Is there way to take a logarithmic sine sweep with an amplitude tilt?

[MrHaelscheir]

I am currently using REW in the context of headphone measurements. I've had success in measuring headphone distortion, but considering my observations through analyzers of contemporary music indeed having a spectral envelope similar to pink noise and classical orchestral music having one similar to Brownian or red noise, such being in contrast to the white noise envelope consistent with the usual constant-amplitude sine sweeps, I was wondering if it is possible to take a logarithmic sine sweep measurement that decreases the amplitude with frequency so as to approximate measurement of the actual distortion conditions of playing music. For example, while I might measure 94 dBA out of my headphones for the first crash of Mahler 5, a sweep may not capture the practical levels seen by the bass and overexaggerate the treble levels, whereby to avoid damaging the driver (or my ears since I'm using in-ear mics for blocked canal measurements), I would have to take higher-level bass measurements with a lower-frequency cut-off.

As for multitone measurements, I am supposing that the "Pink" option for "Spectrum" implements the amplitude tilt I am looking for.

 

[John Mulcahy]

The log sweep REW uses has a pink spectrum, a consequence of its exponential frequency progression.

 

[MrHaelscheir]

The log sweep REW uses has a pink spectrum, a consequence of its exponential frequency progression.

Huh. I hadn't realized that consequence of the sweep rate on the amplitude. So it is already equivalent to exciting each frequency of the headphone at levels consistent with a pink noise spectral envelope (forgive my lack of the proper term)? I am a bit confused then as to what it means for this sweep to plot a neutral speaker's frequency response as flat or largely constant in SPL with respect to frequency. I perhaps have to do more reading, but am I wrong in assuming SPL to be directly related to amplitude?

 

[John Mulcahy]

I hadn't realized that consequence of the sweep rate on the amplitude.

It has no effect on the time signal's amplitude, it affects the energy distribution in the spectrum. The transfer function calculation accounts for the sweep's spectrum, it would be useless if it didn't.

 

[MrHaelscheir]

It has no effect on the time signal's amplitude, it affects the energy distribution in the spectrum. The transfer function calculation accounts for the sweep's spectrum, it would be useless if it didn't.

So the entire measurement signal has a pink spectrum though the signal actually being passed to the transducer in the time domain is of constant amplitude. So are the distortion measurements with this sweep consistent with individual tones within pink or white noise playback through the transducer, or are the distortion measurements also being compensated? Understandably, the transfer function calculation performs that compensation for the spectrum, but if I look at one frequency point of the distortion measurement and look at the plotted levels of its harmonics, does this imply I will measure similar similar harmonic levels through an analyzer when playing a single tone at that plotted fundamental level? This matters to me because we know distortion levels are proportional to the playback levels within the given frequency band, whereby pink and white noise present different relative playback levels between higher and lower playback frequencies. If the measurement signal were to have a pink spectrum but somehow still produce a distortion measurement consistent with a white spectrum of playback, then that measurement on its own would not be very representative of the conditions of music playback. Forgive my confusion.

 

[John Mulcahy]

You appear to be confusing time signal amplitude and spectrum energy. The amplitude during the sweep is constant, the harmonic components are for a signal of that amplitude. The pink spectrum of the sweep reflects it's lower energy at higher frequencies due to the shorter time the sweep spends in any given frequency span (in Hz) as frequency increases, it does not mean instantaneous amplitude at the frequency is any lower.

The same is true for musical content. High frequency content is not quiet, but there's not as much of it as lower frequency content so the overall energy at high frequencies is lower.

 

[MrHaelscheir]

You appear to be confusing time signal amplitude and spectrum energy. The amplitude during the sweep is constant, the harmonic components are for a signal of that amplitude. The pink spectrum of the sweep reflects it's lower energy at higher frequencies due to the shorter time the sweep spends in any given frequency span (in Hz) as frequency increases, it does not mean instantaneous amplitude at the frequency is any lower.

The same is true for musical content. High frequency content is not quiet, but there's not as much of it as lower frequency content so the overall energy at high frequencies is lower.

Is this to say that the " amplitude spectrum" traced out by a transfer function measurement is distinct from the output of a spectrum analyzer showing me a pink or red noise envelope for a given passage of music where both show scales in "dB SPL" or "dBFS"? Here, I am thinking of the amplitude of each frequency in the frequency domain, disregarding the spectrum energy. For further clarification, see the spectrum analyzer output below for the trailing end of the first tutti in Mahler Symphony No. 5:

I would think of the envelope, or the line traced about the top of this chart, as being similar to that of a pink or red noise spectrum. Is it not the case that to generate a harmonic distortion measurement equivalent to every possible tone in said music signal with a spectral envelope equivalent to that of pink noise, the amplitude of the signal in the sweep would have to decrease by 3 dB per octave? E.g. If we had a sine sweep that decreased in amplitude by 3 dB per octave, but with the frequency being increased linearly with respect to time, wouldn't that signal also have a pink "energy spectrum", but now capturing the distortion profile consistent with pink noise music? Theoretically, the same measurement with this 3 dB per octave amplitude decrease could be taken with the frequency increasing exponentially with time, this of course yielding a different energy spectrum. Otherwise, what you are saying seems to imply that REW's current constant-amplitude sweep regardless of its energy spectrum would only be estimating the distortion for every tone in the above signal if its spectrum graph rather looked like white noise with a horizontal rather than slanted envelope.

Am I completely misinterpreting the above spectrum analysis as measuring amplitude as opposed to "sound energy" with respect to frequency? It is already clear that sine sweep transfer function measurements are showing the amplitude with respect to frequency.

