10khz square wave + masterlink = sine wave???

[carival]

I've recently been doing some repairs/testing in my primarily analog studio and I came across something that sort of surprised me. I've been using an Otari mtr-10 as a source for a 10k square wave. It's stored pretty far from the control room, so I've been running a long cable. The square wave looks fine on a scope in the control room. I got tired of the cable, so for convenience, I decided to record it to an Alesis Masterlink. So there you have it. A healthy 10khz square wave feeding the analog input of the Masterlunk, and a perfect sine wave coming out of the analog output. huh?? Setting the recorder for highest resolution changed the wave, but not to a square wave. Now I'm curious, so I tried it with an old 3800 DAT. Same deal. Anybody willing to inform me as to why this occurs?
thanks,
chris rival

[dkatz42]

Originally posted by carival
A healthy 10khz square wave feeding the analog input of the Masterlunk, and a perfect sine wave coming out of the analog output. huh?? Setting the recorder for highest resolution changed the wave, but not to a square wave. Now I'm curious, so I tried it with an old 3800 DAT. Same deal. Anybody willing to inform me as to why this occurs?l

A 10 KHz square wave is "really" an infinite series of sine waves of odd harmonics (at 10 KHz, 30 KHz, 50 KHz, etc.) The low pass filters on your digital machines make sure that there's nothing left above 22.05KHz (or it would alias and things would be ugly) so all you're left with is the first harmonic, the 10 KHz sine wave.

Isn't it cool when reality matches theory?

I bet the "square" wave coming off of your analog machine is something less than square as well...

[carival]

thanks for the explanation. much appreciated!

[space2012]

that answare its unlogic.

square its square. at 10hz or at 25ghz.
wordclock its square wave at 3ghz for 44.1khz 16bits
s/pdif blank its also square

44.1khz does not have enough resolution
chips are not perfect.

a sine at 22050hz at 44.1khz its = 10101010101010101010 = square
but some chips have interpolation, aproximation,
spline, rounding.

that creates the intersample peaks

wordclock jitter can affect the samplig process.

[DeeDrive]

here's some good visuals on the subject:

Fourier synthesis

[memphisindie]

Why the drama, get "un-tired" of the cable, you can't do it with a masterlink.
Buy an oscillator if you don't already have a standalone unit, and put it in the other room.

[nofi]

Originally Posted by space2012

square its square. at 10hz or at 25ghz.

No, it isn't.

"square" is an ideal. A mathematical concept. It has 2 discontinuities in its period, and signals with true discontinuities cannot exist in anything except imagination.

All real world signals are bandlimited in some way, whether you want to look at frequency limits, or slew rates. And as a result all "square waves" generated in hardware or in software, are non-ideal to some extent.

they may happen to look close on a scope, but none of your examples are actual square waves.

[memphisindie]

Originally Posted by nofi

No, it isn't.

"square" is an ideal. A mathematical concept. It has 2 discontinuities in its period, and signals with true discontinuities cannot exist in anything except imagination.

All real world signals are bandlimited in some way, whether you want to look at frequency limits, or slew rates. And as a result all "square waves" generated in hardware or in software, are non-ideal to some extent.

they may happen to look close on a scope, but none of your examples are actual square waves.

Hey, that's right and if a scope can be fooled into showing a square wave that doesn't exist, using that standard to determine that two mic pre's from different manufacturers are identical and then to posit that as empirical data is bogus as well.

[nofi]

Originally Posted by memphisindie

Hey, that's right and if a scope can be fooled into showing a square wave that doesn't exist, using that standard to determine that two mic pre's from different manufacturers are identical and then to posit that as empirical data is bogus as well.

A scope DOES NOT EVER show a square wave.
There's always a finite rise time... therefore the wave is not square.

Once you understand that, it's just a matter of the amount of bandwidth and slew limited channel degradation you're talking about, and the associated reduction of harmonics, till you get to a sine wave.


but yeah..... I wouldn't choose a mic pre based on pictures of two "square" waves that have been through them..... that's ********. Personally, for online comparisons, I'd rather hear mic pres processing real audio.

