Help me understand Impulse Response, Step Response, and Time Alignment

[audiofooled]

Thx for showing what exactly is going on with the modulation producing the sidebands.
And please know I did not mean to question the validity of Fourier analysis.

What I do question though, is how fully representative a slice in time measuring, ie steady state, fully characterizes how our loudspeaker respond to a continually changing stimulus.

I guess my question to you and bmc0 and others more advanced in the math, is how much amplitude modulation occurs with music as it changes from instant to instant?
Is it at all significant?

This is one of JJ's signals for phase audibility:

Part one of the signal:

My system's response at MLP:

Part 2 of the signal (everything the same, except phase):

System response:

Considering that the frequencies align with my room modes, system's ability of tracking the signals is less than accurate amplitude wise for the first part, nor is it able to start and stop on a dime in case of the second part of the signal, again considering measurement distance, wave propagation and modal region.

Still, it ain't half bad either and more importantly, it's very audible.

 

[bmc0]

I think it actually does cancel cyclically.

It does in a sense, but I think the explanation given in the figure you posted is misleading. The 900Hz and 1100Hz components drift in and out of phase with each other. They add constructively when the relative phase is 0°, and cancel when it is 180°.
In effect, the black trace is an amplitude-modulated 1kHz wave just like the original input. The only differences are the attenuation and the phase of the modulating signal (90° relative).

I guess my question to you and bmc0 and others more advanced in the math, is how much amplitude modulation occurs with music as it changes from instant to instant?

Music is full of both amplitude and frequency modulation. What point are you trying to make?

 

[audiofooled]

In addition to my post above, this is steady state at approximately the same position (3,5m distance):

Group delay:

This is summed response of total of 7 bass radiators in this configuration, BTW:

Dr. Toole's 4th Edition Book is Coming! (Discount)

I'm still waiting for my copy. Has everyone else gotten theirs?

www.audiosciencereview.com

It can be somewhat intuitive when viewing the scope captured response of the phase test signal that room modal behavior will affect the response, amongst other things even more complex.

This is an attempt at rather ugly 46Hz square wave:

And no, it is not captured at the same measurement position, which is too close to the boundaries where waves cannot always propagate because particles have nowhere to move and upper harmonics are very much affected by the reflections.

Edit: Phase in the first image was unwrapped at -360 degrees.

 

[gnarly]

Considering that the frequencies align with my room modes, system's ability of tracking the signals is less than accurate amplitude wise for the first part, nor is it able to start and stop on a dime in case of the second part of the signal, again considering measurement distance, wave propagation and modal region.

Still, it ain't half bad either and more importantly, it's very audible.

Nice work. Thx for showing. I need to look into JJ's test signals.

For me, phase is no longer an issue. I simply tune my DIY's for flat phase. Reasoning whether audible or not, I know flatter smoother phase is technically correct.
And is therefore one less potential source of signal degradation coming out of the speaker. One less factor to be concerned with.

 

[gnarly]

Music is full of both amplitude and frequency modulation. What point are you trying to make?

Not trying to make a point. Was an innocent question........ just wondering your personal take, on whether amplitude modulation in music is significant/relevant.

 

[bmc0]

Not trying to make a point. Was an innocent question........ just wondering your personal take, on whether amplitude modulation in music is significant/relevant.

The question is too open-ended to give a reasonable and succinct answer. Relevant to what, exactly? If you're asking whether an ideal crossover can be completely characterized using steady-state analysis, the answer is yes. Do note that the amplitude modulation demo is in fact steady state. If you're instead asking whether a real loudspeaker system can be completely characterized this way, the answer is no. Loudspeakers are not perfectly time invariant.

 

[gnarly]

The question is too open-ended to give a reasonable and succinct answer. Relevant to what, exactly? If you're asking whether an ideal crossover can be completely characterized using steady-state analysis, the answer is yes. Do note that the amplitude modulation demo is in fact steady state. If you're instead asking whether a real loudspeaker system can be completely characterized this way, the answer is no. Loudspeakers are not perfectly time invariant.

Sorry for the vagueness.

I've been enjoying proaudio system measurement and alignment classes, where a number of sessions have delved into tuning via time domain based measurements.
What I've seen, is that the deep nulls from a polarity inversion, that we see when using regular transfer functions based on time averaged pink, or sine sweeps, aren't nearly as deep with modulating signal. But of course this is with steady state modulation as you noted. So anyway, I can't help but be curious about non-steady state modulation, that I assume is constantly occurring with music. Thx for the reply.

