Part of the way it works is that the sample rate is so high that even if there was no low-pass filter you would hear a smooth, musical sound. The filter gets rid of the high-frequency artifacts that result from sampling. There is a lot more to it than that, of course.
exactly exactly right it is very very hard to see steps of the 44KHz carrier at 1KHz resolution scale the problem is bandwidth of an amplifier sees it and amplifies it and feeds the energy into the driver's coils, that is why the carrier better be filtered out
This is the answer: The right-half of the whiteboard that showed one half of a 1KHz sinewave sampled at 44KHz... is not a 1KHz square wave. It is a 1KHz sinewave with many high frequency harmonics added to it. The harmonics are caused by the stairsteps, and they are all ABOVE 20khz. When you pass that through a 20KHz low pass filter, all of those harmonics are filtered out, leaving you with just a 1KHz sinewave. I don't know why Paul is talking about 1KHz square waves. That just confuses the issue, because a 1KHz square wave consists of sinewaves of 1KHz, 3KHz, 5KHz, 7KHz, 9KHz, etc... Putting that through a 20KHz low pass filter will not result in a 1KHz sinewave! And I think the question asker knows this. That is why the question asker is confused in the first place! The answer is what I said in my first paragraph: The sampled 1KHz sinewave is made up of 1KHz + only harmonics above 20KHz. Filter out those harmonics and you're left with a 1KHz sinewave.
@Jorge-Fernandez-Lopez There's a difference between what the data represents and how an analogue signal is reconstructed using a DAC. If the bandwidth of the DAC output is more than 44KHz it will produce steps since there's enough bandwidth there for the voltage to stay at that level during the 1/44khz period. A cutoff filter gets rid of those higher frequencies and smooths out the signal as if those points are way points on a curve. Now there are multiple ways to reconstruct a digital signal to analogue of course, but the same rules apply even if it's a R2R ladder or PWM.
@@imqqmi Analog stair steps would need a function that produces that stair. Which is the mathematical equation for that stair or the electronic circuit? We can do some tests by our own in Audacity or watch the video of Xiph.
@@Jorge-Fernandez-Lopez You could do it with an arduino and an 8 bit R2R DAC without cutoff filter and a bandwitdh of say 200khz or just use resistors in R2R configuration then hook up an oscilloscope then send 8 bit representation of a sinewave of say 500hz and carrier of 44khz. Audacity can only use DACs that already have cutoff filters, ie audio dacs in soundcards, usb, integrated sound etc.
I think you touched on this subject previously. This subject is like the time I was managing an electro-mechanical development project and our electrical engineer was developing a speed control for the electric motor that fed the mechanical power tool device. The mechanical device was operating in events of milliseconds due to the high speeds and I was told that because of the 60 cycle/sec power limitations on a typical US wall socket we couldn't pull power out of the supply fast enough. Once he explained what was going on I thought, "oh, I get it". I'm kinda there on this one. What's great is that I don't have to understand it, I just go buy what works!
Man, this is a painful watch. I understand what you are trying to explain, but if I didn't, I'd be totally bamboozled. Sometimes, you're trying too hard to keep it simple.
@edd2771 I do get that. He has great understanding in depth, but sometimes struggles to explain more complex fundamental concepts. I do look forward to my daily dose of Paul.
The video would have been much better aimed at the original question if Paul had edited out about the first half of it. It got on-track when he started to talk about square waves being composed of sine waves of progressively higher frequencies.
@@SteveWille Not really, because Paul talked about 1KHz square waves, which has nothing to do with a 1KHz sinewave sampled at 44KHz. With 8 minutes to answer the question, Paul would have been better off telling what a Fourier Transform is, and drawing a rough estimate of what the frequency domain plot of what a 1KHz sinewave sampled at 44KHz looks like.
Wrong.. the statement that square wave is multiple sine waves is false. A square wave is a sinewave that was unable to be made because of running out of head room..(voltage swing denial) . Its a different problem if its clipped in preamp .or in the finals of the amp driving the speakers. But .in sound production..clipping in esrly stages gives us the growl. That bands love.. but clipping the preamp and then having it played ( processed ) . Changes everything. .its not Hifi..period.
@@davidstevens7809 Squarish waves can be created by sine wave addition, e.g. a clarinet or FM synth, or other methods, either way, as long as waves are constant they can be analyzed by a sine wave breakdown. Transient analysis is where it gets tricky.
Appreciate all the work you do, but pedagogically the following might be a better approach: emphasize that the analog signal coming *out of the DAC (physical box one has bought) is the output of an analog component* , not the output of the digital components. The digital signal output never gets to the human ears. There is always an analog filter upstream of the human ear (or the oscilloscope attached to the analog output.) *And that's it.* Don't try to go into more detail unless you want to do a real discussion of waveforms, circuits, etc.