[Geoff_T]

Originally Posted by carival

I've recently been doing some repairs/testing in my primarily analog studio and I came across something that sort of surprised me. I've been using an Otari mtr-10 as a source for a 10k square wave. It's stored pretty far from the control room, so I've been running a long cable. The square wave looks fine on a scope in the control room. I got tired of the cable, so for convenience, I decided to record it to an Alesis Masterlink. So there you have it. A healthy 10khz square wave feeding the analog input of the Masterlunk, and a perfect sine wave coming out of the analog output. huh?? Setting the recorder for highest resolution changed the wave, but not to a square wave. Now I'm curious, so I tried it with an old 3800 DAT. Same deal. Anybody willing to inform me as to why this occurs?
thanks,
chris rival

Hi

I concur with dkatz42. Even in a totally analogue world, you would have issues with rounding off a 10KHz square wave. Neve always provided a polaroid photo of a square wave response of their consoles but it was a 1KHz wave. I don't think we ever used more than 3KHz for a test square wave.

10KHz square waves are made up of countless higher order frequency sine waves and if you pass it through a low pass filter, you will strip off all the higher frequencies that create the vertical part of the wave and you'll finish up with sloping/rounded wave.

[Audiop]

Originally Posted by space2012

that answare its unlogic.

Talking about "unlogic"..

square its square. at 10hz or at 25ghz.

No one said anything that contradicts that (other than those will not exist in the real world..)

wordclock its square wave at 3ghz for 44.1khz 16bits
s/pdif blank its also square

The precision clocks that I have used in a couple of CD-players and DAC's have a crystal with aprox. 11MHz and 45MHz or so frequency. Where do you find a 3GHz crystal in use for 44.1kHz audio?

44.1khz does not have enough resolution
chips are not perfect.

Not enough resolution for what?

How did you investigate this?

a sine at 22050hz at 44.1khz its = 10101010101010101010 = square
but some chips have interpolation, aproximation,
spline, rounding.

Really?

You are saying that a sine as represented in a PCM system has a fixed sample value?

wordclock jitter can affect the samplig process.

Yes, therefore the use of a precision clock makes sense so that the jitter-induced artifacts stays below the threshold of audibility.


/Peter

[memphisindie]

Wasn't there a big investigation into "precision" wordclock and the outcome was that the clocks were all precision but the connections weren't and they had the biggest effect on clocking along with cable length and voltage output of the clock/distribution?
Clockity clock clock clock.

[d_fu]

Originally Posted by space2012

square its square. at 10hz or at 25ghz.

There is no such thing as a perfect square wave...

44.1khz does not have enough resolution
chips are not perfect.

You are confusing resolution and bandwidth and this has nothing to do with the quality of "chips" (I prefer plain salted...)

a sine at 22050hz at 44.1khz its = 10101010101010101010 = square

Whenever you think you've seen all of the the most ridiculous ideas people have about digital audio, someone comes along and takes ignorance to hitherto unknown levels...

that creates the intersample peaks

Sure. Do you actually make money with audio work?

[EDIT]
Guess I fell for an obvious forum troll. This is a major-league doofus, see e.g. here (at the risk of immediate spontaneous self-combustion of your brain...). Previously posted as "sexxy", until he was banned.

[nucelar]

Originally Posted by space2012

that answare its unlogic.

square its square. at 10hz or at 25ghz.
wordclock its square wave at 3ghz for 44.1khz 16bits
s/pdif blank its also square

44.1khz does not have enough resolution
chips are not perfect.

a sine at 22050hz at 44.1khz its = 10101010101010101010 = square
but some chips have interpolation, aproximation,
spline, rounding.

that creates the intersample peaks

wordclock jitter can affect the samplig process.

I disagree, a 22050 Hz sine at 44.1kHz would be:
x, -x, x, -x, x, -x ...

where x is the digital representation of the ampitude of the incoming voltage.
The DA converter has no means of knowing wether this sequence was originally a sinewave, a squarewave, a ramp or a dalek singing "ahhhhh". DAs use (analog) interpolation filters to constuct the analog waveform. These filters can be more or less sophisticated, but when you smoothly interpolate the above sequence you should get a perfect sine wave.

Nyquist states that the minimum sampling rate must be twice the maximum frequency you wish to represent.
A perfect square wave has infinite bandwith, so you will never be able to sample it accurately. All you get is approximate. Of course the lower the source frequency, the better the approximation, as more harmonics are sampled.

[JohnRoberts]

You guys have too much time on your hands..

An analog square will not convert to a simple digital +x, -x, +x... series. It will be LPF by the A/D conversion scraping off all or most the above band content leaving just the 10k sinewave component.

Why argue with the reality of the OP's observed result?

