is this distortion or what

http://www.carterdemo.com/sinewaves.htm

i recorded some sine waves in protools tonight. i looked at the waves zoomed in close after the fact. i had already thought that there must be some distortion to a sine wave that gets sampled at 44.1, which equals 2 samples per cycle for a 20k sine sinew wave. i had always thought that there was no way to reproduce the wave accurately, since you can only get 2 slices of the wave during its cycle. i have never heard of this as distortion. what would you refer to this as? the 20 hertz looks great. after about 2.5k the sine wave turns more radically into a triangle.

possible wrong forum though

I have done the same experiment in pro tools with the same result.
Maybe converter distortion?Don't really know.
Wish I had an o-scope.

> i looked at the waves zoomed in close after the fact. i had already thought that there must be some distortion to a sine wave that gets sampled at 44.1, which equals 2 samples per cycle for a 20k sine wave. i had always thought that there was no way to reproduce the wave accurately,

Play it back through a steep 20KHz low-pass filter into a linear oscilloscope.

You will find perfect sinewaves again.

The points are at just the right places to regenerate a sine.

If you define "signal" as "just the stuff at or below 20KHz", then by definition you can't have harmonic distortion of a 20KHz wave. The harmonics are 40KHz, 60KHz, etc. Even without a low-pass filter, if you play these jaggy-waves through a clean channel to an average human ear, they will be "undistorted". All the flaws are supersonic.

The theorem holds even for multi-tone signals. There won't be any IM distortion below 20KHz and above -96dBfs (or whatever bit-depth you use).

> after about 2.5k the sine wave turns more radically into a triangle.

The "triangle" is your display tool connecting the dots. What you really have is discrete samples, without connecting lines. Your display tool is using straight-line connect-the-dots. A low-pass filter will use a least-bend smooth-curve method to connect the dots. "Points" will be rounded.

Here is how CoolEdit displays a 19.990KHz wave, as discrete samples and with a 22KHz (1/2 of 44KHz sample rate) connect-the-dots method:


This is actually the simplest way to connect the dots with no curve sharper than what can pass a 22KHz filter. (A real filter can't be infinitely steep: 48KHz and 44KHz sample rates were picked to pass 20KHz with a little leeway for practical filtering.)

PRR,

You are too freakin' cool man! THanks for 'splainin' that. I have always wondered, and for lack of a better explanation I always eventually diverted my thoughts to more meaningful questions....since the sound was always okay to my ears.

Thanks!
Shane

o.t. cool edit 96/32 is a nice program for creating brainwave binaural beats. another program that is awesome for this is bwgen. very fun stuff for trippy head stuff. worth fooling around with for the mind effects.

regarding the 20k waves: i guess it is hard for me to comprehend, because it seems that at 44100 a 20k cycle is sampled approx 2.2 times for a complete cycle. i can understand connecting the dots, but are you saying that the connecting of the dots is an oversampling method of playback, or just for drawing purposes? i just don't see how you can accurately reproduce a wave that only got 2.4 slices taken. if the sampler fills in the blanks, or connects the dots, how does it know whether it should be drawing a sine wave, trinagle, saw etc? i just see it as--- a voltage reading is taken at one point in time, then another voltage reading is taken 1/44100th of a second later.

i appreciate your showing the cool edit sine wave. if you had sampled a 20k triangle, would you get a triangle as a result as well? i guess i can attempt it myself later tonight as i have the cooledit96

For some explanation on sampling theorem and why 20khz is accurately represented at a 40k sampling rate you might look into these resources.

Free DSP book:
http://www.dspguide.com/

Also go to Dan Lavry's forum on PSW and read all the threads on sampling rates. Especially the 'eq for 192' and ones on high sample rates
http://recforums.prosoundweb.com/index.php/f/38/5989/?SQ=c88fe1289f24c282d0045015474023fc

Lavry Engineering has some tech docs on the topic as well, go to the support page
http://www.lavryengineering.com

Brian

Buz's references will probably explain in great theoretical detail. Let me try a common-sense no-theory approach:

> if you had sampled a 20k triangle, would you get a triangle as a result as well?

A 20KHz-22KHz lowpass is essential to clean output from a 44KHz sampled-data system. If you don't low-pass input and output, you DO get all sorts of garbage.

Now don't think digital, think pure analog: run a 19,999Hz triangle through an infinitely sharp 20,000Hz low-pass. What is the output? It will be a pure sine. Same for a 19,999Hz square wave, or the 19,999 partial of a cymbal-crash that spews over the range 2,000Hz to 40,000Hz. As you approach the upper end of the low-pass band, the ONLY thing that can come out is sine waves. Any detail is smoothed-over. And the ear does not hear anything higher than 20KHz.(*)

In fact, put a low frequency square wave through a VERY high-Q (about Q=50) 2KHz bandpass. The output will be a pure decaying 2KHz sine repeating at the square-wave rise-points. If you can actually find a high-Q analog filter, this experiment is very clear. Since we don't love sine-waves and prefer complex tones that cover much of the 20Hz-20KHz range, we use systems that have a 20KHz low-pass.

(*) OK, this is simply a convenient approximation. Young people do hear above 20KHz. Personally, I have not heard above 17KHz in years, and probably much less today. And there is evidence that higher partials "matter", though some of it may be nonlinearity aliasing higher tones into the audible range that are noticed when they are missing. But when going to higher cut-off frequencies, problems increase (need more/faster tape, or more data bits) and benefits decrease (40KHz is not twice as good as 20KHz, and for most people 40KHz isn't at all better than 20KHz). We have to draw a line somewhere. 20KHz is traditionally "enough". Many recordists today prefer to work to 40KHz bandwidth (96KHz sampling): it may be better, and the price of bits is low enough that it isn't a concern.

buz thanks for the reading tips, very interesting stuff. prr i greatly appreciate the detailed response. i certainly learned a great deal from the info.

