A concise explanation of digital vs. analog?

Discussions about anything analog, digital, MIDI, synth technology, techniques, theories and more.
User avatar
synthroom
Senior Member
Senior Member
Posts: 879
Joined: Sat Sep 08, 2012 3:16 pm
Real name: Kirk
Gear: Fairlight IIx(!), JP-8, D-50, S-50+550, S-760, JX-3P, JD-800, EII, Emax II, Mini, ARP 2600, P-5 Rev.1, Pro-One, Performer, K1m, K5m, few other things.
Location: pdx
Contact:

Re: A concise explanation of digital vs. analog?

Post by synthroom » Fri Nov 22, 2013 5:16 pm

silikon wrote:
That is an excellent explaination!
Fairlight IIx (Mid-Life Crisis - cheaper than a Corvette!)
Roland JP-8, D-50, S-50, S-550(2x), S-760(2x), JX-3P, JD-800
EII, Emax II, Minimoog, ARP 2600, P-5 Rev.1 (broken...), Pro-One, Crumar Performer, K1m, K5m, MS-2000B, Virus KC, a few other things.

User avatar
madtheory
Supporting Member!
Supporting Member!
Posts: 5424
Joined: Mon May 01, 2006 12:45 pm
Real name: Tomas Mulcahy
Gear: Wurlitzer Opus 1536, Model F, Morovdis Arpeggiator, Maplin My First EQ, Jeff Wayne Thunderchild rack, Thermostat, Buck Owens' Moog.
Location: Cork, Ireland
Contact:

Re: A concise explanation of digital vs. analog?

Post by madtheory » Fri Nov 22, 2013 9:36 pm

commodorejohn wrote:The problem here is that you keep trying to make this about digital-sucks-versus-digital-is-cool and analog-totally-has-limitations-too when that's not what the discussion ever was, and until that stops we're just going to go 'round and 'round the mulberry bush until the end of time.
Only if YOU want to. That's why I said "flaws of a similar magnitude". To expand on that, a DAC/ADC needs amplifiers, those are still analogue so it makes no sense to separate the two. False dichotomy.

Just admit you learned something new and are no longer propagating a myth :)

commodorejohn
Synth Explorer
Synth Explorer
Posts: 1589
Joined: Mon Aug 12, 2013 2:39 am
Real name: John
Gear: Roland JX-10/SH-09/MT-32/D-50, Yamaha DX7-II/V50/TX7/TG33/FB-01, Korg MS-20 Mini/ARP Odyssey/DW-8000/X5DR, Ensoniq SQ-80, Oberheim SEM
Location: Sacramento, CA
Contact:

Re: A concise explanation of digital vs. analog?

Post by commodorejohn » Fri Nov 22, 2013 10:16 pm

It's like talking to a brick wall. Once again: Digital-to-analog converters, in base form, output a stream of values correspondent to the numeric values fed into them. These numbers are presented in a fixed number of bits and therefore have a lower limit on their granularity. This causes artifacts in the output due to quantization of the signal from its original input into an ADC. The fact that DACs commonly integrate filters to smooth out the output and remove these artifacts does nothing to change that fact.
Computers: Amiga 1200, DEC VAXStation 4000/60, DEC MicroPDP-11/73

User avatar
madtheory
Supporting Member!
Supporting Member!
Posts: 5424
Joined: Mon May 01, 2006 12:45 pm
Real name: Tomas Mulcahy
Gear: Wurlitzer Opus 1536, Model F, Morovdis Arpeggiator, Maplin My First EQ, Jeff Wayne Thunderchild rack, Thermostat, Buck Owens' Moog.
Location: Cork, Ireland
Contact:

Re: A concise explanation of digital vs. analog?

Post by madtheory » Fri Nov 22, 2013 10:35 pm

Stop trying to move the goalposts: "in base form" is nonsense, because that would violate Nyquist. No one makes a converter in "base form". What you originally stated was the stair step myth, which lead you to your current misunderstanding.

Here, you should read this:
http://en.wikipedia.org/wiki/Nyquist%E2 ... ng_theorem

Or Monty's video. You have watched that, yes?

commodorejohn
Synth Explorer
Synth Explorer
Posts: 1589
Joined: Mon Aug 12, 2013 2:39 am
Real name: John
Gear: Roland JX-10/SH-09/MT-32/D-50, Yamaha DX7-II/V50/TX7/TG33/FB-01, Korg MS-20 Mini/ARP Odyssey/DW-8000/X5DR, Ensoniq SQ-80, Oberheim SEM
Location: Sacramento, CA
Contact:

Re: A concise explanation of digital vs. analog?