That's because it is a bogus thing TI invented for an explanation and it causes more confusion than if they never tried using it. It's just like Technics trying to claim they removed the cogging in the SL1200 they claimed to never have had in the first place.
This gets sort of confused with explaining a 1 KHz square wave. That could be analyzed as a harmonic series of square waves going up to infinity. If filtered at 22 KHz, it would become a square with slightly rounded corners. But this is a 1 KHz sine wave plus a jagged wave at 44 KHz, easily distinguished. The jagged wave could include lower frequency components if frequencies above 22 KHz are allowed into the A->D converter or other imperfections, but certainly the largest part is 44K.
With 16 bits you can resolve 65,536 voltage steps or 96dB (16x6) dynamic range. With 24 bits you can resolve 16,777,216 voltage steps or 144dB (24x6) dynamic range. Any audio wave can be considered as a combination of sine waves and the sharper the sound wave the higher frequencies of sine waves are involved. A low pass filter cutting at 20kHz essentially limits the sound curve sharpness to how fast a 20kHz sine wave can change level. What it means is that, for example, a 10kHz square wave becomes a 10kHz sine wave to your speakers because any harmonics adding to the sharpness will be filtered out. In fact, a square wave combines odd harmonic sine waves to make the shape of a square wave. Thus, if your low pass filter is 20kHz, any square wave of 20/3=6.67kHz or higher to 20kHz will become pure sine wave. But guess what? This is also how our hearing works. We can’t hear the difference between a sine wave and square wave above 6.7kHz. If your hearing stops at 12kHz due to aging, you hear every square wave above 12/3=4kHz as sine waves…the Red Book CD standard from 1982 was well thought about against how our hearing works and that’s why even today we audiophiles can be impressed by CD music when well produced.
Red Book was designed to work with existing technologies and acknowledged as having major issues. I've met and talked with some original engineers for it. Interestingly their reactions to the various digital distortions I brought up was that the brick wall filters and integration filters on the output cause enough distortion that the ones I brought up were secondary.
@@glenncurry3041 It is a standard in-line with the Nyquist Theorem. Aliasing distortion is avoidable from the mastering process. The low pass filter with or without over-sampling can make audible difference at higher frequencies. Which kind of distortion did you raise as concern?
@@glenncurry3041 Google says: No results found for "frequency linear time shift distortion". I assume you mean phase distortion. Most of us can't hear much above 12kHz anyway and it's debatable how much phase shift we can hear at frequencies where this occur. Still I prefer higher sample rates and have had moments where I believe I got a perception of higher clarity.
@@ThinkingBetter Nope not phase, time. Because of the ratio of sampling to frequency, fewer relative samples at higher frequencies, e.g. Red Book would sample a 100Hz sine wave roughly 440 times, 10Khz 4.4 times. There is a bit shift which is far more noticeable as frequencies increase. And the percent of distortion goes up linearly.
think of it like a wheel on a bicycle standing still you see all the spokes. spinning a a high velocity it looks like one smooth solid signal, that's what happens at 44.1 or above.
It would seem to me a bunch of little teeny tiny square waves bunched together mapping out a bigger sine wave, would move the speaker cone the same, as well as amplify the same.
Well here we go again :D I'm guessing paul has watched a monty video on the subject, hoping no one will find it on youtube. Monty explains really well the digital audio in that video "clearly" I myself from what I've read and interpreted from the depths of the web, dsd is just worse than what pcm is. Without going further than that, question for paul --> if dsd is so much better than what pcm is, then why is it not used in many major studios? obviously money can't be an issue as many big studios could afford that format if it was just a better format to record in.
This is a lousy explanation: there simply are no stairsteps! Explaining this without at least mentioning Nyquist is useless. Also it's totally unneccessary to introduce square waves (which btw only consist of the fundamental and odd harmonics). As has been said in another comment: watch Monty Montgomery's D/A and A/D Digital Show and Tell video, that is three times longer, but so much more insightful.
While I'm not saying you're wrong, it was sufficient given the bandwidth he was working with ie, a short video. Also I believe the person was looking for precisely this level of explanation. They obviously aren't looking to become an engineer in this discipline.
@@InsideOfMyOwnMind Sorry, but I have to disagree; even given the limited time, he could have done a better job in eight minutes. He seems to improvise his way through this video without hardly any preparation (my guess is: none) and that doesn't help. For somebody who knows only little, or nothing at all, about this subject matter this video does nothing to make it clearer. But apart from the lack of clarity it's seriously flawed: saying that a stairstep is a square wave might be theoretically right, but plays no role in answering the question.