JR

[Geoff_T]

Originally Posted by JohnRoberts

You guys have too much time on your hands..

An analog square will not convert to a simple digital +x, -x, +x... series. It will be LPF by the A/D conversion scraping off all or most the above band content leaving just the 10k sinewave component.

Why argue with the reality of the OP's observed result?

JR

Amen!

[sysexguy]

Freshman's rule of calculus:

lim (n-->infinity) sinx/n = 6 (the n's cancel)

Andy

[cornutt]

Originally Posted by d_fu

[EDIT]
Guess I fell for an obvious forum troll. This is a major-league doofus, see e.g. here (at the risk of immediate spontaneous self-combustion of your brain...). Previously posted as "sexxy", until he was banned.

I thought I recognized that particular flavor of rambling nonsense!

[space2012]

Originally Posted by nofi

No, it isn't.

"square" is an ideal. A mathematical concept. It has 2 discontinuities in its period, and signals with true discontinuities cannot exist in anything except imagination.

All real world signals are bandlimited in some way, whether you want to look at frequency limits, or slew rates. And as a result all "square waves" generated in hardware or in software, are non-ideal to some extent.

they may happen to look close on a scope, but none of your examples are actual square waves.

ther is AC Alternate Current and DC Direct Current,
Alternating current - Wikipedia, the free encyclopedia
Direct current - Wikipedia, the free encyclopedia

music is AC, Digital equipment is DC

infinite sines are used to emulate DC in AC circuit.
also called additive synthesis.

Square is true DC.
true DC is Square.

Slew rate - Wikipedia, the free encyclopedia
slew rate is for high current equipment,
like AC power amplifiers.
for smaller values is called the rise time and the fall time .

square emulation can also be made with Sine + HardClipping/overload/saturation in AC.

Digital sound is Binary = DC.
DC does not have a negative value.
from 0v to what ever the circuit design, usually 5V.

AC has negative value.
Square wave - Wikipedia, the free encyclopedia


Digital audio - Wikipedia, the free encyclopedia



Sampling rate - Wikipedia, the free encyclopedia


Word clock - Wikipedia, the free encyclopedia

Biphase mark code - Wikipedia, the free encyclopedia


Signal bitrate is 2.8Mhz (Fs=44.1kHz), 2Mhz (Fs=32kHz) and 3.1Mhz (Fs=48kHz).


epanorama.net/S/PDIF Interface

[space2012]

Originally Posted by Audiop

The precision clocks that I have used in a couple of CD-players and DAC's have a crystal with aprox. 11MHz and 45MHz or so frequency. Where do you find a 3GHz crystal in use for 44.1kHz audio?

epanorama.net/S/PDIF Interface
Signal bitrate is 2.8Mhz (Fs=44.1kHz), 2Mhz (Fs=32kHz) and 3.1Mhz (Fs=48kHz).

read the brochures for high quality s/pdif cable, gepco, etc... and see the freq. responce measurenments over 2ghz.

some Manufacturers,
to lower clock jitter in DACs, and sampling jitter in the ADC, usuallly use a higher crystal clock, and divide the clock, to achieve a lower clock jitter signal.
also some manufacturers use two crystals, one for 44.1khz and multiples x2 88.2khz x4 176.4khz, and other crystal for 48khz and multiples: 2x 96khz, 4x 192khz

for example: all atomic clocks are 10Mhz sine.
CESIUM ATOMIC CLOCKS
Atomic clock - Wikipedia, the free encyclopedia

the opposite of ADAT, and MADI, that mutiply the clock signal. also multiply the jitter.
RME: Support TechInfo
heavily jittery MADI data signal. The embedded MADI clock suffers from about 80 ns jitter, caused by the time resolution of 125 MHz within the format. Common jitter values for other devices are 5 ns, while a very good clock will have less than 2 ns.
The picture to the right shows the MADI input signal with 80 ns of jitter (top graph, yellow). Thanks to SteadyClock this signal turns into a clock with less than 2 ns jitter (lower graph, blue).


Jitter - Wikipedia, the free encyclopedia
Higher clock frequencies have commensurately smaller eye openings, and thus impose tighter tolerances on jitter.

