Debunking the Digital Audio Myth: The Truth About the 'Stair-Step' Effect

are you ready to shatter some of your beliefs about digital audio because I'm about to show you a video that reveals the truth about the digital stair step myth and proves that 16-bit 44.1 kilohertz audio playback is just as good as high-res formats if not better I know this goes against what many experts out there are saying but you're about to see the evidence to back it up so sit back relax and get ready to read some angry comments below I was introduced to this video back in college by the instructor of my digital audio course in the video Monty Montgomery sets up a fully analog system including an analog signal generator an analog oscilloscope and an analog Spectrum analyzer then he drops a digital audio interface in the middle to convert the signal from analog to digital and then back to analog if the stair step myth about digital audio were true we would see a jagged waveform when the signal is played back from the audio interface and through the analog oscilloscope that's what I expected to see the first time I watched this video I thought that a higher sample rate would result in a more accurate representation of the signal it does make intuitive sense if you think about it wouldn't a higher sample rate mean that you could capture the spaces between the samples with more resolution well let's see okay it's go time we begin by converting an analog signal to digital and then right back to analog again with no other steps the signal generator is set to produce a one kilohertz sine wave just like before we can see our analog sine wave on our input side oscilloscope we digitize our signal to 16-bit PCM at 44.1 kilohertz same as on a CD the spectrum of the digitized signal matches what we saw earlier and what we see now on the analog Spectrum analyzer aside from its high impedance input being just a smidge noisier for now the waveform display shows our digitized sine wave as a stair step pattern one step for each sample and when we look at the output signal that's been converted from digital back to analog we see it's exactly like the original sine wave no stair steps okay one kilohertz is still a fairly low frequency maybe the stair steps are just hard to see or they're being smoothed away fair enough let's choose a higher frequency something close to Nyquist say 15 kilohertz now the sine wave is represented by less than three samples per cycle in the digital waveform looks pretty awful well looks can be deceived the analog output is still a perfect sine wave exactly like the original let's keep going up 16 kilohertz 17 kilohertz in kilohertz 19 kilohertz 20 kilohertz welcome to the upper limits of human hearing the output waveform is still perfect no Jagged edges no drop off no stair steps let me clarify some things Monty mentioned in this first clip he started with a one kilohertz sine wave but human hearing ranges from 20 Hertz all the way up to 20 kilohertz so he increased the frequency until it reached 20 kilohertz the highest frequency we can hear you may have heard Monty say a frequency closer to Nyquist in digital audio the Nyquist frequency is the highest frequency that can be accurately sampled and recreated by the system the Nyquist frequency is determined by the sample rate that's being used a digital audio system can capture and reproduce a signal perfectly and completely as long as the highest frequency content of the signal is less than half the sample rate so if we wish to reproduce the full range of human hearing from 20 Hertz to 20 kilohertz we need to use a sample rate that's at least 40 kilohertz in this example the system he was using had a sample rate of 44.1 kilohertz which is the standard for CV quality audio the signal was still perfectly recreated on the analog oscilloscope if the stairstep myth were true that wave would have looked something like this so where were the stair steps well let's keep watching so where'd the stair steps go don't answer it's a trick question they were never there drawing a digital waveform as a stair step was wrong to begin with why a stair step is a continuous time function it's Jagged and it's piecewise but it has the defined value at every point in time sampled signal is entirely different it's discrete time it's only got a value right at each instantaneous sample point and it's undefined there is no value at all everywhere in between a discrete time signal is properly drawn as a lollipop graph The Continuous analog counterpart of a digital signal passes smoothly through each sample point and that's just as true for high frequencies as it is for low now the interesting and not at all obvious videos there's only one band limited signal that passes exactly through each sample point it's a unique solution so if you sample a band limited signal and then convert it back the original input is also the only possible output and before you say oh I can draw a different signal that passes through those points well yes you can but if it differs even minutely from the original it contains frequency content at or Beyond Nyquist breaks the band limiting requirement and isn't a valid solution so how did everyone get confused and start thinking of digital signals as stair steps I can think of two good reasons first it's easy enough to convert a sampled signal to a true stair step just extend each sample value forward until the next sample period This is called a zero order hold and it's an important part of how some digital to analog converters work especially the simplest ones so anyone who looks up digital to analog converter or digital to analog conversion is probably going to see a diagram of a stair step waveform somewhere but that's not a finished conversion and it's not the signal that