@@InsideOfMyOwnMind Short explanation of a wrong concept isn't information. No stairs or steps, no squares waves to filter: that's a shorter information. More information by yourself with Audacity or in Xiph by Monty" Montgomery.
I wonder whether that is really the low pass filter who smoothes out the sine wave? And, since the ADC takes samples of the analogue sine wave multiple times per second (say, 44.1K), it must be producing 44.1K codes per second each representing designated number of voltage. And these codes don't really last long enough to come together and for the stairs. I'd rather imagine they must come together in a picket fence. And the DAC has to fill the gaps between the pickets smoothly by performing VERY INTENSOVE calculations. Or am I wrong?
The picket fence analogy suggests that it's a process of 'connecting the dots' and that is not how DA conversion works. Read (or view videos) about the Nyquist theorem. Without that you'll never have a good understanding about digital audio.
Yes you are wrong. A DAC is basically a device that takes the digital code value given it and produces that output until it is told to change with the next sample. If a sample value representing one volt is given to it, it will put out one volt until given the next sample. Then it will generate that voltage until.... Yes flat steps for each sample duration. That's the DAC part of an "audio DAC" device which includes output integration, filtering.
@@tmjcbs Nyquist theorem describes the minimum required (double) sample rate to adequately encode the electric analogue of soundwave. As far as i understand it is not about the pickets/steps in the output of the DAC, which is rather a practical, not scientific theme.
@@glenncurry3041 Thanks, this was good to know. However, when looking into the logical circuits of the simplest "ladder" DACs I stil cannot see where these flat stable voltage "steps" can arise from because this type of DAC just puts out certain voltage signals in certain moments of time resulting from the incoming combinations of onn/off or one/zero impulses. And those obviously come as frequently as the sample rate.
@@OlehZavadskyPart of the Nyquist theorem is indeed the Nyquist frequency, but for me the beauty is also that the bandwidth limited signal can be reconstructed perfectly, not only approximately (ignoring the quantization error for the moment). I don't know what you meant with your picket fence analogy, but it suggested the output signal will be the sample points connected by straight lines. If I misunderstood I'd like to know what you did mean.
Interesting complication with digital. Your drawing uses the positive half of a sine wave. You reference a zero volt base line. Which means that first sample at zero volts would be all 00000000's (8 bit displayed) in the sample bitstream. So what would the negative voltage sample be? You are already at all zeros and there is no negative sign in the PCM code. So with a base line of all 0000s for zero volts, all negative voltage would also be all 000s, no difference. You could not sample a negative voltage. So basically in PCM the most significant bit represents the zero voltage line we see in analog.
Ok Paul, Now you need to do this with DSD. The Monty video is great but he is missing a few things in there. Just because your scopes show it is the same from measurements that is great…but it doesn’t sound the same.
Higher bit-depth does give you fuller tonality with smoother and more coherent decay, at the expense of soundstage width. I'm pretty sure it has to do with frequency specific amplitude accuracy. That's why DSD recordings sound distinct even when converted to PCM.
How it’s explained in this video is exactly how NOS R2R dacs work. What Paul left out is that we often perform the lowpassing in the digital domain using a mathematical filter, not physical components like capacitors. To represent all the little points that form the smooth waveform in between the big stairsteps, these digital lowpass filters also increase the sample rate (oversampling). Every DAC needs some sort of low pass filter, what NOS dacs lack is a digital lowpass filter, so they also lack “oversampling.”
@@glenncurry3041 well i saw some british manufacturer that says their dacs are completely filterless..check this in red ketter no filters.. sw1xad.co.uk/products/sw1x-dac-iv/
@@endrizo The URL was blocked. But I went to the manufactures site. You fail to understand what they are saying. "All SW1X DACs are 𝒅𝒊𝒈𝒊𝒕𝒂𝒍-filterless designs, i.e. there is no over-sampling, no jitter reduction, no noise-shaping and no re-clocking. Since all our DACs are designed to operate without any 𝒅𝒊𝒈𝒊𝒕𝒂𝒍 filtering or any kind of digital signal manipulation that is required for over-sampling, 𝒂𝒍𝒍 𝒇𝒊𝒍𝒕𝒆𝒓𝒊𝒏𝒈 𝒊𝒔 𝒅𝒐𝒏𝒆 𝒊𝒏 𝒕𝒉𝒆 𝐚𝐧𝐚𝐥𝐨𝐠𝐮𝐞 𝒅𝒐𝒎𝒂𝒊𝒏 for the best possible signal integrity. IOW Because they do not do any processing to the original input code, they do not use or need DIGITAL filters. But of course they do have to use filtering in their 𝐚𝐧𝐚𝐥𝐨𝐠𝐮𝐞 section.
