Is non-flat frequency response a nonlinear distortion?

[Fluffy]

Hi! I'm new to this site so I'm hoping I'm posting to the right forum.

My question regards the relationship between non flat frequency response and nonlinear distortion. To my understanding, nonlinear distortion is a deviance from linearity, meaning that the output signal does not correspond perfectly to the input signal. In that case, a frequency response that is not flat will definitely change the output signal so it doesn't match the input signal.
Let's say, if the frequency response of an amplifier is such that frequencies above 10khz are reduced by 1 db, then a complex signal entering it, such as music, will come out the other side changed. A peak that should have been of some value given the gain of the amplifier, will be at another value because the high frequency component of the signal is relatively reduced in level by the amplifier. And thus, it will be distorted relative to the original signal.
Am I missing something here?

 

[sergeauckland]

Yes, by convention, distortion is defined as a non linearity in the input output transfer function at one or more frequencies. Frequency response errors are not generally non linear so don't generate distortion as defined previously.

S

 

[solderdude]

A peak that should have been of some value given the gain of the amplifier, will be at another value because the high frequency component of the signal is relatively reduced in level by the amplifier. And thus, it will be distorted relative to the original signal.

This is called linear distortion and is a form of distortion but not the same as non-linear distortion.
In the case of non-linear distortion there will be additional frequencies there that aren't in the incoming signal.

Below a plot (@Patrick1958 may recognize it ) that shows linear distortion of a headphone transducer + measurement setup in the upper trace
The bottom traces are non-linear distortion products. H2, H3, H4

There is some relation (of course) but not 100% relation between linear (upper brown trace) and non-linear distortion products.

 

[Fluffy]

In the case of non-linear distortion there will be additional frequencies there that aren't in the incoming signal.

I guess that was the part I misunderstood. Thanks for clearing that up!

In the case of transducers, I know what the effects are of the frequency response curve, but I don't really understand why it would actually respond differently to different frequencies. I understand how resonances and destructive\constructive waves could produce different perceived efficiency in different frequencies. But if we eliminate resonances and say even suspend the transducer in midair and feed it pure sine waves, it will produce each wave at different amplitude. I don't really understand why that happens. What are the mechanical or electrical effects that make it basically move less or more when you feed it different frequencies?

 

[NTK]

... What are the mechanical or electrical effects that make it basically move less or more when you feed it different frequencies?

Are you familiar with the response of a spring-mass-damper system (or the electrical analogue of LCR circuit)? Each of these systems will have a natural frequency. In the case of the spring-mass-damper system, if you push on the mass with an oscillating force at a frequency much less than its naturally frequency, the mass will oscillate at an amplitude determined only by the magnitude of the applied force and the stiffness of the spring (i.e. not frequency dependent).

However, when the frequency of the oscillating force approaches the natural frequency or exceeds it, with the magnitude of the force staying the same, the amplitude of the movement will start to decrease as the oscillating force frequency increases , i.e. it becomes frequency dependent (and you can look at this system as a low-pass filter).

When a spring-mass-damper system is over-damped (Q < 0.5), it will not self-oscillate, and you wouldn't see ringing responses for them (say, when you excite it with a step or impulse).

A loudspeaker has a very complex combinations of many of these spring-mass-damper systems (air loading, speaker diaphragm mass, speaker diaphragm surround stiffness, speaker diaphragm stiffness, characteristics of the motor assembly, etc.). They act/interact together to result in non-flat frequency responses.

 

[Fluffy]

Ok than, so let's put aside loudspeakers for a moment. I can understand why this complex system could arise with multiple drivers and crossovers and room interactions and case resonances etc.

What if we take something like a headphone transducer, say the beryllium disc in the Focal Utopia (https://www.innerfidelity.com/images/FocalUtopia.pdf). It's really stiff and light and basically suspended in air, and it's only one element that delivers full spectrum sound. And yet, it's frequency response is all wacky (relative to perfect flatness), especially at 1khz and above, where the difference between response of different frequencies can be 10 db and more. Why would one piece of stiff metal would react so differently to different frequencies? And how could one possibly tune it to a desired response?

 

[jonfitch]

In a passive loudspeaker, you can tune a driver by equalizing with crossover components. Of course this is not practical in a headphone, some of these components weigh as much as a headphone by itself, so there's a limit you can passively EQ a full-range headphone and still make it a wearable product...for headphones digital EQ is probably the only practical solution.

 

[solderdude]

What if we take something like a headphone transducer, say the beryllium disc in the Focal Utopia (https://www.innerfidelity.com/images/FocalUtopia.pdf). It's really stiff and light and basically suspended in air, and it's only one element that delivers full spectrum sound. And yet, it's frequency response is all wacky (relative to perfect flatness), especially at 1khz and above, where the difference between response of different frequencies can be 10 db and more. Why would one piece of stiff metal would react so differently to different frequencies? And how could one possibly tune it to a desired response?

When you have a look at the measurements here then it can become clear (pun intended) that the stiff driver isn't as stiff as one would hope for the higher frequencies. Above 2kHz it has unusually low amounts of distortion compared to say plastic drivers.
Still the material does have quite a few resonances at high frequencies which is seen in all the plots basically.
I reckon it is the membrane breaking up as the dome is quite large. So they are (most likely) partial vibrations in the membrane.
The membrane is moved from its edges and due to the speed the inner part does not 'feel' it yet and doesn't move yet, it is delayed as it were.
For high frequencies the membrane thus doesn't move as a whole.
This one cannot EQ out.
One can apply EQ to the resonance frequencies, which are really sharp so filters there will also ring, and get the amplitude 'better'.
Personally I would only address the 6kHz peak as that is where the 'sibilance' resides and leave the others alone.
removing too much will take away some of its 'awesome' aspects.

What I did hear in it was that some (specifically metal object) instruments had an unnatural resonance to it. At first impressive until I compared it to another 'excellent' headphone that had been EQ'ed and knowing how instruments should sound IRL but stood out unnaturally.

The 'Clear' was 'better' in that aspect. That one also has a huge resonance (the Utopia will most likely also have it but above 30kHz) but that is certainly for my hearing out of range.

 

[Fluffy]

Headphone manufacturers say they tune their headphones. If the driver is essentially the same across different models, how can they really tune it? How can they reduce peaks like this solely by mechanical differences between different models?

 

[solderdude]

A: Headphone manufacturers do not always use the same drivers, they may well use the driver frame/magnet but membranes can differ.
There are LOTS of different drivers, even within a product line of a manufacturer, some may look the same but may differ substantially.
Material choice, geometry, (local) thickness, embossing all are factors that one can play with in membrane/cone design resulting in quite different response yet may appear the same or very similar.
B: 'Tuning' is done with pads, enclosures, porting be them holes, small ports or 'acoustic paper' or nifty constructions.
Lots of ways to change tonal balance, resonances etc.

 

[Fluffy]

One can apply EQ to the resonance frequencies, which are really sharp so filters there will also ring, and get the amplitude 'better'.

What do you mean by "the filters will ring"?

 

[solderdude]

When one uses sharp software or hardware filters (which are in the audible band) these will also introduce 'ringing' of their own IN the audible band. Unlike reconstruction filters which 'ring' at inaudible frequencies.
It is a property of a sharp filter.
In the case of removing a peak the decrease in level is far more important than the ringing afterwards which resonances in drivers usually do anyway.
So removing peaks has a positive effect on the 'tone' but doesn't shorten the ringing.