Beyond the Ariel

[john k...]

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.

[john k...]

Originally Posted by mige0
Seen as a whole – meaning from time zero to eternity, a CMP system definitely *is* both : time invariant and linear (and hence *can* be accessed for 100% correction in theory) - though I guess, the term „time invariant“ could also be interpretated differnently here. For sure a CMP system is „time invariant“ for each of the three time spans :
zero to delay time
delay time to end of input
end of input to end of input plus delay time

This is a distortion of the meaning of time invariant, again, to suit your interpretation. TI simple means that the system will perform tomorrow or the next day, or then day after that in exactly the way it performs today.

[Elias]

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

Originally Posted by mige0

Sure a sine burst is a transient signal !
But - for the purpose used, I'd say it's absolutely suitable.
Compare the simus and the measurements > perfect correlation to theory.

Where do you see my logic flawed ?
If we clearly see the amplitude of a given frequency varying with time, the most simple conclusion is to state: "there is different FR depending on the time we look at".

Originally Posted by john k...

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.

[JohnPM]

Originally Posted by Elias

Indeed "frequency response" is a steady state measure

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.

[Elias]

Originally Posted by JohnPM

No, it is not.

Yes it is


Because :

Originally Posted by JohnPM

It is related to the impulse response by the FFT.

and FFT calculates the steady state response.


- Elias

[Robh3606]

Quote:
Originally Posted by JohnPM

No, it is not.

Yes it is

Here we go

YouTube - ‪Argument Clinic‬‎


Rob

[soongsc]

I wonder, measurement discussion in this thread? With the cable thread closed this place is tempting.

[Pano]

Um..... Let's not go there

[mige0]

Originally Posted by john k...

The problem here is that you keep looking at the time domain and divining the frequency response form what you see. That is incorrect. .

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 :

Originally Posted by john k...

It makes no difference if that turn on is continuous or discontinuous (an abrupt change in amplitude vs time).

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...

---------

Originally Posted by john k...

This is a distortion of the meaning of time invariant, again, to suit your interpretation. TI simple means that the system will perform tomorrow or the next day, or then day after that in exactly the way it performs today.

??? – 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

[JohnPM]

Originally Posted by Elias

FFT calculates the steady state response.

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.