Well last week I exposed how the band aid used to smooth the plots into looking like an analog sinewave has a big flaw..it makes all impulse signal come out sinusodial. READ THAT TWICE.. its great..except. .. it changes the impulse of cymbols. And most any thing thats percussion... hmm. ITS BEEN HIDDEN.. in the industry.. the filter takes any shape wave. And rounds it off. It makes the leading edge the same as trailing edge.. no matter what the instrument. SOON. CLASS D.. AND DIGITAL..WILL BE BEHIND US.
Paul Has Opened The Back Door Walked Down The Ally Passed The Dumpster Squeezed Through The Fence Went To The Convenient Store Bought Some Flaming Hot Chili Cheese Doritos and a Gator Aid and Before We Know It Paul Has Gone Where No Man Has Gone Before…..! Does Anyone Say or Use The Word Amplitude Anymore ? After This Video I Stabbed Myself With a Pencil ✏️ And Gouged Out My Eye 👁️ Balls Paul Need To Have a Disclaimer Before You Watch His Videos “This Video May Be Harmful to Your Health “”
@@SteveWille it is job of a clock to generate "square" wave, however these waves are not truly square a search engine can show pictures for oscilloscope clock signal undershoot/overshoot this imperfection in reality among others that are comprising so called jitter equalizer's fancy dancing led/vfd/lcd bars is where FFT took place
@@sarabarabu-mq1ci Sorry, my mistake… Paul’s discussion about square waves being composed of progressively higher-frequency sine waves recapitulates Fourier “Series”, not the Fourier “Transformations” the original poster mentioned.
Hi Paul, with all due respect, I think you miss understood the question, he was basically asking how the Nyquist theorem works, or why don’t we have aliasing on a analog signal when all we have are digital “lollipops” as input 😉 en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem
@@patrickmeylemans9627 "a point is an exact location in space that has no size, shape, or dimension." Please provide the Laws of Physics that allow for an instantaneous, no time duration, sample.
A digital sample is not a snap shot every X period of time. That would mean some instantaneous sample. That is technically impossible. So the signal is sampled over the entire duration of the sample period and either an average or peak representation is used.
OMG this is amazingly off point. I think Paul is trying to explain how a discontinuous square wave can be represented using a Fourier Series. This has nothing to do with digital to analog conversion.
Maybe you are correct, and maybe you are totally off base. You started with an assumption and then proceeded to conclude that he is way off base. Of course, if your assumption is incorrect then so are you. I have no way to evaluate which of you is correct, but I do know that Paul is an excellent engineer that has run a company in a very difficult industry for damn near half a century; and, I know absolutely nothing about you. So, if you want us to take your criticism seriously, it would be helpful to know what qualifications you have. Just trying to evaluate your comment. Thanks.
Thanks, Paul...now it's MY brain that's hurting!
Hahahahaha .... you're not alone 😂.!
Paul is a very funny guy ... now and then he likes us all to have a good laugh 😂!
Part of the way it works is that the sample rate is so high that
even if there was no low-pass filter you would hear a smooth, musical sound.
The filter gets rid of the high-frequency artifacts that result from sampling.
There is a lot more to it than that, of course.
exactly
exactly right it is very very hard to see steps of the 44KHz carrier at 1KHz resolution scale
the problem is bandwidth of an amplifier sees it and amplifies it and feeds the energy into the driver's coils, that is why the carrier better be filtered out
Wrong. at Red Book specs, the steps are very audible and highly distorted.
This is the answer: The right-half of the whiteboard that showed one half of a 1KHz sinewave sampled at 44KHz... is not a 1KHz square wave. It is a 1KHz sinewave with many high frequency harmonics added to it. The harmonics are caused by the stairsteps, and they are all ABOVE 20khz. When you pass that through a 20KHz low pass filter, all of those harmonics are filtered out, leaving you with just a 1KHz sinewave.
I don't know why Paul is talking about 1KHz square waves. That just confuses the issue, because a 1KHz square wave consists of sinewaves of 1KHz, 3KHz, 5KHz, 7KHz, 9KHz, etc... Putting that through a 20KHz low pass filter will not result in a 1KHz sinewave! And I think the question asker knows this. That is why the question asker is confused in the first place! The answer is what I said in my first paragraph: The sampled 1KHz sinewave is made up of 1KHz + only harmonics above 20KHz. Filter out those harmonics and you're left with a 1KHz sinewave.