comes out second and this is probably the more likely reason Engineers who supposedly know better like me draw a stair steps even though they're technically wrong it's sort of like a one-dimensional version of fat bits in an image editor pixels aren't squares either they're samples of a two-dimensional function space and so they're also conceptually infinitely small points practically it's a real pain in the ass to see or manipulate infinitely small anything so big squares it is digital stair step drawings are exactly the same thing it's just a convenient drawing the stair steps aren't really there another component of the stair-step myth has to do with bit depth bit depth describes how many digital bits are contained within each sample each bit can represent two values on or off so each time you add a bit you double the possible values that can be represented by that sample again intuition might suggest that more bit depth makes for a smoother representation of the amplitude of the signal leading to a more accurate representation of the original waveform but as I learned from Monty's video this isn't actually the benefit of increasing bit depth when we convert a digital signal back to analog the result is also smooth regardless the bit depth 24 bits or 16 bits or eight bits it doesn't matter so does that mean that the digital bit depth makes no difference at all of course not Channel 2 here is the same sine wave input but we quantize with dither down to 8 Bits on the scope we still see a nice smooth sine wave on channel 2. look very close and you'll also see a bit more noise that's a clue if we look at the Spectrum of the signal aha our sine wave is still there unaffected but the noise level of the 8-Bit signal on the second Channel is much higher and that's the difference the number of bits makes that's it when we digitize the signal first we sample it the sampling step is perfect it loses nothing but then we quantize it and quantization adds noise the number of bits determines how much noise and so the level of the noise floor what does this dithered quantization noise sound like let's listen to our 8-bit sine wave that may have been hard to hear anything but the tongue let's listen to Just the noise after we Notch out the sine wave and then bring the gain up a bit because the noise is quiet those of you who have used analog recording equipment may have just thought to yourselves my goodness that sounds like tape hiss well it doesn't just sound like tapius it acts like it too and if we use a gaussian dither then it's mathematically equivalent in every way it is tapis intuitively that means that we can measure tape hits and thus the noise floor of magnetic audio tape in bits instead of decibels in order to put things in a digital perspective compact cassettes for those of you who are old enough to remember them could reach as deep as nine bits in perfect conditions though five to six bits was more typical especially if it was a recording made on the tape deck that's right your mixtapes were only about six bits deeper if you were lucky the very best professional open reel tape used in studios could barely hit any guesses 13 bits with Advanced noise reduction and that's why seeing DDD on a compact disc used to be such a big high-end deal so the advantage of increased bit depth is a lower noise floor and therefore an increased dynamic range but even 16-bit digital audio files have more than enough dynamic range to account for the full dynamic range of human hearing especially when you consider the environmental noise that's all around us a 16-bit digital audio file has a theoretical dynamic range of 96 decibels first of all 96 DB SPL is definitely loud if you consider 0db SPL to be the quietest sound we can hear you would need to be listening at an extremely high level to require the full dynamic range of even 16-bit audio although in theory the full dynamic range of human hearing between the quietest sound we can hear and the point where it's so loud it's painful is between 130 and 140 DB still at any reasonable listening level 96 DB is more than enough when you consider it the Noise Within even the most exceptionally quiet listening environment let's say with a noise floor of 20 DB SPL if you still don't believe that 16-bit audio has more dynamic range than we'll ever need consider that this 96 DB figure is actually quite misleading it refers to the RMS noise level of the entire Broadband signal not just a narrow band in fact the effective dynamic range of 16-bit audio with proper dithering reaches 120 DB this next quote from zif.org article is so mind-blowing that it made me literally laugh out loud when I read it so get ready 120 DB is greater than the difference between a mosquito somewhere in the room and a jackhammer a foot away think about that for a second all this to say 16-bit 44.1 kilohertz audio is more than enough for playback even on the very best Hi-Fi system in fact attempting to play back ultrasonic content by playing a 192 kilohertz file not only takes up four times the hard drive space without any audible benefit but it might actually cause audible distortions that lead to decreased fidelity I'll leave some resources below so you can do some research on your own but there are very good reasons why we use 24-bit audio with high sample rates in music production which is what I'll talk about in a future video so make sure to subscribe to audio University so you won't miss it when it comes out

Channel: Audio University

Views: 545,317

Keywords: digital audio show and tell, digital audio, xiph.org, xiph monty, monty montgomery, analog vs digital audio, 16 bit vs 24 bit, 44.1 vs 48 vs 96, hi res audio, digital show and tell

Id: cD7YFUYLpDc

Length: 13min 16sec (796 seconds)

Published: Thu Jun 01 2023