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# A couple of questions about frequency response measurements.

As far as I know, a frequency response is the recording of the total energy of a sine sweep. One frequency is being played at a time.

So I was wondering, is it possible that a device could have a flat frequency response, but not be able to handle multiple frequencies at once as well?

Also, does harmonic distortion add onto the magnitude of those frequencies that it adds? If so, is it possible for a frequency response to look flat but only be flat as the result of harmonic distortion, and in reality sound like garbage?

The way a speaker workers - using speaker to mean a device with a single cone/ribbon/whatever - is that it play one wave at a time. If you have a complex overall sound  - Tom Waits singing over horns and drums, say - then the waves of the different sources add to a single wave at the the microphone when they are recorded, and it is this wave that it is reproduced.

Of course when you add already complex and irregular waves, the result becomes very complex and irregular indeed - which is why good speakers are such a pain to build and can absorb infinite quantities of money - because they have have to change vibration frequency and amplitude so incredibly fast and with such such precision.

A square wave test measures this ability because a square wave can only be built of a large number of sines of many different frequencies in superposition. However, things still aren't that damn simple because a transducer can have a great 500Hz square wave and a lousy one at 50Hz.

Quote:
Originally Posted by chewy4

As far as I know, a frequency response is the recording of the total energy of a sine sweep. One frequency is being played at a time.

So I was wondering, is it possible that a device could have a flat frequency response, but not be able to handle multiple frequencies at once as well?

Yes, this is true - a sine wave is not the same thing as a proper musical performance. What it is is a scientific tool to measure whether something works in theory, which means it is for the most part a starting point. While it is true that you can get a bunch of speakers to bench very similarly then sound drastically different when using one's own ears on real music, it does not invalidate the use of sine waves as a measuring tool. While one should ultimately use one's own ears to choose a headphone or speaker, it's still preferable that you start with ones that graph well enough. One that has a weird graph cannot simply be relied upon to do that well for one's ears (unless you prefer that coloration) as an accurate enough representation of what the artist and engineers were listening to when they were working on that release.

Quote:
Originally Posted by chewy4

Also, does harmonic distortion add onto the magnitude of those frequencies that it adds? If so, is it possible for a frequency response to look flat but only be flat as the result of harmonic distortion, and in reality sound like garbage?

Plausible in theory (I think) but unlikely in practice - this needs all components in a system to measure badly in ways that are complimentary to produce something that measures or sounds close to a flat response. I think the common misuse of the term "system matching" is the understanding that this will happen, like "a warm this into a bright that," as opposed to "choose an amp that won't run out of steam driving this speaker(headphone) in a room this large that presumably has reasonable levels of acoustic isolation and dampening."

Edited by ProtegeManiac - 2/27/13 at 7:35am
Quote:

Originally Posted by chewy4

So I was wondering, is it possible that a device could have a flat frequency response, but not be able to handle multiple frequencies at once as well?

Yes, if it has a high amount of non-linear distortion.

Quote:
Originally Posted by chewy4
Also, does harmonic distortion add onto the magnitude of those frequencies that it adds? If so, is it possible for a frequency response to look flat but only be flat as the result of harmonic distortion, and in reality sound like garbage?

It is possible in theory, but the distortion needs to be very high to significantly affect frequency response measurements. Maybe it can happen with something like Apple ear buds, but with a high quality amplifier, it is not really an issue. Even a good headphone is linear enough for reasonably consistent frequency response measurements (I have actually posted an example of this in an older thread).

Quote:
Originally Posted by chewy4
As far as I know, a frequency response is the recording of the total energy of a sine sweep. One frequency is being played at a time.

There are a number of ways to measure frequency response, for example:

- sine sweep (the frequency may also be increased in discrete steps, rather than continuously) - only one frequency is played at the same time, and it also gives a THD vs. frequency measurement

- multi-tone: sine waves at several frequencies are played at the same time; this has a limited frequency resolution, but does not require as accurate pitch and timing. RMAA uses this method, for example. With carefully chosen frequencies, THD products will not overlap with the test tones

- impulse - simply record an impulse and calculate the Fourier transform of it; this is the easiest method, but is sensitive to noise

- maximum length sequence (MLS): generate a special binary pattern using a linear feedback shift register algorithm (this may sound complex, but is in reality fairly simple to code), which has a perfect "white" spectrum when looped (all harmonics have exactly the same amplitude), and use that instead of an impulse. It is possible to transform the recorded MLS into an impulse response. The advantage of this method is that it is much less sensitive to noise than a simple impulse, but on the other hand it is sensitive to pitch accuracy and jitter. It is frequently used for measuring headphones and loudspeakers, where rejecting microphone and ambient noise is important, without having to use a very loud test signal that is distorted too much

Only the first one of these plays one frequency at a time.

Edited by stv014 - 2/27/13 at 10:25am
Quote:
Originally Posted by chewy4

As far as I know, a frequency response is the recording of the total energy of a sine sweep. One frequency is being played at a time.

So I was wondering, is it possible that a device could have a flat frequency response, but not be able to handle multiple frequencies at once as well?

Yes, because distortion and frequency response are only loosely related.  It would be possible to have a device with flat FR but a high amount of IMD, which is essentially not handling multiple frequencies well.  Intermodulation Distortion is where two frequencies interact to create products of the two, which are more objectionable to listen to than harmonic distortion.  However, because IMD and THD are both caused by nonlinearities, they usually don't occur exclusive to each other.

Quote:

Originally Posted by chewy4

Also, does harmonic distortion add onto the magnitude of those frequencies that it adds?

No, harmonic distortion adds harmonics of the original, which are then part of the total signal.  They may add to the total spectrum, if that's what you mean.