A digital clock signal is a square-wave with a "fixed" frequency and amplitude and, desirably a 50% duty cycle.
welcome to www.jitter.de
welcome to www.jitter.de
there is no such thing as a jitter-free clock!
but atomic clocks are near with 0.03ppb or +- 0.00003ppm

read all the brochures & manuals of wordclocks like TEAC esoteric, Antelope 10M, Drawmer M-Clock, lucid genx192, BLA microclock, apogee big ben, mutec iclock, dCS 995 verona, etc.., etc...

Originally Posted by Audiop

Not enough resolution for what? /Peter

for sampling 100% accurate, 100% all fundamentals and harmonics.

[space2012]

Originally Posted by nofi

A scope DOES NOT EVER show a square wave.
There's always a finite rise time... therefore the wave is not square.

Once you understand that, it's just a matter of the amount of bandwidth and slew limited channel degradation you're talking about, and the associated reduction of harmonics, till you get to a sine wave.


but yeah..... I wouldn't choose a mic pre based on pictures of two "square" waves that have been through them..... that's ********. Personally, for online comparisons, I'd rather hear mic pres processing real audio.

clipping:

[space2012]

Solid State Logic | Music#

[top]Inter-Sample Peaks

When a digitally-recorded sound is played-back it must be converted into an analogue representation at some point. This is performed by the DAC (digital to analogue converter). Commonly used over-sampling DACs apply a ‘reconstruction’ filter to convert the periodic sample levels back into a discrete signal. In simple terms they ‘fill in the gaps’ using interpolation so that digital artefacts are reduced to a minimum.
Regardless of the reconstruction filter’s design, in certain circumstances it is possible for a reconstruction filter to produce signals greater than 0dBfs even if the samples used to create these signals are all within the 0dBfs limit.
Take the following example:



Here is a portion of a high frequency sine wave that is represented in the digital domain by 4 consecutive samples. The line that joins these points is the product of an interpolation algorithm designed to provide a smooth, discrete wave between the points.
As can be seen, all 4 samples have a value of less than 1.0 (0dBfs in this case) but the smooth line joining the points clearly contains values which are greater than 1.0. It is this mechanism which can cause analogue signals to theoretically exceed 0dBfs even though the digital representation of the signal is within limits. This is an ‘Inter-sample Peak’.
It can be seen that it is possible for all of the digital samples to be below full scale but they could still produce a signal which has sections which are >0dBfs.
The current trend to produce louder and louder mixes ultimately can result in commercial recordings containing more inter-sample peaks than those of say 20 years ago. In reality, a highly compressed piece of audio that has been normalized to digital full-scale is almost guaranteed to have some samples in similar positions to those in the example above, and therefore the audio at an oversampling DAC is almost guaranteed to have inter-sample peaks of >0dBfs!

[top]Is this a problem?

As already mentioned, the reconstruction filter is typically part of common Digital to Analogue converters (DAC) and the quality of this process is a factor in the overall quality of the DAC. Low quality DACs may not have the digital resolution to handle values larger than full-scale, and subsequent analogue stages may not have the headroom to handle signals larger than the theoretical maximum. Another possibility is that the DAC may be quite capable of handling >0dBfs but the surrounding design may not have taken this eventuality into consideration.

[memphisindie]

Just get out of prison?

[RyanC]

Space-

The thing is 0101010 only describes a 1 bit signal.

Assuming 24bit PCM audio data, then it would possibly be 00000000000000000000000,
and 111111111111111111111111, and so on.

From my understand this (in 16 bit) is the language used by redbook CD (and why NOS DACs work). However there is nothing that would prevent a language from being created where 1010 etc was + max and 0101 etc is - max.

Your wiki thing there shows a 4 bit digital signal, each of the 16 values can be assigned with any 4 bit word the format creator wanted to use. These do not HAVE to logically translate to analog values (although for the sake of easiness they probably do in most cases).

The signal bit rate for the actual clock is running at each I or O in the digital stream (not the byte words but each single presence or lack of voltage). So for stereo 44.1/24 bit is 2.1168 MHZ. This is simply 2*44100*24= how many times there will be either voltage or a lack thereof. Spdif is higher (2.8224) because it is actually a 32 bit stream, and the extra bits are used for preambles, stereo delineation and other meta data. Consider the way a lynx aurora can talk to their AES cards (the extra 8 bits at work).

Also calling digital equipment direct current is not very accurate; the whole basis of digital is the ALTERNATING between signal and no signal. Granted it is between DC and nothing, but if it didn't turn it on and off, it wouldn't work. That's what the 1's and 0's are supposed to represent; actually I for input, and O for off.