How Digital Audio Works - Computerphile 

That's why I always record at 88kHz, so my dog can appreciate the fine notes of the super piccolo.

Obligatory correction: The reason that 44.1 was chosen is not because they measured the threshold of human hearing at precisely 22.05, it's because it was "about 20kHz" and they needed to add a bit more on the high end as a transition band, which you might think of as...room for error in how they design the electronics. The reason it's 44,100 and not 44000 or 45000 (or 48,000) is related to how it was stored on old video recording systems. Today, if we didn't care about keeping to standards developed ages ago, it really just needs to be "40,000Hz + a bit more than that" The "Humans can hear 20kHz" thing is just a general guideline, not a hard and fast rule. Biology is not precise enough to say "22.05kHz is exactly the right amount." People vary too much for that. edit: Also, sampling a signal at twice the frequency is called the "Nyquist rate" and will give you alias-free sampling, which is why we use that. It's not just arbitrarily "Yeah, that seems like enough", it's a mathematical rule. That's not really super important to know, but it's a good term to Google if you want to know more.

The very first statement was wrong. The air doesn't move across a room until it hits your eardrums, that would imply that the air in the room moves at the speed of sound across a room. The air on average stays in the same place, but as it is an elastic medium the information it carries moves across the room at the speed of sound, so not so much like billiard balls passing on energy, but rather billiard balls attached by springs that return to where they were initially.

and at 7:20 the Square wave myth!!! This has been disproven countless times. The dots on a waveform although they look like square waves on the screen are actually just average values of where the real waveform is. When it goes through your DAC a perfect sine-wave will ALWAYS be reproduced even at 2-bit 22Khz tone. Furthermore a Square wave is physically impossible in nature (check out Fourier expansion and adding sine-waves to represent square waves)

I'd love to see more videos on digital audio, sound recording and editing.

Correction (at 7:10): The explanation of the noise ("grain") of very low volume signals is wrong. The computer doesn't "connect the samples with lines". Instead, whenever the computer measures the signal, it has to be rounded to the next associated integer value. This causes the so called quantization error - basically the rounding error. So the signal you hear upon playback is the original one plus the quantization error, which causes distortion (unless dithering is used, but that's another story). No square waves here.

3bit are more than enough for the average loudness war song.

Working in IT and being a huge music lover, this gives me a huge level of appreciation for artists and their studio engineers on how much work goes into putting together an album with lots of tiny microdetails never really ever heard. Definitely makes me want to go out and buy some higher end audio rather than all the streaming MP3's we do nowadays.

This is a real shame Computerphile. I find your videos informative and entertaining but this is inaccurate and misleading. I hope that your other videos in areas which i am not knowledgeable in aren't as incorrect as this is.

Drawing lines between points? Sorry but that's just not true. That would produce a lot of aliasing and distortion (like square waves as he said) and that's certainly not what happens. DA converter draws smooth curve with reconstruction filter. Only thing you loose with lowering bit depth is data lost with quantizing, which makes noise floor louder. I think you should correct that statement.

a more in-depth explanation can be found by searching: Digital Show and Tell Monty Montgomery on youtube

(My speaker properties after watching this video) 24-BIT 192,000hz

Great video. Just thought I'd add to the chorus, and comment on an irony in digital audio. Back when CDs were introduced, everyone was trumpeting how amazing their 90+db of dynamic range was. Now, we're lucky to see discs released from major record labels that use more than 10db :-) And, in fact, most albums I've bought recently go one step worse, and use heaps of heavy digital clipping on all of the drum hits. A bit sad, I suppose....

Instruction Clear. Successfully picked up acoustic waves through my red cat. Thank you.

The hearing range is up to 16-20 kHz. The reason it's 44.1 kHz is because it allows to detect 22.05 kHz frequencies. The gap between 20 kHz and 22.05 kHz is because before the A/D converter there is a filter that cuts off anything above 22.05 kHz to avoid aliasing. That filter starts cutting off at 20 kHz and reaches -60dB at 22.05 kHz so that nothing audible is lost. If the filter cut-off at exactly 20 kHz (or much closer to it) it would introduce a lot of distortion in frequncies and phases.

