas you don't have much choice when it comes to generating impulses acoustically.

Cheers

Kris

PS: Regarding Fourier analysis, I often wonder why acoustic analysis software doesn't use the Chirp-Z transform instead of the FFT. It takes a little more calculation time, but you can get better low frequency resolution and end up with fewer points spread across the high frequency range. Also, composite windowing (building a curve from different weighted window sizes) and coherence (a measure of input to output sweep quality) would be useful features in a room analysis software package IMO.
Old 30th December 2010
  #37
Gear Guru
Deep

Very deep. Plus I see that little flash of genious which puts the deep into the hands of all of us. Bravo again Andreas. That ETC trick and now this very illuminating statement.
Quote:
The window times set the start/stop points for the frequency response graph. At 2ms, it's starting ahead of the first impulse, so you see the frequency response as it's seen from 2 to 377 milliseconds. When it starts at 4.77, you see the response from there to 377ms. In this case, excluding the direct sound. The important thing to notice is the end point at 377ms. You're observing a rather long range, most of which have nothing to do with the early reflections.
DD
Old 30th December 2010
  #38
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Quote:
Originally Posted by DrFrankencopter View Post
PS: Regarding Fourier analysis, I often wonder why acoustic analysis software doesn't use the Chirp-Z transform instead of the FFT. It takes a little more calculation time, but you can get better low frequency resolution and end up with fewer points spread across the high frequency range. Also, composite windowing (building a curve from different weighted window sizes) and coherence (a measure of input to output sweep quality) would be useful features in a room analysis software package IMO.
There's not a lot of point to using CZT compared to just using a longer FFT, whilst you can cache the CZT arc coefficients you still end up doing an FFT and an invFFT to generate the results so all you have (potentially, depending on window length) saved is some memory use. Coherence would only be valid for multiple sweeps, it tends to be better to use one long sweep than multiple shorter sweeps as the longer sweep is less sensitive to any underlying time variance.
Old 30th December 2010
  #39
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Thanks for the kind words, Dan! I think these issues are essential for understanding the results as seen in frequency response graphs.

Have to point out that the millisecond figures are based on the particular measurement posted. The initial sound seems to be around 3.7 milliseconds. For a graph where the starting impulse is normalized to 0 millisec, things will be different.


Quote:
Originally Posted by JohnPM View Post
Well on a technical point, there is indeed such a thing as instantaneous frequency, it is the derivative of instantaneous phase, which is in turn the arg of the imag and real components of the signal. In the context of an ETC the original impulse response provides the real component and the Hilbert transform of the impulse response provides the imaginary component.
Which is all good for a sine. What about spectras?

Quote:
Originally Posted by JohnPM View Post
On another technical point () the time-frequency uncertainty in Fourier analysis is a limitation of the analysis method and not an expression of any fundamental limitation in signal analysis.
The problem is that one is trying to display a graph with X on one axis and the proportionally inverted X on the other axis. No matter what unit one choose for X, the sum of the information can never exceed 1.

Quote:
Originally Posted by JohnPM View Post
The difference between this and the situation described by Heisenberg is that Heisenberg's uncertainty principle applies to the simultaneous independent measurement of a pair of properties, typically position and velocity.
Heisenbergs unsharpening principle is based directly on Fouriers ideas.
It does not mean that there is a fundamental limit to measurements of two different units. It applies when trying to describe two viewpoints which are both based on the same physical reality. Velocity (and with mass, momentum) does not exist as such. It's a Newtonian idea that makes those calculations highly useful. There is no physical correspondence to those ideas. Hence the search for the grand new theory in physics, that will eventually replace the by now way too old Newtonian view of the world.


Quote:
Originally Posted by JohnPM View Post
In Fourier analysis there are no independent measurements, just an analysis of the results of a single measurement. If the signal being measured was a sine wave, for example, then just two points would be sufficient to use a parametric analysis to establish its frequency to an accuracy limited only by measurement noise. The basic limitation is the signal's information content, if a signal consists of K frequency components then, in the absence of noise, 2K measurement points are the minimum required to determine their frequencies, amplitudes and phases precisely.
For sine waves. Describing a continuous spectra requires infinite time in the observation window.
Old 30th December 2010
  #40
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Quote:
Originally Posted by SAC View Post
You have plenty of destructive reflections(at least ~5-7 discreet reflections) between 3.7ms and 4.2ms that must be addressed.
Also, please make two ETC measurements with one speaker (L/R) driven at a time...
Hey SAC.
There is a document on the FM help file:

Measuring and Treating a Home Studio Using FuzzMeasure Pro: Part 1

(the ETC part).

