Michael,
The problem here is that you keep looking at the time domain and divining the frequency response form what you see. That is incorrect. Take your example and make the sine wave burst infinitely long. What will you see? A turn on follow by the rise to the steady state response. It makes no difference if that turn on is continuous or discontinuous (an abrupt change in amplitude vs time). As I said, FR is a steady state property of a system.
There are two ways to look at your system. First, you can consider it as two systems, one with impulse delayed a short time after the other. In that case each system has a FR defined by the FFt of its impulse which will be independent of time. Or you can look at it as a single system with double impulse. In which case the FR is the FFT of the double impulse. There is no question about how to define frequency response. It is the FFT of the impulse. So you either have two separate systems with impulses,
h1(1) and h2(t)= h1(t-td)
which have individual frequency responses, FR1 = FFt(h1(t)) and FR2 = FFt(h2(t)), both independent of time, or you have a single system with impulse
h(t) = h1(t) + h1(t-td)
with FR = FFT(h(t).
if h1(t) = u(t), a perfect impulse, then each of system 1 and 2 have perfect transient response and flat frequency response which is not a function of time. But the system with impulse h(t) = h1(t) + h1(t-td), has a turn on and turn off transient of length td and the FR is not flat except at low frequency where 1/f is much greater than td. At higher frequency it will exhibit comb filtering.
The problem here is that you keep looking at the time domain and divining the frequency response form what you see. That is incorrect. Take your example and make the sine wave burst infinitely long. What will you see? A turn on follow by the rise to the steady state response. It makes no difference if that turn on is continuous or discontinuous (an abrupt change in amplitude vs time). As I said, FR is a steady state property of a system.
There are two ways to look at your system. First, you can consider it as two systems, one with impulse delayed a short time after the other. In that case each system has a FR defined by the FFt of its impulse which will be independent of time. Or you can look at it as a single system with double impulse. In which case the FR is the FFT of the double impulse. There is no question about how to define frequency response. It is the FFT of the impulse. So you either have two separate systems with impulses,
h1(1) and h2(t)= h1(t-td)
which have individual frequency responses, FR1 = FFt(h1(t)) and FR2 = FFt(h2(t)), both independent of time, or you have a single system with impulse
h(t) = h1(t) + h1(t-td)
with FR = FFT(h(t).
if h1(t) = u(t), a perfect impulse, then each of system 1 and 2 have perfect transient response and flat frequency response which is not a function of time. But the system with impulse h(t) = h1(t) + h1(t-td), has a turn on and turn off transient of length td and the FR is not flat except at low frequency where 1/f is much greater than td. At higher frequency it will exhibit comb filtering.
Hi,
Indeed "frequency response" is a steady state measure, and not very suitable to analyse temporal phenomena. Why limit yourself to steady state?? I'm yet to hear music signal which is steady state! Music is not steady state!
One can even say "frequency response" is not suitable to analyse systems meant to reproduce music
Analysis is better to be done simultaneously in time-frequency domain -> Go wavelets!
There should be a better name for a "time varying frequency response" to describe what's really going on. Maybe energy variation in time-frequency domain, as it would be more closer to the real thing?
- Elias
Indeed "frequency response" is a steady state measure, and not very suitable to analyse temporal phenomena. Why limit yourself to steady state?? I'm yet to hear music signal which is steady state! Music is not steady state!
One can even say "frequency response" is not suitable to analyse systems meant to reproduce music
Analysis is better to be done simultaneously in time-frequency domain -> Go wavelets! There should be a better name for a "time varying frequency response" to describe what's really going on. Maybe energy variation in time-frequency domain, as it would be more closer to the real thing?
- Elias
No, it is not. The frequency response of a system describes how the system changes the amplitudes and phases of the spectral content of whatever is fed into it. It is related to the impulse response by the FFT. To use the frequency response to determine the output of a system, multiply it by the spectrum of what is fed in. To see the time response to that input take the inverse FFT of that product, or directly convolve the input signal with the impulse response (same thing in a different domain).
The system's frequency response should not be confused with the system's output. Analysis of the spectral content of the output, whether by STFT, Wavelets, Wigner-Ville distributions of any of the myriad time-frequency analysis techniques is an entirely separate subject. The output varies depending on the input. The frequency response remains the same unless the system is changed, in which case it is no longer LTI.
Quote:
Originally Posted by JohnPM
No, it is not.
Yes it is
Here we go
YouTube - Argument Clinic
Rob
Originally Posted by JohnPM
No, it is not.
Yes it is
Here we go
YouTube - Argument Clinic
Rob
I guess I see what you mean but I do not agree.
What you are describing in math terms as to look either to each system aprart or in summ IMO is the same what I say about change in frequency response.
Say the delay is roughly a day – so we can listen all day long to a system thats FR is perfect, even if its a CMP system.
The only drawback is that we *have to* listen to the same pices the other day as well.
So – better not go to listen Cohn Cage stuff
– could end up in quite a CMP mess *after* first day joy.If we are after a „steady“ state – we could IMO just as well say there is one steady state this day and another one past that.
The point here is that „a steady state“ with CMP already does happen at once (immediately) - not after infinity.
---------
With respect to :
I actually do think it does make *quite* a diffenece – we went through that regarding the question „whos ranch now belongs to whom“ ( correctabiltiy of CMP behaviour in other words )
So with a OB or the boxed speaker at hand we have say 2.3 ms of no mess and after that a "less than optimal" FR (to say it polite) or we correct for FR (as good as it gets) and live with the CMP distortion - just as we anyway did ever since...