I love the square wave! Stop hating on the square wave! :D

Hi Computerphile, great video. I'll just add a minor correction for you. Humans can hear up to 20kHz , not 22kHz. In fact, by the time people reach adulthood, the top end of hearing is closer to 16kHz. The reason a sampling frequency of 44.1kHz was chosen as a standard was not because it is twice that of 22050Hz. It's to do with a problem called aliasing. Any frequency content contained within a signal, which is above half of the sampling frequency will introduce low frequency alias signals (See Nyquist Theorem). This is the exact same reason helicopter blades appear to spin backwards or slowly in video. For audio we would like to capture frequency information up to 20kHz, thus determining the sample frequency to be 40kHz. The only problem is, any high frequency information above 20kHz will ruin the audio due to aliasing. So in addition we add a low pass filter, called an anti-aliasing filter. Filters can't have a really steep cut off without causing all sorts of distortion, so we need to leave a little bit of space in the frequency spectrum to fit one in. Hence we oversample at 44.1kHz to allow for that.

egregiously wrong in pretty much every topic he described. sampling frequency explanation was botched, quantization noise explanation was spoken like an audio snob rather than an audio engineer (the computer doesn't "draw lines" between samples, and the effect of quantization isn't like what you described--it mostly sets the dynamic range)

I decided to learn something about digital audio, and ended up here (among other places). Great explanation, you should be a teacher the way you communicate.

I like the fact that 44100 = 2^2 * 3^2 * 5^2 * 7^2 (First four primes squared.) I can't imagine that's a coincidence.

I like the topic *digital audio* but this guy is not the best person to explain it (since he has himself some knowledge gaps).

Excellent succinct explanation! Ironic that the audio had a hum throughout.

Love it! More! For instance a video about the geeky side of compression. It would be nice to understand what I'm doing when I twiddle them knobs...

Best explanation of how Soundwaves are converted to digital. Thank you much!

makes me want to be a sound engineer

Really nice explanation, thank you so much, been looking for a decent explanation for ages

Hmm, I want more of such videos. Music is so interessting when corresponding with electronics and informatics.

I'd love to see a video about different audio formats, not in the .wav or .mp3 file type sense, but rather the encoding methods, like PCM, ADPCM, DPCM, PWM, etc.

Argggh this video made me cringe so many times. He confuses "quality" and "bandwidth" and the purpose of higher sampling frequencies and nyquist frequency and bandwidth. Ahhhhhhh

excellent video... I hope there's more coming from this guy; Amazing, thanks for the upload.

This is great info for a producer trying to approach it from an engineering side.

Awesome video. More like this, please.

Completely skipped over the Nyquist theory!

1:46 with this information, i was able to deduce the solution to my staticky PC audio; I had the sample rate for audio output set to max setting of "24 bit, 192,000 Hz (Studio quality)," and once I lowered the sample rate to "24 bits, 96000 Hz (Studio quality)", all the static noise magically vanished! YAY, thank you, this had been harming me for years.

Make a video about sound, have annoying buzz on the background. Great video though, thank you! :)

maybe one on synths? Different waveforms, envelops, filters, overdrive and such?

Please explain when dynamic compression comes in the process ...

Fascinating and well explained.

Awesome to know how the technical part of my audio work works. Working with orchestral pieces and a lot of low and a lot of high and those 'lingering' cymbal notes I did work at the higher settings like 24 bit. Good to know why exactly I have to do so on a technical level.

How come you didn't mention the Nyquist-Shannon sampling theorem? I know you are trying to make it less 'technical' but sometimes it's nice to mention some of the more technical things.

44.1 kHz was chosen as it captured all desired frequencies and it also just happened to be the perfect rate to store the samples digitally on PAL and NTSC videotape. This was used as the storage method for transporting the audio between locations. Later, when we didnt need to care about storing it on videotape we switched to 48 kHz as it helps with making filtering much simpler. Also you dont get square waves, thats impossible with a band limited signal. You can only get the original signal, smooth and non-square. 16 bits determines where the noise floor is and for playback 16 bits is more than enough to capture the dying cymbal. You use more bits, like 32 bit float, when editing before finally exporting to 16 bits. Editing with 24 bits or 32 bit floats helps because it gives you so much headroom to apply filters etc without adding any more noise that will be noticeable.

Only partially correct about the bit-depth. It really only determines the noise floor (noise made from quantisation). Very important for recording. For consumer-playback - not so much. The human hearing threshold is generally regarded as 20kHz, but sensitivity drops way before that, and both the sensitivity and threshold lowers with age.

Whilst I agree this is a simplification, this is pretty much what A Level music technology teaches and it's explained well.