You can see how they identify the first reflection (0.69 ms). I identified my first reflection point in the same way (as you can see there are all sorts of peaks too, but they only considered the highest one at 0.69), thats how i came out with the original values.
The fact that you mention the 7 discreet reflections confuses me, but probably i am missing something, is it because the fall above the -20 "headroom" threshold?

Thanks a lot.
Old 30th December 2010
  #41
Gear Maniac
 

Quote:
Originally Posted by Lupo View Post
Which is all good for a sine. What about spectras?
Instantaneous frequency and phase are valid for all kinds of signals, they are widely used in the analysis of seismic data, for example.

Quote:
The problem is that one is trying to display a graph with X on one axis and the proportionally inverted X on the other axis. No matter what unit one choose for X, the sum of the information can never exceed 1.
That is not correct, as I tried to explain. The limitations of Fourier analysis apply only to Fourier analysis, not to other methods of analysing a time signal.

Quote:
Heisenbergs unsharpening principle is based directly on Fouriers ideas.
It does not mean that there is a fundamental limit to measurements of two different units. It applies when trying to describe two viewpoints which are both based on the same physical reality. Velocity (and with mass, momentum) does not exist as such. It's a Newtonian idea that makes those calculations highly useful. There is no physical correspondence to those ideas. Hence the search for the grand new theory in physics, that will eventually replace the by now way too old Newtonian view of the world.
Without wishing to be overly provocative, philosophical musings on the nature of reality are irrelevant to the point. Heisenberg's uncertainty principle applies to pairs of variables that are not commutative. In time signal analysis we do not have a pair of variables, we have a single time record. Parametric analysis of signals composed of finite numbers of components (which is the norm rather than the exception) can resolve them to far greater resolution that a Fourier analysis would allow.

Quote:
Describing a continuous spectra requires infinite time in the observation window.
That would only be the case if the signal being measured was composed of an infinite number of components. That does not apply to acoustic impulse responses (or most other signals). The acoustic IR consists of a number of discrete decaying complex exponentials whose frequencies are determined by the physical properties of the space. Parametric analysis can identify those components to accuracies limited by the signal's information content, not its duration. There are more ways than Fourier to skin this cat. heh
Old 30th December 2010
  #42
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yikes

my ceilings must be higher than I had previously thought, as there is a lot of things flying around above my head right now.
Old 31st December 2010
  #43
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gullfo's Avatar
 

JohnPM is cruelly using word-math problem statements to simplify for the masses

heh
Old 31st December 2010
  #44
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DrFrankencopter's Avatar
Quote:
Originally Posted by JohnPM View Post
There's not a lot of point to using CZT compared to just using a longer FFT, whilst you can cache the CZT arc coefficients you still end up doing an FFT and an invFFT to generate the results so all you have (potentially, depending on window length) saved is some memory use. Coherence would only be valid for multiple sweeps, it tends to be better to use one long sweep than multiple shorter sweeps as the longer sweep is less sensitive to any underlying time variance.
CZT lets you place more resolution in the low frequency range and frees us up from the requirement for power of 2 window sizes. It seemed to me that for looking at low frequency modes it might make sense. Maybe it doesn't make too much sense for analysis of rooms. I use it in analysis of helicopter dynamic response, where the modes are well below 1 Hz, and ability to generate the data (via flight test) is limited (i.e. can't dwell too long during sweeps).

As far as coherence is concerned, I was thinking that it could be used to let the user see the effects of their choices in window parameters, as opposed to correlating different sweeps.

Cheers

Kris
Old 4th January 2011
  #45
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wow it's great to see that if I disappear I got a lot of interesting reply.. I'm wondering what's wrong in my posts....
Old 7th January 2011
  #46
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Quote:
Originally Posted by JohnPM View Post
Instantaneous frequency and phase are valid for all kinds of signals, they are widely used in the analysis of seismic data, for example.
Got any references on that? It's not my field, but as far as I know, there is no analysis capable of coping with any and all signals being represented as Intanstaneous Frequency (IF). Seem some approaches works for single tones, some works somewhat for spectra, none seem to work for all. Please update me if I'm missing out on something!