 

[John Mulcahy]

Is this to say that the " amplitude spectrum" traced out by a transfer function measurement is distinct from the output of a spectrum analyzer showing me a pink or red noise envelope for a given passage of music where both show scales in "dB SPL" or "dBFS"?

A transfer function is not a spectrum. The transfer function shows how the system changes signals that pass through it. It can be displayed as an impulse response or as a graph of the magnitude and phase of an FFT of the impulse response.

Am I completely misinterpreting the above spectrum analysis

Yes.

 

[John Mulcahy]

Here is an alternative method for separating the linear and non-linear responses of a system to an arbitrary signal which may better capture what you wish to investigate.

 

[MrHaelscheir]

A transfer function is not a spectrum. The transfer function shows how the system changes signals that pass through it. It can be displayed as an impulse response or as a graph of the magnitude and phase of an FFT of the impulse response.

Okay. I acknowledge my mistake in not distinguishing a transfer function from a raw amplitude sweep. One could plot the amplitude versus frequency of a transducer for an input sine sweep that decreases by 3 dB, but it of course would not represent a transfer function without compensating for that tilt in the input amplitude. So now completely removing "transfer function" from this discussion, is there presently a way to run a sine sweep and distortion measurement that possesses this downward tilt in amplitude?

Every source I am aware of indicates spectrum analyzers as plotting the amplitude of each frequency decomposed from the signal (within a margin of error). If I were to play white noise through a transducer and measure its output, I would expect the spectrum analysis of that output to have an upper envelope of similar shape to its transfer function. Then talking about the previous music example while now disregarding discussion of transfer functions as irrelevant, I am supposing the music as actually containing individual tones of amplitudes that follow that observed tilt with respect to frequency. Are you rather saying that the music signal is capable of being decomposed into tones of equal amplitude, but distributed in energy so as to have the spectrum analyzer display a tilted envelope? Or are sine sweeps completely the wrong way to be estimating the harmonic distortion excited by individual tones within music?

That FSAF measurement method looks interesting, but I am currently focusing on pure tone and multitone analyses generic across music sources.

 

[John Mulcahy]

is there presently a way to run a sine sweep and distortion measurement that possesses this downward tilt in amplitude?

For what purpose? When you listen to that Mahler symphony does it sound like your head is in a giant pillow? High frequencies are not quieter, they just make up less of the overall duration of a piece.

 

[MrHaelscheir]

[1] For what purpose? [2] When you listen to that Mahler symphony does it sound like your head is in a giant pillow? [3] High frequencies are not quieter, they just make up less of the overall duration of a piece.

[1] To within one plot approximate the harmonic distortion that would be excited at every frequency at a given instant where the music's real-time spectrum analysis follows an amplitude distribution similar to pink noise as opposed to the case of capturing the distortion across all frequencies but at the same amplitude.
[2] No, but I can through Reaper's real-time spectrum analyzer correlate observed spikes in those higher frequencies with the instrumental content and perceived brightness, effectively points where the music is better approximated by pink noise than red noise (a greater downward tilt). E.g. Through most string sections with less treble, the spectrum analyzer's output visibly has an envelope with a greater downward tilt akin to red noise, while moments of greater trumpet or higher-pitched string content can push that up to a pink noise envelope.
[3] This unfortunately seems to be a conceptual disagreement in our discussion about the nature of the amplitude of individual tones within music or signals. Is there a disagreement that the amplitudes of each frequency within music signals changes in magnitude with time, not just the spacing between the presence of said amplitudes? Or to clarify, I am not talking about the general spectral distribution across an entire piece so much as the spectrum shown when screenshotting just one loud instant of that symphony amid whatever window Reaper's spectrum analyzer was using at the time.

 

[John Mulcahy]

There is no spectrum at an instant, just a signal amplitude. Spectrum magnitude is only half the response. A flat spectrum magnitude with zero starting phases for the components has an impulse as a corresponding time series, with random starting phases the time series is noise-like. Same spectrum magnitude, completely different time series and completely different system response. I have provided a link to a resource that allows you to use actual music as the stimulus but you have rejected it.

You can generate white or pink multitone sequences with REW's generator and the RTA will provide a Total Distortion + Noise result. You can use Paul Kane's Multitone Analyzer to generate and analyse the responses to multitone signals of your own definition. There is a thread on Paul's software here.

 

[MrHaelscheir]

There is no spectrum at an instant, just a signal amplitude. Spectrum magnitude is only half the response. A flat spectrum magnitude with zero starting phases for the components has an impulse as a corresponding time series, with random starting phases the time series is noise-like. Same spectrum magnitude, completely different time series and completely different system response. I have provided a link to a resource that allows you to use actual music as the stimulus but you have rejected it.

You can generate white or pink multitone sequences with REW's generator and the RTA will provide a Total Distortion + Noise result. You can use Paul Kane's Multitone Analyzer to generate and analyse the responses to multitone signals of your own definition. There is a thread on Paul's software here.

Right. Sine sweeps may provide isolated excitation of the driver up to that amplitude, which incurs certain distortion from non-linearities at that level of excursion, but for actual signals, though their spectral envelopes over some time window may be similar, it is the actual amplitude or excursion in the time domain rather than the decomposed amplitude of the individual tones that has a practical bearing on distortion excitation, spectrum and time domain amplitude only agreeing for single tones.

I will spend some time looking into how to employ FSAF and research into other analysis methods. Otherwise, I have conducted some multitone distortion comparisons in the second half of https://www.head-fi.org/threads/hifiman-he1000-se.886228/post-17865104 (post #4,789) which have already shown the results I was looking for.

Anyways, thank you for bearing with me for clearing up my confusion.