Post by commodorejohn » Fri Nov 22, 2013 10:45 pm

Gah. Even putting aside that they do make cheapo no-filter DACs which see use in, say, crappy Chinese toys (if I had a nickel for every craptastic toy piano/talking action figure/etc. I've seen that relies on the plastic case/speaker grille to filter out the noise that the actual sound generator produces, I'd have approximately what they make in markup over the manufacturing cost for one,) your own link contradicts you:
The Exact Article That You Linked, Emphasis Mine wrote:Practical digital-to-analog converters produce neither scaled and delayed sinc functions, nor ideal Dirac pulses. Instead they produce a piecewise-constant sequence of scaled and delayed rectangular pulses, usually followed by a "shaping filter" to clean up spurious high-frequency content.
Your argument is like saying that because good vodka has all the impurities filtered out, no vodka ever has impurities...
Computers: Amiga 1200, DEC VAXStation 4000/60, DEC MicroPDP-11/73

User avatar
Stab Frenzy
Moderator
Moderator
Posts: 9723
Joined: Tue Jun 06, 2006 5:41 pm
Gear: Eurorack, RYTM, Ultranova, many FX
Location: monster island*
Contact:

Re: A concise explanation of digital vs. analog?

Post by Stab Frenzy » Sat Nov 23, 2013 4:35 am

commodorejohn wrote:It's like talking to a brick wall.
Admitting that is a good start, next you should try to admit that you don't know everything and in this case you just leant something new. :thumbleft:

This is now so far off topic it's ridiculous, but here it is one more time:

DACs don't output a series of values, they output a smooth analogue waveform. They're fed a series of values to get the resulting analogue waveform right, which is where you're getting confused.

The giveaway is in the name, Digital to Analogue Convertor. The input is digital (series of values) the output is analogue (smooth continuous waveform). Your 'in its most basic form' example that you keep trying to bring up is not a DAC. If the output isn't a smooth analogue waveform then it's not a Digital to Analogue Convertor, it's a digital base 2 (binary) to digital base 65,536 (for 16 bit audio, or whatever the corresponding size is for the bit depth of the input) convertor. :idea:

commodorejohn
Synth Explorer
Synth Explorer
Posts: 1589
Joined: Mon Aug 12, 2013 2:39 am
Real name: John
Gear: Roland JX-10/SH-09/MT-32/D-50, Yamaha DX7-II/V50/TX7/TG33/FB-01, Korg MS-20 Mini/ARP Odyssey/DW-8000/X5DR, Ensoniq SQ-80, Oberheim SEM
Location: Sacramento, CA
Contact:

Re: A concise explanation of digital vs. analog?

Post by commodorejohn » Sat Nov 23, 2013 6:05 am

Stab Frenzy wrote:The giveaway is in the name, Digital to Analogue Convertor. The input is digital (series of values) the output is analogue (smooth continuous waveform). Your 'in its most basic form' example that you keep trying to bring up is not a DAC. If the output isn't a smooth analogue waveform then it's not a Digital to Analogue Convertor, it's a digital base 2 (binary) to digital base 65,536 (for 16 bit audio, or whatever the corresponding size is for the bit depth of the input) convertor. :idea:
What. "Analog" in audio reproduction does not mean "smooth and not stepped," it means that the voltage in the line is proportional to the level of the signal. That is all that it means. It is entirely within the realm of possibility for analog audio signals to be stepped. A DAC converts numbers in digital format to proportionate analog line levels; it is not "not a DAC" if it doesn't include a filter to smooth out the result. It's just a crappy DAC.
Computers: Amiga 1200, DEC VAXStation 4000/60, DEC MicroPDP-11/73

User avatar
ninja6485
Synth Explorer
Synth Explorer
Posts: 2771
Joined: Sun Apr 19, 2009 10:13 pm
Gear: Virus Ti, Jx-8p, Juno 60, Radias, Maschine, 101,303,606,707,727,808,909, odyssey, mirage, akai s5K/s2K/s1k, drumtraks, E6400ult, M1R, rx5, fizmo,d50
Band: Subliminal Sea
Location: Exton/ westchester
Contact:

Re: A concise explanation of digital vs. analog?