Quote:
Originally Posted by JohnPM View Post
That is not correct, as I tried to explain. The limitations of Fourier analysis apply only to Fourier analysis, not to other methods of analysing a time signal.

Without wishing to be overly provocative, philosophical musings on the nature of reality are irrelevant to the point. Heisenberg's uncertainty principle applies to pairs of variables that are not commutative. In time signal analysis we do not have a pair of variables, we have a single time record.
Nearly, but not quite. I'll stick with the philosophical layer as that's where the real fun is at.

The problem isn't Fourier as such, the same information barrier applies to all attempts at analysing the world on a similar basis. In physics, the problem is that what we think of as separate entities of position and momentum are based on the same underlying unit. In music, the problem is with the concept of frequency. Frequency is not a parameter existing separately from time. Frequency is the reciprocal of time; 1/time.

The reciprocal is not an amplitude inversion. It's a proportional inversion. What was long in one view becomes short in the other view, and vice versa. It works very well for picking up on repetetive patterns. That's when the inversion excells. What used to be a very long and hard to describe phenomena, a repetetive list of looping events, is described in a maximally compact fashion using the concept of frequency. Conversely, impulsive events are compact to describe in normal time and takes more effort to describe in inverse time.

If we want to make a graph with practically endless precision along both X and Y axes at once, we need two different/distinct parameters so that it actually is an X and Y graph. A time/frequency graph is an X and 1/X graph.

What most people expect and want from a time/frequency or position/momentum graph is a X and Y graph. The big problem is that we do not have the Y in our scientific toolset. The current state of the science based on the Newtonian world view does not provide the Y. It leaves an immensely huge hole in the understanding of the world as we know it!

All the while, people keep using "frequency" when they really mean "spectra". It works fine for everyday language, the problem is when it gets technical. "Instantaneous frequency" as a term can not hold true for any and all signals. It have to assume that it actually is a frequency; a something with a repetetive/oscillating behaviour. Most events do not repeat for what can be assumed to be infinity. "Instantaneous spectra" would be a much more useful figure to operate with. Yet I do have doubts as to how that should work out as time approaches infinitely small. It would be the equivalent of analyzing a single sample point.


This is of course all open for objections and debate. Roll it on!


Best regards,

Andreas Nordenstam
Old 7th January 2011
  #47
Gear Maniac
 

Did you try and search at all, Andreas? Here is the number 1 of 200,000 hits on Google for "instantaneous frequency": Instantaneous phase - Wikipedia, the free encyclopedia, there are further references at the end of the article.
Old 7th January 2011
  #48
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Have been googling for a while. That's why the reply was late! The wikipedia hit gives a procedure for sinusoids. If I'm not mistaken, it doesn't even work for two sines - it have to be a single sine. Then there are other procedures for spectras which give some clues for noise like signals but doesn't work for sinusoids. Have not seen any hint of a general procedure for analyzing signals for instantaneous frequency without a priori knowledge of the signals nature.
Old 7th January 2011
  #49
Gear Maniac
 

You are mis-reading the article, it gives an example of a sinusoid as it is a trivial case. The instananeous frequency is the rate of change of the instantaneous phase. The instantaneous phase is the arg of the analytic function. We can form an analytic function from any time signal by generating an imaginary component which is the Hilbert transform of the original signal. The most common use of this in acoustics is the ETC or envelope, which is a plot of the magnitude of that analytic signal, but it is much more widely used in many other fields of signal analysis, form communications to geology and seismology. Here is a link to a more wordy version of that: http://www.searchanddiscovery.com/documents/2010/40563hardage/
Old 7th January 2011
  #50
SAC
Registered User
 

Here you go Andreas...
And you might find this interesting:
Fourier Transforms and Uncertainty Relations

As far as http://www.searchanddiscovery.com/do.../40563hardage/, Heyser had already long been doing that with sonar and had applied that to acoustics more than 10 years prior based upon Dennis Gabor's Analytic.
Attached Files
File Type: pdf Fourier & Heisenberg.pdf (62.8 KB, 207 views)
Old 10th January 2011
  #51
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Quote:
Originally Posted by JohnPM View Post
You are mis-reading the article, it gives an example of a sinusoid as it is a trivial case.
If I'm not mistaken, the simple approach you suggest gives the correct frequency for a single sinewave. For two sine waves, the result will be the average frequency. This average depends on the amplitude of the signals being equal. Please correct me if I'm wrong.