 

[bmc0]

What I've seen, is that the deep nulls from a polarity inversion, that we see when using regular transfer functions based on time averaged pink, or sine sweeps, aren't nearly as deep with modulating signal.

Any time you modulate a signal, you create new frequency components. Modulation will therefore reduce the apparent depth of a null when viewed in the time domain because the null can only be perfect at a single frequency.

 

[RayDunzl]

Audacity Alignment Experiment:

Generate a 25 Hz sine for 40ms. That's one cycle

At the top of the wave, draw one sample full scale.

This embeds an impulse within the 25 Hz sine.

Copy/paste the waveform to get a few cycles.

Play it back and observe the waveform.

If "aligned" the impulse should be at the top of the wave like the wave you generated.




Old test I performed (but with 30Hz). Looked pretty close to me. Just to visurally explain what I'm talking about.

The digital source.
"Uncorrected" with JBL LSR 308, Playback recorded with UMIK1
"Corrected" with JBL LSR 308, Playback recorded with UMIK1
"Corrected" with MartinLogan reQuest, Playback recorded with UMIK1

The little JBL pretty much got it "right" from the start

 

[levimax]

I started this thread trying to understand how an impulse and step response corresponded the what happens in the physical world. After reading links provided and thinking about them and looking at @RayDunzl post above here is what I think I am seeing.

1. The distorted first cycle of each measurement shows the transient response of the system and it is not perfect.
2. After a few cycles things settle down to steady state and I am seeing the "steady state" response of the system.
3. Filters, electronic or mechanical or both, are causing phase shift which moves the simulated impulse peak away from the center peak of the LF signal.

Is that correct?

If so I am still struggling to understand "steady state" vs "transient" when looking at an impulse response. I originally thought an impulse response showed how the system would react to a transient signal but not sure how to understand that when it is based on "steady state".

 

[Heinrich]

... not Hi-Fi and can be audible. ...

Is it audible? If it is , what's your preference? Probelematizing phase, impulse etc may direct attention to lacking knowledge of Fourier, as a tool, and mathematics of transcendent functions, again tools of decription and understanding. Hifi brings common people to use terminology without proper reasoning, generating misconceptions galore. Analogy: as if I was talking about socializing. No clue, and still argueing about it.

In short: the 'impulse' as seen in the initial post is just normal and mathematically o/k. Fully o/k, and not "-ish". It is what a perfect filter would do, and in isolation rightout perfect. The result in the combined signal sub/mains will be extremely close to perfect to--the eye. Even human ears obey the math. Worry not. You are mislead by half-knowledge spilled out by uneducated predators in the industry, magazines included. Keep your peace of mind and just trust the engineers. Like you do with every bridge you cross. If you do not, why trust obviously fraudulent advertising? Keep track of what you enjoy when listening to the playback. Stop reading magazines and forums.

I started this thread trying to ...

You're welcome. There is no use in starting at that point. Get a solid basis in calculus and theory of functions, implicating a trustworthy foundation in so called complex numbers. Then it will all unravel. Doing less, well.

 

[DWPress]

Well, despite my lack of a solid basis in calculus, I've learned a lot in this thread. That's why I hang out reading forums....

 

[levimax]

Is it audible? If it is , what's your preference? Probelematizing phase, impulse etc may direct attention to lacking knowledge of Fourier, as a tool, and mathematics of transcendent functions, again tools of decription and understanding. Hifi brings common people to use terminology without proper reasoning, generating misconceptions galore. Analogy: as if I was talking about socializing. No clue, and still argueing about it.

In short: the 'impulse' as seen in the initial post is just normal and mathematically o/k. Fully o/k, and not "-ish". It is what a perfect filter would do, and in isolation rightout perfect. The result in the combined signal sub/mains will be extremely close to perfect to--the eye. Even human ears obey the math. Worry not. You are mislead by half-knowledge spilled out by uneducated predators in the industry, magazines included. Keep your peace of mind and just trust the engineers. Like you do with every bridge you cross. If you do not, why trust obviously fraudulent advertising? Keep track of what you enjoy when listening to the playback. Stop reading magazines and forums.

I have specifically avoided any claims of time domain audibility as it is controversial and not completely settled science especially at LF. The audibility I was talking about, and you quoted me about, was about 35% THD at 20 Hz creating harmonics at 40 Hz which will sound louder than the fundamental due to fletcher-munson and this can be audible.

 

[kemmler3D]

I started this thread trying to understand how an impulse and step response corresponded the what happens in the physical world. After reading links provided and thinking about them and looking at @RayDunzl post above here is what I think I am seeing.