Yeah, I will have to call BS about the part about the sound card outputting a square wave if the bit depth is too low. All the bit depth affects is the noise floor.

Now I know why higher sample rates improve treble clarity, in a waveform high frequencies spike up and down a lot very quickly, a slow sample rate misses those spikes. Great video!

Heh, thought it was Alan Davies on the thumbnail for as second.

Ha! I remember asking for a video on this topic ages ago! Its awesome that we finally got it!

Rather inaccurate video imho. 1. It's not 44.1KHz because the limit of human hearing is 22.05KHz. It has to do with the upper limit of human hearing and the choice of anti-aliasing filter (transition band width). The assumed human hearing range is roughly 20Hz to 20KHz. The Nyquist sampling theorem tells us that the sampling rate should be at least twice the max frequency of the signal (so 40Khz). The problem now is that our original signal contains frequency above 20KHz, if we try to sample at 40Khz aliasing will occurs (frequency above 20KHz fold into the hearing range). The signal must be low pass filtered (anti-aliasing filter). We can't perfectly cut frequency right at 20KHz, in practice a transition band is necessary. For practical and economic reasons, a 2.05KHz transition band was chosen. Now our signal contains frequency from 20Hz to 20+2.05 = 22.05KHz. Back to Niquist, we need to sample at 44.1KHz. 2. You DON'T end up with square wave. You could use 4 bits per sample and you still would not get square wave. You'll get a ton of quantization error (rounding error) and the signal will be drawn into noise (low SNR). Moreover, the computer doesn't draw line between point. It finds a continuous signal from the sequence of samples, there is a unique solution.

nice bit of info for when, if ever i use my microphone

You also get "squares" at the top end when you compress to hard as the peak of the waves can be cut off. Any sharp edges are heard as a form of distortion.

quiet signals don't sound grainy because they are square waves, it's because of quantization noise.

Great show!

My DAW has settings up to 192,000 Hz, are there any benefits or downsides of using a sample rate this high? Considering the "industry standard" is significantly lower, what applications make use of this sample rate ?

Square waves don't sound nice? Must've hated listening to NES music.

Computer engineering or electrical engineering? Which is better for audio?

What is the reason microphones have an upper frequency limit? Is it just because they can't oscillate at a rate above a certain frequency?

Will this be a series of videos? Will you go into audio compression and things like that like you did with pictures and JPEG compression?

Very helpful.

I'd love to hear more from this guy!

The human ear, talked about in this video , is the ear of a teenager of 17 years or younger, whose hearing hasn’t been damaged/weakened yet. In the 20s you might be down to 17-18kHz, in the 30s down to 16khz. These are averages. The exact numbers vary individually of course, with the point being, that only a small percentage of humans can hear 20KHz.

Nice illustrations, but this was just the tip of the tip of the iceberg. It would be nice for further episodes about the topic of digital audio to mention Shannon, the logarithmic nature of the decibel scale, real-life annoyances like the noise floor and other concepts, e.g. bit rate, data compression (in FLAC, for example) vs data reduction (i.e. data loss, and that in more than one respect, like in MP3). It's a very interesting field of topics.

Thank you for a great vid... but you guys need to do a follow-up about Shannon-Nyquist theorum. It wasn't just "some guys picked it" xD.

I actually followed this whole thing. great explanation

Could you do sound with a logarithmic scale? such that the shorter waves can get more detail than the larger ones?

I'm loving the audio stuff, between this and Sixty Symbols, I've learned a lot.

When you get an engineer to explains things to users you got a video that few would understand. When you get an user to talk an engineering topic you got a video that people will understand, but with lots of errors and misconceptions. Tough decision...

Sorry Computerphile and David Domminney, This video is over-simplified and has a lot of errors and misconceptions throughout. If one is going to use analogies and simplifications to help make a short explanation then at least point those out at the same time please! - musician, producer, engineer and Computerphile fan!

with fully electronic music, especially noise music, record the highest your software let's you use. 192khz 32bit and then mix down to 96khz 24bit. not enough music is done like this.

The dented speaker is annoying me.

So sample frequency is the "fps" of sounds ?

I followed a course on signal analysis and this video is not that great, incomplete information

That guy is amazing!!!!!