Post by ninja6485 » Sat Nov 23, 2013 7:41 am

Before this gets locked in an embarrassing ensemble of butt-hurt and bruised egos:

This was a great post!
cornutt wrote:Hmm. Let's do the math. Take your garden variety 16-bit DAC, set up for an output voltage range of 0 to 10 volts. 16 bits provides 65536 (2^16) possible output values. Assuming the DAC's output is scaled linearly, the step increment between any two adjacent values is about 0.15 millvolts. Any value N that I send the DAC will result in an output that is N * 0.15 mV.

The DAC will hold that output value until I send it another value. When I do send it another value, its output will jump more or less instantaneously to the new value. If I send it output values on a periodic basis, I can approximate a waveform. The "easiest" waveform to reproduce with the DAC is a square wave. To make a square wave, I send it output value A, let that hold for a period of time, send it output value B, let that hold for an equal period of time, send output value A again etc. How fast I can send these values determines the maximum frequency of square wave I can produce. I need to send two values (A once and B once) for each cycle. So if I can send values to the DAC at a rate of, say, 16000 times per second, then given that I need to send two per output cycle, the maximum frequency of square wave I can produce is 8 KHz.

We can use the DAC to send values that allow us to approximate other waveforms. However, any other waveform we generate is going to have the frequency spectrum of a square wave imposed on it. How "loud" this square wave is in the output depends on the waveform we're approximating, but it's always there to some extent or another. The fundemental frequency of this square wave is half of the DAC output rate, per our example above. This is why we need output clocking filters: to get that unwanted square wave out of the output. The filter has to take effect at a low enough frequency to get adequate cutoff of the square wave fundemental. As a practical consequence, this usually means we need to set up the system so that frequency is somewhat above the highest frequency that we wish to produce in the output, since practical filters have finite slope.

Most pro audio ADC/DAC systems operate at a minimum frequency of 48 Khz. That gives a frequency for the "clock" square wave fundemental of 24 KHz, above the maximum 20 KHz frequency that we generally take as the top end of the audio spectrum. Back in the day, the sampling frequency for the ordinary audio CD format was chosen to be 44.1 KHz, giving a clock frequency of 22.05 KHz, just barely above the 20 KHz maximum desired frequency. This caused a lot of problems with early CD players since the difference is only about 1/10 of an octave, and with technology of the day it was very difficult to build a filter that would go from passband to a high degree of rolloff in that short a span, and early CD systems had a lot of problems with the clocking filters not being flat at the upper end of the audio spectrum, producing a variety of undesirable effects. Filters have gotten better since then, but the trend in pro audio has been to go to much higher sampling frequencies to move the clock frequency further away from the audio band, which makes it easier to build a good clock filter.

Incidentally, the above applies to any sampling process, whether it's analog or digital. Analog delays that use bucket-brigade samping have the same problems with stepping and needing clock filters.

Learned me somethin' fierce 8-) :idea:
This looks like a psychotropic reaction. No wonder it's so popular...

User avatar
madtheory
Supporting Member!
Supporting Member!
Posts: 5424
Joined: Mon May 01, 2006 12:45 pm
Real name: Tomas Mulcahy
Gear: Wurlitzer Opus 1536, Model F, Morovdis Arpeggiator, Maplin My First EQ, Jeff Wayne Thunderchild rack, Thermostat, Buck Owens' Moog.
Location: Cork, Ireland
Contact:

Re: A concise explanation of digital vs. analog?

Post by madtheory » Sat Nov 23, 2013 11:50 am

Ya, that is a great post.

Ya, brickwall, that was funny :)

Now commodorejohn is talking about DACs used in cheap plastic toys. If he can give an example of one being used for actual audio for music, I'm all ears. But it's an interesting example. I would imagine even something that cheap has a c**p reconstruction filter made of an RC network, no? You do need some intelligibility so people will buy the toy.

There is no contradiction in the wiki, it's actually spot on. A pulse is still NOT a stairstep. It's a series of pulses, which are actually points averaged in time. Hence PCM.