There are more elaborate methods to achieve instantaneous frequency readings, primarily using pre-filtering techniques. They all presume a priori knowledge of the signal to be analyzed.

Have googled quite a bit but never found any mention of instantaneous frequency being valid for analysis of arbitrary signals. Though I may be looking in the wrong places.

How would you describe white noise using instantaneous frequency? How would you describe an impulse?
Old 10th January 2011
  #52
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Quote:
Originally Posted by SAC View Post
Here you go Andreas...
And you might find this interesting:
Fourier Transforms and Uncertainty Relations

As far as Instantaneous Seismic Attributes Calculated by the Hilbert Transform, Bob Hardage, #40563 (2010), Heyser had already long been doing that with sonar and had applied that to acoustics more than 10 years prior based upon Dennis Gabor's Analytic.
Thanks, SAC!

It's also worth mentioning Heyser excellent Time Domain Spectrometry anthology from AES: AES Anthologies and Monographs
It's not only about TDS, it also have some extremely interesting philosophical ideas about the nature of measurements as we use them.
Old 10th January 2011
  #53
Gear Maniac
 

Andreas, the main issue would seem to be an assumption on your part that if you haven't heard of something it is either not useful or not relevant. "There are more things in heaven and earth than are dreamt of in your philosophy". I don't feel any particular need to educate you on every aspect of signal analysis, if you want to learn something, make the effort to educate yourself. It is foolish to use ignorance as a basis for dismissing the utility of an analysis method.
Old 10th January 2011
  #54
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You're too kind.

The more I read about the subject, the more reason I see that there is no measurement program available with practically near arbitrary precision in the time/frequency representation. If it's as simple as using the wiki equations, why don't you implement it in REW? It shouldn't take much time, given that you have all the framework done already.

Then try analysing two tones and see what happens!

This is about the general complex phase derative approach:
"For a sinusoidal wave, this definition coincides with the usual frequency. Unfortunately, the instantaneous frequency of the sum of two ordinary sinusoidal waves is the average of their frequencies, which does not coincide with the result of a Fourier analysis.

Hence the caracterization of the instaneous frequency of a signal in a sense that is consistent with the Fourier analysis in simple cases requires other mathematical tools."
Instantanous Frequency of an Analytic Signal


"For a signal that is a pure sinusoid, such as ,equation (13) clearly gives the right answer. When various frequencies are simultaneously present, we can hope that (13) gives a sensible average."
Instantaneous frequency

Again - average.


"Time-varying frequency is a natural occurrence, the mathematical and physical description of which has been evolving for many decades. One description of time-varying frequency is the instantaneous frequency proposed by Gabor, defined as the derivative of the phase of the (analytic) signal. The interpretation of this quantity has been a subject of much investigation. One interpretation arising from time-frequency distribution theory is that instantaneous frequency is the average frequency at each time in the signal. We explore this interpretation in detail, and derive conditions on an arbitrary two-component AM-FM complex signal for which this interpretation is plausible. The situations for which these conditions are met are limited. "
Instantaneous frequency and the conditional mean frequency of a signal

Again - average.



The general approach to solve the problem of being served a single average frequency as the answer, seems to be to filter the input signal. Thereby trying to isolate each of the sinusoids in a complex signal, giving an unique answer for each of them. The filtering can be adaptive and automatic, but it still places restrictions on the input signal that can be analyzed.


"This example illustrates that even for a simple signal, a meaningfull
instantaneous frequency can be obtained only if some restrictive conditions are imposed on the data. "
The Handbook of Data Mining - Google Bøker

More: http://musicweb.ucsd.edu/~sdubnov/Mu...ClassTalk2.pdf



Here's another one, for sparse sounds:
"Classical time–frequency analysis is based on the amplitude responses of bandpass filters, discarding phase information. Instantaneous frequency analysis, in contrast, is based on the derivatives of these phases. This method of frequency calculation is of interest for its high precision and for reasons of similarity to cochlear encoding of sound. This article describes a methodology for high resolution analysis of sparse sounds, based on instantaneous frequencies. In this method, a comparison between tonotopic and instantaneous frequency information is introduced to select filter positions that are well matched to the signal. Second, a cross-check that compares frequency estimates from neighboring channels is used to optimize filter bandwidth, and to signal the quality of the analysis. These cross-checks lead to an optimal time–frequency representation without requiring any prior information about the signal. When applied to a signal that is sufficiently sparse, the method decomposes the signal into separate time–frequency contours that are tracked with high precision. Alternatively, if the signal is spectrally too dense, neighboring channels generate inconsistent estimates—a feature that allows the method to assess its own validity in particular contexts. Similar optimization principles may be present in cochlear encoding"
Instantaneous frequency decomposition: an applicat... [J Acoust Soc Am. 2005] - PubMed result