Time for some new dark color whiteboard markers maybe?? 🤔
Time to go touch screen.
There's no "stairstepped"; no stairs of any kind. There are just points with nothing in between.
@Jorge-Fernandez-Lopez There's a difference between what the data represents and how an analogue signal is reconstructed using a DAC. If the bandwidth of the DAC output is more than 44KHz it will produce steps since there's enough bandwidth there for the voltage to stay at that level during the 1/44khz period. A cutoff filter gets rid of those higher frequencies and smooths out the signal as if those points are way points on a curve.
Now there are multiple ways to reconstruct a digital signal to analogue of course, but the same rules apply even if it's a R2R ladder or PWM.
@@imqqmi Analog stair steps would need a function that produces that stair. Which is the mathematical equation for that stair or the electronic circuit? We can do some tests by our own in Audacity or watch the video of Xiph.
@@Jorge-Fernandez-Lopez You could do it with an arduino and an 8 bit R2R DAC without cutoff filter and a bandwitdh of say 200khz or just use resistors in R2R configuration then hook up an oscilloscope then send 8 bit representation of a sinewave of say 500hz and carrier of 44khz. Audacity can only use DACs that already have cutoff filters, ie audio dacs in soundcards, usb, integrated sound etc.
That would violate the laws of physics. Nothing is instantaneous in the real world.
@@Jorge-Fernandez-Lopez That function is known as the sample duration.
Funny to read Jay and Erin on the whiteboard 😂
I think you touched on this subject previously. This subject is like the time I was managing an electro-mechanical development project and our electrical engineer was developing a speed control for the electric motor that fed the mechanical power tool device. The mechanical device was operating in events of milliseconds due to the high speeds and I was told that because of the 60 cycle/sec power limitations on a typical US wall socket we couldn't pull power out of the supply fast enough. Once he explained what was going on I thought, "oh, I get it". I'm kinda there on this one. What's great is that I don't have to understand it, I just go buy what works!
Man, this is a painful watch. I understand what you are trying to explain, but if I didn't, I'd be totally bamboozled. Sometimes, you're trying too hard to keep it simple.
Man that’s a painful comment. “I understand what you are trying to get to explain, but if I didn’t, I wouldn’t”.
Man… either it’s too simple or too complicated. Paul just can’t win! I see what you did there!🎉
@edd2771 I do get that. He has great understanding in depth, but sometimes struggles to explain more complex fundamental concepts.
I do look forward to my daily dose of Paul.
The video would have been much better aimed at the original question if Paul had edited out about the first half of it. It got on-track when he started to talk about square waves being composed of sine waves of progressively higher frequencies.
@@SteveWille Not really, because Paul talked about 1KHz square waves, which has nothing to do with a 1KHz sinewave sampled at 44KHz. With 8 minutes to answer the question, Paul would have been better off telling what a Fourier Transform is, and drawing a rough estimate of what the frequency domain plot of what a 1KHz sinewave sampled at 44KHz looks like.
That's the beauty of nature: it's not just maths, there really are only sine waves! All other waveforms are multiple superimposed sine waves.
Wrong.. the statement that square wave is multiple sine waves is false. A square wave is a sinewave that was unable to be made because of running out of head room..(voltage swing denial) . Its a different problem if its clipped in preamp .or in the finals of the amp driving the speakers. But .in sound production..clipping in esrly stages gives us the growl. That bands love.. but clipping the preamp and then having it played ( processed ) . Changes everything. .its not Hifi..period.
@@davidstevens7809 Squarish waves can be created by sine wave addition, e.g. a clarinet or FM synth, or other methods, either way, as long as waves are constant they can be analyzed by a sine wave breakdown. Transient analysis is where it gets tricky.
@@spentron1 yes.. your correct..
Appreciate all the work you do, but pedagogically the following might be a better approach: emphasize that the analog signal coming *out of the DAC (physical box one has bought) is the output of an analog component* , not the output of the digital components. The digital signal output never gets to the human ears. There is always an analog filter upstream of the human ear (or the oscilloscope attached to the analog output.) *And that's it.* Don't try to go into more detail unless you want to do a real discussion of waveforms, circuits, etc.
I am not impressed that Paul doesn’t know what lollipop diagram is when taking about digital signals.
That's because it is a bogus thing TI invented for an explanation and it causes more confusion than if they never tried using it. It's just like Technics trying to claim they removed the cogging in the SL1200 they claimed to never have had in the first place.
a video on digital filters and which one to chose and why on our dacs would be great
This gets sort of confused with explaining a 1 KHz square wave. That could be analyzed as a harmonic series of square waves going up to infinity. If filtered at 22 KHz, it would become a square with slightly rounded corners. But this is a 1 KHz sine wave plus a jagged wave at 44 KHz, easily distinguished. The jagged wave could include lower frequency components if frequencies above 22 KHz are allowed into the A->D converter or other imperfections, but certainly the largest part is 44K.