As you approach the upper end of the low-pass band, the ONLY thing that can come out is sine waves. Any detail is smoothed-over

Click to expand...

in essense, what you are saying regarding the output: high freq stuff all seems to come out as a sine wave(that is, if i am reading you correctly). therefore, if you put in a triangle/square/etc wave, and you get out a sine, but that is still distortion? correct? and the sine wave not being as pleasing as complex waves, would this contribute to the worn out analog vs. digi debate? i am ignorantly assuming that a highend phonograph or tape player will more accurately reproduce complex waveforms.

i originally was trying to understand this high end thing after recently receiving from a well knowm tdm plugin maker, a set of all his eqs, comps, etc. included was a tape simulator. there are numerous controls on the thing, bias, bump, ips etc. i noticed on some of the simulations, there is a distinct highend roll off. in using the roll off, i started to find the music more pleasing.

i had been listening to the radio in my car, which has a pretty nice system, and i was trying to figure out what was lacking in my studio mixes compared to the car radio(FM). the obvious occured to me that FM is not full bandwidth(at least i have heard that). the other part is some obvious mastering, radio compression and possible stereo enhancement. anyways, it seems that the reduction of highend appeals to me, so i was trying to see if it was because of distortion, or just to much of the highs.

i am concluding that digital high end is irritating to some extent, relative to analog.

> i am ignorantly assuming that a highend phonograph or tape player will more accurately reproduce complex waveforms.

At 7.5 or 15ips, tape will have a pretty steep low-pass filter at the top of the frequency response. You have to FIGHT to get the top octave to go on and off of tape: use micro-fine oxide, big recording boost, ultra-thin playback gap. You can only peak it up so far, then you have to give up, and it falls off pretty fast.

And put any shape of 20KHz wave onto 7.5 or 15ips tape, it will come back all rounded and sine-y.

Yes, pros like 30ips. Partly because it isn't a big fight to get 20KHz on and off, but also because the S/N ratio improves from OK to good.

Do note that there is NO musical instrument that plays 20KHz. The highest fundamentals are 4KHz, and rarely played. (Think what the top note of most pianos sounds like!) A 4KHz fundamental will have 8KHz, 12KHz, 16KHz, and 20KHz harmonics. 24, 28, and 32KHz, too though maybe only your dog will notice. However all real instruments have roll-offs too, and in fact a piano makes very little output above 6KHz or 10KHz. That's part of why the top note is so "tink-y": it does not have a lot of overtones, the darn string is too stiff, the soundboard too damped to make or pass 5KHz and up. Piccolo will blow 4KHz and several harmonics, but a 20KHz wave mostly gets sideways in the pipe and self-cancels. Anything above 15KHz is random blow-noise, not tones.

> in using the roll off, i started to find the music more pleasing.

> i am concluding that digital high end is irritating to some extent, relative to analog.

I'm not sure the observation supports the conclusion.

Many people do hate digital sound. Many possible reasons. The low-pass filter is VERY steep, even steeper than a 7.5ips tape cranked-up to 20KHz bandpass, and has some response ripple and significant internal ringing. People who can hear 23KHz may miss the little bit lost behind a 20KHz filter. Digital "noise" is very low, but very annoying, much more than tape hiss. Digital boxes are designed by digital engineers who don't know squat about that last inch in the analog domain, and are likely to use 4558 chips soaked in digital garbage. And digital tools (like ProTools) allow much more stupid messing with the sound, layered processing we could never afford to do with analog boxes. Rounding errors can accumulate real quick, making a muck of your sound. I learned the hard way to convert to 24-bit before doing any extended whacking on 16-bit audio.

> what was lacking in my studio mixes compared to the car radio(FM).

That is unfair. The "sound" of pop-radio is a VERY big and cut-throat business. There are guys who get big bucks for setting up processing to make a radio station sound louder/better than all others in town, so you will stop and linger on that station (and increase listenership and the value of ad-time). The really spectacular advances(?) in automatic compression and EQ came with radio limiters of the 1980s and 1990s. There is more happening in a good car radio and car speakers. My Honda's speakers are clearly un-flat yet very pleasing.

Also: the mixing engineer should let someone else finish the job. Mastering is really a special art and skill. While the same person can either mix or master, s/he should not do both on the same project. Same reason books and newspapers have writers and also editors. The person who assembles all the little pieces tends to lose sight of the whole pie, and tends to read/see what s/he intended instead of what s/he actually typed or recorded. Let someone else with good ears have a whack at your stereo master and see what difference it makes.

FWIW: US FM is generally limited to 15KHz, and always sharply notched at 19KHz. However I really don't think the difference between 15KHz and 20KHz or even 25KHz is what you are hearing. And I suspect that some FM sound-directors cut above 10KHz, especially loud 10KHz, because many listeners won't hear it, few car speakers handle it well, and dropping the top octave may allow 0.5dB more in the rest of the audio band without overmodulation. (The FM pre/de-emphasis curve predates modern top-heavy music, and a "flat" FM channel can easily over-modulate the highs before the midrange is maxed-out. Same problem on 78s: the NAB-78 EQ was too much for late-1930s musical balance.)

There is some interesting correlation between "pleasing sound", rolloff of high frequencies, and distortion, though. I've been reading that Harry F. Olson book, "Music, Physics, and Engineering" (title possible misphrased), and there was a really interesting section on blind testing (with average audience) on various HF cutoffs with various amounts of distortion. Bear in mind that this was in the fifties, when distortion was still fairly high in a lot of audio equipment.
Anyway, the upshot was that people preferred even a drastic loss of HF to a full-range signal with a couple percent distortion. And that's in the day of "warm tube distortion".