[stv014]

  Floats (singles) use 24 bits to hold the argument and the final 8 for the exponent. meanwhile, audio data fits into 16 or 24 bit integers, with hardware capable of reproducing it at best, about 22 ENOB (effective noumber of bits) . What sort of eigenvalues does a typical eq filter have? Either way, since only the 16 most signifcant bits are going to matter, id be awfully surprised if a good digital eq would lose 8 bits of precision to truncation error.

 
On current hardware, 64-bit double precision floats can be used for most DSP algorithms (including EQ) without performance issues. Precision is not a problem (no analog hardware can get close to the "noise floor" of 64-bit floats), discrete time (sampling) might be for accurate IIR filter design near the Nyquist frequency; however, this does not result in non-linear distortion, and the FR inaccuracy can be made low enough not to be an issue for practical (EQ) purposes.

 

[wakibaki]

On current hardware, 64-bit double precision floats can be used for most DSP algorithms (including EQ) without performance issues. Precision is not a problem (no analog hardware can get close to the "noise floor" of 64-bit floats).

OK.

discrete time (sampling) might be for accurate IIR filter design near the Nyquist frequency;

...what exactly might be a problem in exactly what circumstances? You want a higher sample rate to ease the filter design?

...however, this does not result in non-linear distortion, and the FR inaccuracy can be made low enough not to be an issue for practical (EQ) purposes.

Can't follow you here, possibly because the bit about the IIR filter, discrete-time sampling and Nyquist frequency went past me.

w

 

[stv014]

I meant the filters might not have exactly the same response as the analog filters they are emulating. For example, a simple parametric EQ that adds a boost of 6.02 dB at 18 kHz with a Q of 2 has a frequency response like this at 44.1, 88.2, and 176.4 kHz sample rate (click to zoom):

Ideally, the response should be symmetrical on a logarithmic X scale, but it gets "compressed" towards the Nyquist frequency. Of course, this is a somewhat extreme example with a center frequency of 18 kHz, and it is normally not a major problem in practice (note that I did have to change the Q at the lower sample rates to better match the FR graphs, but that could have been avoided with better EQ code). Especially since for equalizing by ear, it does not matter if some theoretical EQ curve is perfectly matched. Nevertheless, some EQ plugins can actually oversample the signal to more accurately emulate the "ideal" analog filters.
 
With FIR filters, the limitation is the frequency resolution, depending on the length of the impulse response. Although modern CPUs are fast enough to convolve with IR lengths of millions of samples in real time, so this is again not much of an issue for practical (EQ) purposes.
 
Of course, none of the above has anything to do with non-linear distortion, only the accuracy of the frequency response.

 

[riverlethe]

1% THD is only -40dB, so that seems like a pretty low standard., even for an "objective" audiophile.

 

[bigshot]

With speakers, you generally have a room tone of about 30dB. Add that to the 40dB and you're up to an output level that is normal for listening to music. 1% is the threshold. It's good to be a little below the thresholds.

 

[riverlethe]

With speakers, you generally have a room tone of about 30dB. Add that to the 40dB and you're up to an output level that is normal for listening to music. 1% is the threshold. It's good to be a little below the thresholds.

1. So, this wouldn't apply to headphones.

2. Who only listens at 70dB?

 

[bigshot]

With headphones the ambient tone would be lower, so the THD threshold would be a little lower... perhaps around .5dB. Pro grade digital equalizers aren't that expensive and they don't add anywhere near 1dB of distortion. Most modern electronics perform more in the range of .1%. THD which is well below audibility. But remember the headphones or speakers themselves add distortion at levels considerably higher than electronics. It's not likely you'd even hear the threshold unless your heaphones or speakers were remarkably clean.

70dB is a pretty typical medium loud listening volume. People sometimes listen louder, but not that much louder. Comfortable normal listening level is between 45 and 60dB, depending on how compressed the music is.

 

[ab initio]

1. So, this wouldn't apply to headphones.

2. Who only listens at 70dB?

 

With headphones the ambient tone would be lower, so the THD threshold would be a little lower... perhaps around .5dB. Pro grade digital equalizers aren't that expensive and they don't add anywhere near 1dB of distortion. Most modern electronics perform more in the range of .1%. THD which is well below audibility. But remember the headphones or speakers themselves add distortion at levels considerably higher than electronics. It's not likely you'd even hear the threshold unless your heaphones or speakers were remarkably clean.