Quote:

Originally Posted by chewy4
If so, is it possible for a frequency response to look flat but only be flat as the result of harmonic distortion, and in reality sound like garbage?

Well, in the absolute, yes.  If a device is driven hard into clipping, FR will probably be flat regardless of what's really going on, but that kind of think is only a result of operator error.  Harmonic distortion is typically 40dB or more below the fundamental, which is too low to add significantly.  So long as a device is operated below clipping or extreme nonlinearity, distortion won't affect response.

Sounding like garbage is usually the result of non-flat FR, or high distortion, or both, but they are not really related.  You can have non-flat response without distortion, or high distortion with flat response.

Quote:
Originally Posted by scuttle

A square wave test measures this ability because a square wave can only be built of a large number of sines of many different frequencies in superposition. However, things still aren't that damn simple because a transducer can have a great 500Hz square wave and a lousy one at 50Hz.

We've sort of been around on this one before.  You have to be very careful about how much weight you put on your square wave tests.  I've already shown in another thread where a completely scrambled square wave sounds identical to a nearly clinical looking one.  There are far too many things going on that affect a square wave's image to use it to evaluate anything but very basic characteristics.  And, of course, "great" and "lousy" isn't really quantifying much.

Quote:

No, harmonic distortion adds harmonics of the original, which are then part of the total signal.  They may add to the total spectrum, if that's what you mean.

It can also change the amplitude of the original, so the measured frequency response may depend on the level of the test signal. But again, the distortion needs to be unusually high for this to really matter.

Thanks for the responses. I realize I did phrase that THD question poorly, but it looks like everyone got what I was trying to say.

Intermodulation distortion doesn't seem to measured much at all with headphones, is it not usually a problem? Or is it difficult to measure?

Quote:
Originally Posted by chewy4

Thanks for the responses. I realize I did phrase that THD question poorly, but it looks like everyone got what I was trying to say.

Intermodulation distortion doesn't seem to measured much at all with headphones, is it not usually a problem? Or is it difficult to measure?

It's easy to measure, and there are several different types of measurements.  It is a problem, often bigger than the THD problem.  No idea why it's not shown, other than it might "look" pretty bad.

Quote:
Originally Posted by stv014

It can also change the amplitude of the original, so the measured frequency response may depend on the level of the test signal. But again, the distortion needs to be unusually high for this to really matter.

Yeah, that's what I was referring to by talking about frequency response when something is driven into clipping.  Sort of pointless to talk about harmonics changing the level of the original at that point, no?

Quote:
Originally Posted by chewy4
Intermodulation distortion doesn't seem to measured much at all with headphones, is it not usually a problem? Or is it difficult to measure?

I have posted an example of that too in another thread. Intermodulation of mid to high frequencies by loud bass (i.e. what is measured by the 60 Hz + 7000 Hz 4:1 IMD test) can indeed be a problem with dynamic headphones at high volume. On the other hand, I found that high frequency intermodulation (19 + 20 kHz, for example) is less of an issue, and can be fairly low. But it probably depends on the headphones tested. Generally, if there is high IMD, there is normally also high THD at at least one of the frequencies (either the test tones, or the IMD products).

Quote:

Originally Posted by stv014

- multi-tone: sine waves at several frequencies are played at the same time; this has a limited frequency resolution, but does not require as accurate pitch and timing. RMAA uses this method, for example. With carefully chosen frequencies, THD products will not overlap with the test tones

Here is what the spectrum of the RMAA frequency response test signal looks like:

Quote:
Originally Posted by chewy4

Thanks for the responses. I realize I did phrase that THD question poorly, but it looks like everyone got what I was trying to say.

Intermodulation distortion doesn't seem to measured much at all with headphones, is it not usually a problem? Or is it difficult to measure?

I have already posted these in an older thread, but here is an example of 55 Hz + 2000 Hz (4:1), and 15000 Hz + 16000 Hz (1:1) IMD test. The frequencies are different from the "standard" ones because of the limitations of the recording equipment used (i.e. there are large frequency response errors above 5-6 kHz):

The red traces were measured at a voltage that gives an SPL of about 100 dB (calculated from the sensitivity of the headphones), and the yellow ones are at 90 dB. In the high frequency IMD test, the level of the tones should actually be -6 dB without frequency response problems.

Also, here is the frequency response (on the left) measured with a "90 dB" sine sweep (green), a "100 dB" sine sweep (yellow), and a maximum length sequence (cyan and magenta). On the right, the THD vs. frequency from the sine sweeps is shown. Given that moving the headphones or microphone even slightly changes the frequency response, the results do not show major variation depending on the level or the method of testing. Obviously, with much higher distortion (at a higher SPL, or using other headphones), that might not necessarily be the case, but if the distortion is reasonably low, the frequency response should measure consistently.

Edit: another example, this time using B.flac from here, and the frequency response measured using an MLS (blue and red), vs. calculated from the music with a large FFT of the entire track compared to the original sample (cyan and magenta). This shows no significant difference above about 50 Hz, while at the lowest frequencies the (still small) error is probably from the analysis, rather than an actual FR difference:

Edit 2: the low frequency response difference is there because I forgot to apply the correction filter for the FR of the ADC in the MLS case.

Edited by stv014 - 3/2/13 at 10:57am

Thanks for the examples.

Do you know of any websites that actually do these IMD measurements for headphones?

Quote:
Originally Posted by chewy4

Thanks for the examples.

Do you know of any websites that actually do these IMD measurements for headphones?

There are 100 Hz + 1 kHz + 10 kHz IMD graphs at this site, but the measurements there might be unreliable. Also, the SPL is not specified, or maybe I just could not find it in the Japanese text. Other major sites that I know of with a large number of headphone measurements usually only have THD, or no distortion graphs at all (like goldenears.net).

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