With 16 bits you can resolve 65,536 voltage steps or 96dB (16x6) dynamic range. With 24 bits you can resolve 16,777,216 voltage steps or 144dB (24x6) dynamic range. Any audio wave can be considered as a combination of sine waves and the sharper the sound wave the higher frequencies of sine waves are involved. A low pass filter cutting at 20kHz essentially limits the sound curve sharpness to how fast a 20kHz sine wave can change level. What it means is that, for example, a 10kHz square wave becomes a 10kHz sine wave to your speakers because any harmonics adding to the sharpness will be filtered out. In fact, a square wave combines odd harmonic sine waves to make the shape of a square wave. Thus, if your low pass filter is 20kHz, any square wave of 20/3=6.67kHz or higher to 20kHz will become pure sine wave. But guess what? This is also how our hearing works. We can’t hear the difference between a sine wave and square wave above 6.7kHz. If your hearing stops at 12kHz due to aging, you hear every square wave above 12/3=4kHz as sine waves…the Red Book CD standard from 1982 was well thought about against how our hearing works and that’s why even today we audiophiles can be impressed by CD music when well produced.
Red Book was designed to work with existing technologies and acknowledged as having major issues. I've met and talked with some original engineers for it. Interestingly their reactions to the various digital distortions I brought up was that the brick wall filters and integration filters on the output cause enough distortion that the ones I brought up were secondary.
@@glenncurry3041 It is a standard in-line with the Nyquist Theorem. Aliasing distortion is avoidable from the mastering process. The low pass filter with or without over-sampling can make audible difference at higher frequencies. Which kind of distortion did you raise as concern?
@@ThinkingBetter For one a frequency linear time shift distortion.
@@glenncurry3041 Google says: No results found for "frequency linear time shift distortion". I assume you mean phase distortion. Most of us can't hear much above 12kHz anyway and it's debatable how much phase shift we can hear at frequencies where this occur. Still I prefer higher sample rates and have had moments where I believe I got a perception of higher clarity.
@@ThinkingBetter Nope not phase, time. Because of the ratio of sampling to frequency, fewer relative samples at higher frequencies, e.g. Red Book would sample a 100Hz sine wave roughly 440 times, 10Khz 4.4 times. There is a bit shift which is far more noticeable as frequencies increase. And the percent of distortion goes up linearly.
think of it like a wheel on a bicycle standing still you see all the spokes. spinning a a high velocity it looks like one smooth solid signal, that's what happens at 44.1 or above.
It would seem to me a bunch of little teeny tiny square waves bunched together mapping out a bigger sine wave, would move the speaker cone the same, as well as amplify the same.
Well here we go again :D I'm guessing paul has watched a monty video on the subject, hoping no one will find it on youtube. Monty explains really well the digital audio in that video "clearly" I myself from what I've read and interpreted from the depths of the web, dsd is just worse than what pcm is. Without going further than that, question for paul --> if dsd is so much better than what pcm is, then why is it not used in many major studios? obviously money can't be an issue as many big studios could afford that format if it was just a better format to record in.
This is a lousy explanation: there simply are no stairsteps! Explaining this without at least mentioning Nyquist is useless. Also it's totally unneccessary to introduce square waves (which btw only consist of the fundamental and odd harmonics). As has been said in another comment: watch Monty Montgomery's D/A and A/D Digital Show and Tell video, that is three times longer, but so much more insightful.
While I'm not saying you're wrong, it was sufficient given the bandwidth he was working with ie, a short video. Also I believe the person was looking for precisely this level of explanation. They obviously aren't looking to become an engineer in this discipline.
@@InsideOfMyOwnMind Sorry, but I have to disagree; even given the limited time, he could have done a better job in eight minutes. He seems to improvise his way through this video without hardly any preparation (my guess is: none) and that doesn't help. For somebody who knows only little, or nothing at all, about this subject matter this video does nothing to make it clearer. But apart from the lack of clarity it's seriously flawed: saying that a stairstep is a square wave might be theoretically right, but plays no role in answering the question.
@@InsideOfMyOwnMind Short explanation of a wrong concept isn't information. No stairs or steps, no squares waves to filter: that's a shorter information. More information by yourself with Audacity or in Xiph by Monty" Montgomery.
Please show us all graphically how PCM exists without stair steps. Include the laws of physics that allow for instantaneous change in voltage level.