And so forth. I find no mention anywhere that the concept of instantaneous frequency is able to describe arbitrary signals. Please provide a link to some reference if you believe this is not the case.

Edit: these are not the only texts I've referenced, just to make that clear. They exemplify the general trend I've seen across many sources.
Old 10th January 2011
  #55
Gear Maniac
 

Andreas, adequate links to resources describing the uses to which instantaneous phase and frequency can be put have already been served up to you on a plate in this thread. I am not about to spend time spoon-feeding you just because you don't feel inclined to pick up your knife and fork, or have already decided you won't like the taste of this new food so you will not try it.
Old 10th January 2011
  #56
Gear Guru
Topic

The OP elan started this with
Quote:
I started this thread to have more information about how to doing this measurement and how to interpreter the graph.
There was a Topic here and some very useful contributions.

What is going on now, and why?

DD
Old 10th January 2011
  #57
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Quote:
Originally Posted by johndykstra View Post
seems hard to believe a sine sweep would be useful for a time based measurement.
I feel your pain.

In order to make things as easy as possible: A sine sweep is sort of the exact opposite of an impulse burst. While the sweep is loooong (the longer the better) the burst is short (the shorter the better). While the sweep has only one frequency at a time the impulse burst has everything at the same time.

Sounds familiar? Here is a mathematical pair of such opposites:

X and 1/X

The bigger the one, the smaller the other. You get the picture.

Exact opposites are good for mathematics because then people tend to find a method to calculate the one from the other. And vice versa. Same happens with sweeps and bursts.
Old 10th January 2011
  #58
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Dan: the original poster wanted to analyse both in time and frequency at once. Hence the digression.

Quote:
=JohnPM]I am not about to spend time spoon-feeding you just because you don't feel inclined to pick up your knife and fork, or have already decided you won't like the taste of this new food so you will not try it.
You misunderstand. Having simultaneous access to time and frequency at once would be amazingly cool!

You claim the instantaneous frequency can be used for any and all signals.

These links have been provided:
Instantaneous phase - Wikipedia, the free encyclopedia
Instantaneous Seismic Attributes Calculated by the Hilbert Transform, Bob Hardage, #40563 (2010)

They both show the procedure of taking the derative of the complex phase. This gives the correct answer if there is a single frequency sine present. If there are two frequencies at the same amplitude, the result is the average frequency - not two frequencies.

(another reference to that: http://rcada.ncu.edu.tw/2010%20Vol.2...0FREQUENCY.pdf)

Have seen plenty of schemes for breaking up more complex signals into distinct components. They are all subject to many limitations. None seem to provide the elusive arbitrary precision both in time and frequency at once.

I'd love to see some links to literature about instantaneous frequency being valid for any and all signals.
Old 10th January 2011
  #59
Gear Guru
OP and TOPIC

Quote:
So, I'd like to know if there are more correct way to do an ETC or if that way is reliable

Second question is: how to interpreter the ETC graph? What should I see?
Sorry Andreas, but that looks like a very simple practical question to me.
I see no request to unravel space and time continuum here.
The early replies IMHO answered the questions very well and are very welcome.

I do concur that the current carry on is a digression. May I suggest that it would be better done in PM?
It seems a waste to see the REW author, who could provide great insight into the practical use of his creation, as requested by the OP, instead being challenged on matters of 'academic' 'fact', when clearly there is no such thing as a 'fact' in that realm, as evidenced by the debate.

DD
Old 10th January 2011
  #60
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If it weren't for digressions we wouldn't learn anything around here...

I've been following this thread with great interest and have been looking forward to seeing where it ends up. I can't contribute to the content of this latest debate but I can just barely follow along on the general concepts. And my folder of papers-to-read has been growing rapidly.

I found johndykstra's comment pretty funny
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7
jlsgear / Music Computers
5

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