70dB is a pretty typical medium loud listening volume. People sometimes listen louder, but not that much louder. Comfortable normal listening level is between 45 and 60dB, depending on how compressed the music is.

 
Just to clarify this, I believe bigshot's quoting RMS (i.e., the typical average) listening levels in the 45--70dB SPL range while riverlethe seems to think that this figure is low. I think the confusion stems from the forum's discussions on target maximum SPL people desire from their headphone+amp combinations to be capable or reaching, but certainly not for extended listening, and the typical number quoted for that is 110dB (ish) SPL. (Here, SPL = Sound Pressure Level and is given in dB referenced to the typical human threshold of hearing around 20 microPascals). There is a big, big, big difference between peak sound pressure levels and the typical sound pressure levels. If a recording is particularly dynamic, the peak SPLs could be +20 dB or more than the rest of the recording. One of my favorite examples of this is in King Crimson's "Lizard":
 

 
 
At the beginning of the piece is "Prince Rupert Awakes," a part of which is shown in the figure. Jon Anderson provides guest vocals, which are pretty quiet. For example, from t = 5 seconds to 10 seconds (highlighted in green), the RMS level is 0.0057 of full scale, which is -44.8 dB. The peak level during this section is 0.0258, or -31.8 dB.
 
After Jon finishes his verse, Andy McCulloch's drums come pounding in (see the bit highlighted in red), which is a huge dynamic change. Here, the RMS levels during this section are 0.0537 (-25.4 dB) while the peaks of the drums reach 0.3573 (-8.9 dB) (and even exceed it in the blue part immediately after the red!). Overall, the recording ranges from RMS levels of -44.8 dB to a peak value of -1.9 dB.
 
That's a 42.9 dB range in the recording between the RMS value of the nominally quite part to the loudest drum strike. If you were listening to the piece on your system, you'd probably have typical volume parts around 60dB SPL or so (like the red bit in the figure above), which puts the quite parts around 40dB SPL. Meanwhile, your system will stlil have to reproduce the peak transients that would be at 83dB SPL.
 
Perhaps you're like me, and you really like the piece and want to hear Jon Anderson (Yes!) sing with Fripp and friends, so you turn the thing up until the quiet bit is medium-loud (say 60 dB SPL), then the typical parts of the music are a loud 80 dB SPL and the peak transients are over 100 dB SPL.
 
So, hopefully this little example helps to illustrate the difference between the average (RMS) listening loudness versus the peak transient loudness levels. To sum it up, bigshot's number of 45--60dB SPL is certainly in the ball park of listening levels. Meanwhile, the 110 dB SPL levels that seem to get quoted all over these message boards are for Peak SPL levels and one certainly should never listen to their music at 110 dB RMS SPL levels under any circumstances (unless they hate their hearing!). There can be a big difference between the RMS loudness of a piece of music and the peak level. Conversely, it is also possible that the RMS and peak loudesses are very close to one another ( equality holds in the case of a square wave, or metallica's "death magnetic" \end{snark})
 
Cheers

 

[bigshot]

Exactly. The loudness of quick transient peaks doesn't tell you anything about how loud the music sounds. That depends on the overall average volume and the degree of compression.

And when it comes to distortion, good speakers can have as high as 3% distortion and still sound good. In most cases, with solid state equipment, distortion is not a problem. It certainly isn't an issue with a good equalizer. An equalizer improves the sound, it doesn't audibly degrade it.

 

[stv014]

An equalizer improves the sound, it doesn't audibly degrade it.

 
That is, of course, assuming competent usage.

 

[ximen]

Provided the system is linear then basically yes the frequency response is it. It is the real world non-linearity (distortion essentially) of things that can lead to a frequency response looking identical to another but in fact having a different 'sound'. As someone else mentioned, in the end it is all about whether or not the assumptions on which a frequency response measurement are built hold true or not, for any fairly decent headphone they are going to be true enough.