1. The distorted first cycle of each measurement shows the transient response of the system and it is not perfect.
2. After a few cycles things settle down to steady state and I am seeing the "steady state" response of the system.
3. Filters, electronic or mechanical or both, are causing phase shift which moves the simulated impulse peak away from the center peak of the LF signal.

Is that correct?

If so I am still struggling to understand "steady state" vs "transient" when looking at an impulse response. I originally thought an impulse response showed how the system would react to a transient signal but not sure how to understand that when it is based on "steady state".

Not exactly.

Step and impulse responses both show what happens when a system, in this case the speaker tries to reproduce a pure "click", i.e. with a truly perfect system you'd just see a vertical line, no wobbles before or after.

Phase differences between drivers can cause multiple peaks, so you are right about that part.

"steady state" should not actually show up in impulse or step response charts, the ripples off to the right show the speaker settling back to steady state, resonances, or other residual energy decaying after the initial click.

But a "steady state" measurement is more like, "what does it look like if I just play a simple tone".

 

[Heinrich]

I have specifically avoided any claims of time domain audibility as it is controversial and not completely settled science especially at LF. The audibility I was talking about, and you quoted me about, was about 35% THD at 20 Hz creating harmonics at 40 Hz which will sound louder than the fundamental due to fletcher-munson and this can be audible.

That's not true, actually. The hearing substitutes the harmonics for an imagined base frequency and so on. So much detail there is. And mathematics. still the *very* basics.

 

[RayDunzl]

If so I am still struggling to understand "steady state" vs "transient" when looking at an impulse response. I originally thought an impulse response showed how the system would react to a transient signal but not sure how to understand that when it is based on "steady state".

I didn't see how you could take a frequency swept sine wave and find the "edges" that an Impulse or Step response calculates.

So another old experiment:

Impulse response calculated from a ten second 10-24kHz sweep tone sent through the speakers in REW:

Single Full Scale Bit (an Impulse) sent through speakers, playback in room recorded in Audacity:

Step response calculated by REW from a swept sine test tone, and "step" response recorded through the speakers playing a 10hz square wave, zoomed in on the rising "edge" and "flat top" of one cycle of that wave.

This convinced me the math works (somehow).

 

[bmc0]

If so I am still struggling to understand "steady state" vs "transient" when looking at an impulse response. I originally thought an impulse response showed how the system would react to a transient signal but not sure how to understand that when it is based on "steady state".

To add a bit to @RayDunzl's practical demo: If one can make certain assumptions about a system—namely that it is approximately linear and time invariant—it is possible to calculate transient response from steady-state response and vice versa. Using convolution, one can predict an LTI system's behavior for an arbitrary input from its impulse response. The inverse operation, deconvolution, allows computing an LTI system's impulse response from its response to some other suitable stimulus, such as a sine sweep, a maximum length sequence (as used by the MLSSA measurement software), etc.

 

[levimax]

That's not true, actually. The hearing substitutes the harmonics for an imagined base frequency and so on. So much detail there is. And mathematics. still the *very* basics.

Please show me a scientific study that shows 35% THD is not audible even at 20 Hz. What you are talking about is "rolled off" bass that is not as audible as you would think because the brain fills in the fundamental based on the harmonics. No argument there. What I am talking about is that 35% distortion at 20 Hz, where the distortion product at 40 Hz is heard louder than the fundamental, is clearly audible with some content. As was pointed out up thread some people "prefer" this heavy LF distortion but that is not the same thing as not audible or accurate.

I understand about the value and power of math and have some experience with complex and imaginary numbers but not enough to work through the calculus required to gain insights in the the relationships about how filters interact in different domains. Impulse responses and step responses, while based on math, are a visual way to represent things occuring in the physical world. I believe I and hopefully others can better understand these visual tools with some help from people that can work through the math as intuition is not always useful for a lot of this stuff.

 

[Audionaut]

In a real world scenario, you might look at a really wiggly long tail in your step response and you feel disappointed. That feeling of utter failure as an audiophile starts to creep in. Some doubt might creep into your mind - maybe it's time to end it all?

In a real-world scenario, I couldn't care less, when I am completely satisfied with the sound result based on my own subjective opinion.

 

[3ll3d00d]

That's not true, actually. The hearing substitutes the harmonics for an imagined base frequency and so on. So much detail there is. And mathematics. still the *very* basics.

While that might be true in general terms, and is even a way to cheat on apparent extension for higher frequencies, for the specific example, it's v much audible. Clean 20Hz does not sound like 20Hz with as heavy dose of distortion on top