I think this could easily be compared to and illustrated through digital imaging and sequencing. An 8 bit image will look grainy and lack color space and an animation running at 10 frames per second will looks choppy. For comparisons sake then, 16 bit and 24 bit audio can be likened to 16 bit and 24 bit images respectively. One can see some hard edges in color tone on 16 bit images with color gradients (which can be likened the the wave's peaks and troughs) and one can perceive choppiness at 24 frames per second vs 30 frames per second. The latter being the reason SOME audiophiles use 96 KHz because just like with their audio i can tell the difference between 30 FPS and 60 FPS and even 60 FPS vs 90 or 120 FPS. It's the reason monitors come with syncing technology like GSync and FreeSync these days that support 144 Hz and even more. Some people are just more sensitive to different stimuli, be it a master chef, an FPS competitive gamer, a musical prodigy or a tightrope walker with a very keen sense of balance. Some of us get seasickness or motion sickness while others have no idea what the other person is experiencing. Obviously for me, visuals is my frame of reference hence why i draw the comparison with audio fidelity and visual quality.

aaaaamazing video thank you thank you thank you!!!

the air doesn't move, it's a pressure wave moving through the air

The sound in the background is really really distracting

This is exactly what I have been wondering about lately. I just got a Zoom H5 and was confused about all the recording settings! This explained it.

If sampling of a signal with frequency higher than half of the sampling frequency occurs then the signal will not be 'cut off', it will transform into a signal with another frequency.

it helps me to understand this because i have a subject digital audio..i am a MT student multimedia technology

Good audio should always be sampled at Planck time.

Nice.

I know he was simplifying but to be sure, if you sample frequencies higher than twice the sample rate, you're not simply "cutting them off." It's actually much worse: you're introducing kind of "phantom frequencies" that weren't in the signal but turn up in your digital signal. Those are mirrored at the highest frequencies you can represent, so the higher you go into "you didn't filter properly" territory, the lower the frequency gets (until it can't anymore, then it gets higher again), thus being more off and mostly more noticeable, too.

It would be nice to parallel this with analog recordings, such as tape and vinyl. Vinyl, especially, is very interesting because the headroom is 'technically' unlimited and really only limited by volume. The higher volume you stick onto the vinyl the wider the channels become and you end up having less time available on the record which is why vinyl is always given a much lower volume than today's modern music because the idea is at the end of your vinyl player you will have a sound system with a volume control to amplify it up. I am one who wants to see the digital audio industry cut out the bullshit 'volume war' and instead educate everyone on having an amplifier to turn volume up. There are even headphone amplifiers; there should be no excuses for quality of music to suffer.

10:00 There is another reason for softwares to use 32bits. Most computers can only allocate memory in lots of 8, 16, 32 and 64 bits, so 24 bits are awkward to use. So the software may use the larger 32bits because it is easier and faster, and just convert it to 24bit when you ask it to save/export the file.

I saw on another channel that the 44.1 kHz sampling rate was because we kept the human limit of hearing as 20 kHz and added a 2.05 kHz extra limit because low pass filters weren't accurate enough to cut off exactly above 20 kHz, so we added a bit of leeway. Double that and you end up with 44.1 kHz

The sampling rate is (at least) 2x the highest frequency you plan to sample..because,aliasing,Nyquist,something,something.

The video's thumbnail made me think :"Wow, Alan Davies is in Computerphile! Great!" I probably watch way too much QI.

Thank you for the information

Hey you got the same speakers as I. Gotta love the alesis!

So that's why you tidied up Dave

Interesting, would be nice with a video on how the data is stored/compressed in files.

Just not what I was looking for I wanted a way to listen to the text(read) for the book

Wow the discrepancy between the title and what is actually discussed is immense

Now can you explain mp3 compression?

Very nice video guys!

Wow! This is just what I was waiting for! Thank you!

if the wave does not fit in the bit depth , why don't we just increase the bit depth like 32 bit or 48 bit ? Another question is why not bit depth is 16 bit or 32 bit ? why 24 bit ?

5:25 Why use negative volumes? If you didn't, you'd get double the bit depth, and you wouldn't have to deal with phase cancellation. I'm sure there's a good reason why, so tell me

Am I only one hearing some kind of background fuzzy noise throughout the whole video? Like a distorted sinewave, but it's very quiet

when we say 44.1 kHz is recorded. I means 44100 samples values are recorded in each second But the bass typically ranges from about 20 Hz to 250 Hz or so But the bass can be recorded for more than 300 seconds, right? and 300 seconds would be 13230(300*44.1) So how it is between 20 to 250 Hz only. Correct me if in understood something wrong