@@glenncurry3041… that’s the problem. Physics doesn’t allow for instantaneous voltage changes, nor does it allow for them in air pressure changes.
I wonder whether that is really the low pass filter who smoothes out the sine wave? And, since the ADC takes samples of the analogue sine wave multiple times per second (say, 44.1K), it must be producing 44.1K codes per second each representing designated number of voltage. And these codes don't really last long enough to come together and for the stairs. I'd rather imagine they must come together in a picket fence. And the DAC has to fill the gaps between the pickets smoothly by performing VERY INTENSOVE calculations. Or am I wrong?
The picket fence analogy suggests that it's a process of 'connecting the dots' and that is not how DA conversion works. Read (or view videos) about the Nyquist theorem. Without that you'll never have a good understanding about digital audio.
Yes you are wrong. A DAC is basically a device that takes the digital code value given it and produces that output until it is told to change with the next sample. If a sample value representing one volt is given to it, it will put out one volt until given the next sample. Then it will generate that voltage until.... Yes flat steps for each sample duration.
That's the DAC part of an "audio DAC" device which includes output integration, filtering.
@@tmjcbs Nyquist theorem describes the minimum required (double) sample rate to adequately encode the electric analogue of soundwave. As far as i understand it is not about the pickets/steps in the output of the DAC, which is rather a practical, not scientific theme.
@@glenncurry3041 Thanks, this was good to know. However, when looking into the logical circuits of the simplest "ladder" DACs I stil cannot see where these flat stable voltage "steps" can arise from because this type of DAC just puts out certain voltage signals in certain moments of time resulting from the incoming combinations of onn/off or one/zero impulses. And those obviously come as frequently as the sample rate.
@@OlehZavadskyPart of the Nyquist theorem is indeed the Nyquist frequency, but for me the beauty is also that the bandwidth limited signal can be reconstructed perfectly, not only approximately (ignoring the quantization error for the moment). I don't know what you meant with your picket fence analogy, but it suggested the output signal will be the sample points connected by straight lines. If I misunderstood I'd like to know what you did mean.
Interesting complication with digital. Your drawing uses the positive half of a sine wave. You reference a zero volt base line. Which means that first sample at zero volts would be all 00000000's (8 bit displayed) in the sample bitstream. So what would the negative voltage sample be? You are already at all zeros and there is no negative sign in the PCM code. So with a base line of all 0000s for zero volts, all negative voltage would also be all 000s, no difference. You could not sample a negative voltage.
So basically in PCM the most significant bit represents the zero voltage line we see in analog.
Ok Paul, Now you need to do this with DSD. The Monty video is great but he is missing a few things in there. Just because your scopes show it is the same from measurements that is great…but it doesn’t sound the same.
But Paul, you forgot to mention the Nyquist frequency.
Excruciating!!!
Look up over sampling, aliasing, and dither.
Tell them about sinx/x correction and their heads will explode. (Please don't!)
The capacitor of a simple RC low pass filter essentially “sucks in” and attenuates high frequency components thus leaving a low frequency waveform. 😂
Higher bit-depth does give you fuller tonality with smoother and more coherent decay, at the expense of soundstage width. I'm pretty sure it has to do with frequency specific amplitude accuracy. That's why DSD recordings sound distinct even when converted to PCM.
Sounds the same as circular modulation, this is used in CNC maching.
A Sine Wave is a circular wave transposed from Radians to time domain.
very well explained by Paul Sir.
ok so fr5 reviews soon😛😉😍
so.. you need a filter... so... what about nos dacs or r2r filterless dacs ??
How it’s explained in this video is exactly how NOS R2R dacs work.
What Paul left out is that we often perform the lowpassing in the digital domain using a mathematical filter, not physical components like capacitors. To represent all the little points that form the smooth waveform in between the big stairsteps, these digital lowpass filters also increase the sample rate (oversampling).
Every DAC needs some sort of low pass filter, what NOS dacs lack is a digital lowpass filter, so they also lack “oversampling.”
Please show us all any PCM DAC that is filterless. It is possible in up sampling to DSD. But that would be a Sigma Delta DAC.
@@glenncurry3041 well i saw some british manufacturer that says their dacs are completely filterless..check this in red ketter no filters.. sw1xad.co.uk/products/sw1x-dac-iv/
@@glenncurry3041 I think even DSD needs a low pass filter to eliminate the noise from audible frequencies that gets “shaped” into high frequencies.
@@endrizo The URL was blocked. But I went to the manufactures site. You fail to understand what they are saying.