User avatar
Black Tomorrow
Active Member
Active Member
Posts: 367
Joined: Sat Apr 15, 2006 7:52 am
Real name: kp Catalano
Gear: MG-1, V-Synth w/ VC1, Poly800, PSR740, Triton, SHS10, Boss DR770, Stylophone, Hammond M-143, acoustic piano, reed organ, didgeridoo, Garritan library.
Location: North Carolina
Contact:

Re: A concise explanation of digital vs. analog?

Post by Black Tomorrow » Sun Nov 24, 2013 7:25 am

Another thing to consider...

Unless my understanding of how the universe works is wrong, you still need time to "jump" from one value to the next, and that by itself would be a factor in reducing the "stair step" effect. Same reason there's no such thing as a perfect square wave, yadda yadda...
You can't synthesize love

commodorejohn
Synth Explorer
Synth Explorer
Posts: 1589
Joined: Mon Aug 12, 2013 2:39 am
Real name: John
Gear: Roland JX-10/SH-09/MT-32/D-50, Yamaha DX7-II/V50/TX7/TG33/FB-01, Korg MS-20 Mini/ARP Odyssey/DW-8000/X5DR, Ensoniq SQ-80, Oberheim SEM
Location: Sacramento, CA
Contact:

Re: A concise explanation of digital vs. analog?

Post by commodorejohn » Sun Nov 24, 2013 7:35 am

Well, technically, yes, but on the scale of human hearing that's basically irrelevant.
Computers: Amiga 1200, DEC VAXStation 4000/60, DEC MicroPDP-11/73

User avatar
madtheory
Supporting Member!
Supporting Member!
Posts: 5424
Joined: Mon May 01, 2006 12:45 pm
Real name: Tomas Mulcahy
Gear: Wurlitzer Opus 1536, Model F, Morovdis Arpeggiator, Maplin My First EQ, Jeff Wayne Thunderchild rack, Thermostat, Buck Owens' Moog.
Location: Cork, Ireland
Contact:

Re: A concise explanation of digital vs. analog?

Post by madtheory » Sun Nov 24, 2013 2:32 pm

commodorejohn wrote:Well, technically, yes, but on the scale of human hearing that's basically irrelevant.
Not irrelevant, not even basically. This is fundamental- it's where the Nyquist-Shannon theorem comes in.

commodorejohn
Synth Explorer
Synth Explorer
Posts: 1589
Joined: Mon Aug 12, 2013 2:39 am
Real name: John
Gear: Roland JX-10/SH-09/MT-32/D-50, Yamaha DX7-II/V50/TX7/TG33/FB-01, Korg MS-20 Mini/ARP Odyssey/DW-8000/X5DR, Ensoniq SQ-80, Oberheim SEM
Location: Sacramento, CA
Contact:

Re: A concise explanation of digital vs. analog?

Post by commodorejohn » Sun Nov 24, 2013 4:16 pm

Dude, if a computer can sustain a stable, square-wave clock signal at over a gigahertz, it's not going to be an issue for a circuit at less than one-forty-thousandth of that.
Computers: Amiga 1200, DEC VAXStation 4000/60, DEC MicroPDP-11/73

User avatar
madtheory
Supporting Member!
Supporting Member!
Posts: 5424
Joined: Mon May 01, 2006 12:45 pm
Real name: Tomas Mulcahy
Gear: Wurlitzer Opus 1536, Model F, Morovdis Arpeggiator, Maplin My First EQ, Jeff Wayne Thunderchild rack, Thermostat, Buck Owens' Moog.
Location: Cork, Ireland
Contact:

Re: A concise explanation of digital vs. analog?

Post by madtheory » Sun Nov 24, 2013 6:55 pm

Still moving the goalposts: now you're talking about jitter. I agree that it's an over-rated problem. But it's not the issue.

Aaron2
Active Member
Active Member
Posts: 720
Joined: Tue May 15, 2012 5:18 am
Real name: Aaron
Gear: Pioneer: Toraiz SP-16
Elektron: AK, AR, MnM, MD, OT
DSI: Evolver, MEK, P08, Pro2
Korg: Arp Odyssey
Waldorf: Blofeld Keyboard
Location: Phoenix, AZ

Re: A concise explanation of digital vs. analog?

Post by Aaron2 » Sun Nov 24, 2013 8:40 pm

Wow, I really started a s**t-storm here, didn't I? :shock:

Post Reply