---------
??? – is a system with discontinuities *in the math sense* to be considered TI or not ?
(you know - lets keep organized : *I'm* just the monkey...)
Michael
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That is another incorrect statement. FFT is a transform (the clue is in the name
) that we can use to move between domains, it does not know or care what it is transforming. It is as happy being used to generate slices of a waterfall or spectrogram as it is being used to transform a system's frequency response into its impulse response or vice versa. The frequency and impulse response of an LTI system are time invariant.
Member
Joined 2003
Here's the measured response of the Radian 745 in the Azurahorn:
Gary Dahl
Gary,
Do you have off-axis measurements of the horn you can share?
Thanks,
Paul
One can measure "frequency response" of the LTI system by inserting a number of sinusoids each having infinite duration. Then output will have a number of sinusoids each having infinite length. The "frequency response" is amplitude and phase of these sinusoids at each frequency included in the analysis. When input and output of the system consists of sinusoid of infinite length, the system is at steady state.
One can measure exactly the same "frequency response" by calculating the fourier transform of the system's impulse response.
Since the system can be only at one state at a time, steady state in this case, thus the output of the fourier transform of the impulse response is a steady state response at each particular frequency where the analysis is calculated.
"Frequency response" IS a steady state measure.
- Elias
One can measure exactly the same "frequency response" by calculating the fourier transform of the system's impulse response.
Since the system can be only at one state at a time, steady state in this case, thus the output of the fourier transform of the impulse response is a steady state response at each particular frequency where the analysis is calculated.
"Frequency response" IS a steady state measure.
- Elias
That is another incorrect statement. FFT is a transform (the clue is in the name
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I do, but not with the Radian driver. These were made using a GPA 288-16H:
The 10-degree curve follows the on-axis curve almost exactly! From there, it does much what one would expect from the simulations.
These readings were taken fairly close-up...about 26 inches from the front of the horn. Ignore the dB scale -- the gain of my power amp hasn't yet been entered into ARTA.
Gary Dahl
"Steady State" has nothing at all to do with it. Frequency Response is more typically measured with a log swept sine, inverse transforming the determined FR to get the impulse response. Is a log swept sine steady state? Is the system's response to the log swept sine steady state? The FR is a characterisation of the system's behaviour and can be determined by examining how the system alters a stimulus passed through it, no steady states required.
Apologies for the off-topic posts on this, I have an aversion to misconceptions. I'll stop now
. Steady as you go, Elias.
To be accurate, log sweep cannot measure system's impulse response. Not unless you start the sweep from DC. But one cannot do that because it would take infinite time to play the sweep. Anything else yields only approximation of the impulse response. In practise approximations are often sufficient, but it does not remove the (approximate) steady state condition requirement. The more 'steady stateiness' in the log sweep the more accurate is the measured impulse response. That is, the longer the sweep the more accurate is the impulse response. To understand this try to think what will happen if you make your log sweep infinitesimally short in duration.
- Elias
- Elias
"Steady State" has nothing at all to do with it. Frequency Response is more typically measured with a log swept sine, inverse transforming the determined FR to get the impulse response. Is a log swept sine steady state? Is the system's response to the log swept sine steady state? The FR is a characterisation of the system's behaviour and can be determined by examining how the system alters a stimulus passed through it, no steady states required.
Apologies for the off-topic posts on this, I have an aversion to misconceptions. I'll stop now
After over 7000 posts there's little that can be considered off the topic(s) of this thread.
JohnPM: Thanks for your concise, and I believe accurate, descriptions of the nature of frequency response measurements. I think you hit the crux of the matter when you highlighted the fact that the frequency response of a system is just a description of the way the system changes the amplitudes and phases of the various frequency components of any signal that passes through it (sorry for the paraphrasing). The variable t (time) does not appear in the frequency response; the frequency response has no time dependence. Nonetheless--and this seems to be the source of the confusion--the frequency response can still be used to compute the way a system will respond to any time-varying signal, such as music. In short, the system's response to an arbitrary input varies over time but its frequency response does not. For the mathematically inclined, here's another link that describes the relationship between frequency response, impulse response, and transfer function.
On the subject of approximations: It's certainly true that in the real world we make measurements which only approximate the system's true frequency response, but that doesn't alter the definition of the frequency response. It just means we need to take care when making use of our measurements to be sure we only apply them only within the range of their accuracy.
Okay, I'm probably contributing to a subthread that's depleted the patience of some, so I'm going to go fishing for a few days. I hope my input yields the desired output. Wish me luck.
Few
JohnPM: Thanks for your concise, and I believe accurate, descriptions of the nature of frequency response measurements. I think you hit the crux of the matter when you highlighted the fact that the frequency response of a system is just a description of the way the system changes the amplitudes and phases of the various frequency components of any signal that passes through it (sorry for the paraphrasing). The variable t (time) does not appear in the frequency response; the frequency response has no time dependence. Nonetheless--and this seems to be the source of the confusion--the frequency response can still be used to compute the way a system will respond to any time-varying signal, such as music. In short, the system's response to an arbitrary input varies over time but its frequency response does not. For the mathematically inclined, here's another link that describes the relationship between frequency response, impulse response, and transfer function.
On the subject of approximations: It's certainly true that in the real world we make measurements which only approximate the system's true frequency response, but that doesn't alter the definition of the frequency response. It just means we need to take care when making use of our measurements to be sure we only apply them only within the range of their accuracy.
Okay, I'm probably contributing to a subthread that's depleted the patience of some, so I'm going to go fishing for a few days. I hope my input yields the desired output. Wish me luck.
Few