"All SW1X DACs are 𝒅𝒊𝒈𝒊𝒕𝒂𝒍-filterless designs, i.e. there is no over-sampling, no jitter reduction, no noise-shaping and no re-clocking. Since all our DACs are designed to operate without any 𝒅𝒊𝒈𝒊𝒕𝒂𝒍 filtering or any kind of digital signal manipulation that is required for over-sampling, 𝒂𝒍𝒍 𝒇𝒊𝒍𝒕𝒆𝒓𝒊𝒏𝒈 𝒊𝒔 𝒅𝒐𝒏𝒆 𝒊𝒏 𝒕𝒉𝒆 𝐚𝐧𝐚𝐥𝐨𝐠𝐮𝐞 𝒅𝒐𝒎𝒂𝒊𝒏 for the best possible signal integrity.
IOW Because they do not do any processing to the original input code, they do not use or need DIGITAL filters. But of course they do have to use filtering in their 𝐚𝐧𝐚𝐥𝐨𝐠𝐮𝐞 section.
Paul
Just Give Me Half Of
What You Took
…..Just 1/2
Well last week I exposed how the band aid used to smooth the plots into looking like an analog sinewave has a big flaw..it makes all impulse signal come out sinusodial. READ THAT TWICE.. its great..except. .. it changes the impulse of cymbols. And most any thing thats percussion... hmm. ITS BEEN HIDDEN.. in the industry.. the filter takes any shape wave. And rounds it off. It makes the leading edge the same as trailing edge.. no matter what the instrument. SOON.
CLASS D.. AND DIGITAL..WILL BE BEHIND US.
Paul Has Opened The Back Door Walked Down The Ally Passed The Dumpster Squeezed Through The Fence Went To The Convenient Store
Bought Some Flaming Hot Chili Cheese Doritos and a Gator Aid and Before We Know It Paul Has Gone Where No Man Has Gone Before…..!
Does Anyone Say or Use The Word Amplitude Anymore ?
After This Video
I Stabbed Myself With a
Pencil ✏️ And Gouged Out My Eye 👁️ Balls
Paul Need To Have a
Disclaimer Before You Watch His Videos
“This Video May Be
Harmful to Your Health “”
Well explained without mentioning fourier transformations. 😊
that is for spectrum analyzers
Hmmm… as soon as Paul mentioned that square waves are composed of sine wave, Fourier was evoked. 😊
@@SteveWille it is job of a clock to generate "square" wave, however these waves are not truly square
a search engine can show pictures for oscilloscope clock signal undershoot/overshoot
this imperfection in reality among others that are comprising so called jitter
equalizer's fancy dancing led/vfd/lcd bars is where FFT took place
@@sarabarabu-mq1ci Sorry, my mistake… Paul’s discussion about square waves being composed of progressively higher-frequency sine waves recapitulates Fourier “Series”, not the Fourier “Transformations” the original poster mentioned.
Hi Paul, with all due respect, I think you miss understood the question, he was basically asking how the Nyquist theorem works, or why don’t we have aliasing on a analog signal when all we have are digital “lollipops” as input 😉
en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem
No! ... It didn't help! 👎🤣
Incorrect there are no stair steps, it are points on the curve in time who last 0 seconds….
So just ignore the Laws of Physics?
@@glenncurry3041 digitizing a curve in a plane (2 dimensions) is done by points on the curve. Please read the definition of a point
@@patrickmeylemans9627 "a point is an exact location in space that has no size, shape, or dimension." Please provide the Laws of Physics that allow for an instantaneous, no time duration, sample.
@@mjk4554 Nope. Throw a scope probe onto points before filtering in the DAC and you will see them.
A digital sample is not a snap shot every X period of time. That would mean some instantaneous sample. That is technically impossible. So the signal is sampled over the entire duration of the sample period and either an average or peak representation is used.
OMG this is amazingly off point. I think Paul is trying to explain how a discontinuous square wave can be represented using a Fourier Series. This has nothing to do with digital to analog conversion.
Maybe you are correct, and maybe you are totally off base. You started with an assumption and then proceeded to conclude that he is way off base. Of course, if your assumption is incorrect then so are you. I have no way to evaluate which of you is correct, but I do know that Paul is an excellent engineer that has run a company in a very difficult industry for damn near half a century; and, I know absolutely nothing about you. So, if you want us to take your criticism seriously, it would be helpful to know what qualifications you have. Just trying to evaluate your comment. Thanks.
@@spenceralridge4958 PhD in mathematical physics, 35+ years in computational applied mathematics, devoted hi-fi enthusiast.
@@matthewrichey8542 Then show us all how the laws of physics allows for less than Planck Time samples.
I think we’re getting a bit off topic here!
@@matthewrichey8542 IOW you can't We understand.
Too much like school