I was assigned to watch this for my college audio-editing class, and I found this quite an informative video! I have learned several new terms today: sample rate, bit depth, and bit rate, as well as some other terms. Thanks for the video! I'll subscribe!
Yes exactly, wav is only a container and its "codec" (if you can call it that) is usually PCM. The wav container can hold almost any other codec actually but most devices/ software won't know what to do with it 😂
This is a good video going over some stuff that's tough to explain, but the analogy of digital images is a little bit misleading. Because it's not possible for us to create a mathematical function that describes the image coming from the sensors in our camera, our only option for making the digital copy closer to the analog equivalent is to reduce the amount of information lost at the sensor (increasing the resolution and bit depth). But audio is not like this - it actually is possible for us to create a mathematically perfect description of the analog signal such that it can be perfectly recreated again (much like lossless compression), and that's what the sampling theorem is all about. As long as you stick to the rules (fourier transform of 0 above Fmax / 2, constantly spaced samples etc), the digital signal is perfectly describing the analog input wave, and the reconstructed wave will sound identical to the input wave (ignoring aliasing filter slope and time domain distortion caused by it). This means that (again, with an ideal aliasing filter), there is literally 0 audible difference in the audible range between 44.1KHz, 48KHz, 96KHz, etc. Obviously this isn't true with photos, because you will always get something positive out of increasing the resolution! In this sense, a better analogy to audio is vector images, like SVG or PDFs. These use mathematical descriptions of the images, such that you can zoom in infinitely without degredation, and they perfectly represent the continous nature of the shapes despite being stored as a long discrete string of numbers.
I disagree with your statement that vector graphics are a useful analogy. The ability to create a function to “perfectly” is very similar to vector graphics, but that’s not what’s happening when audio is recorded. Using FFTs and related techniques to model a sound is like vectorizing a bitmap, it’s a separate thing from the bitmap itself. Most audio is _never_ represented by a mathematical model. What you described is like a vector, but that’s not what I described in the video.
@@lyntedrockley7295it is very much not like vector graphics in the way the data is stored digitally. Vector graphics would be more analogous to basic synthesis from unit generators.
It is a common misconception that the Nyquist Limit allows accurate reconstruction of analog signal. It does not. The source of the Nyquist Limit comes from two papers pubished in 1928 and 1948 (Nyquist and Shannon, respectrively) and those papers are focused on digital communication. These papers do not deal with continuiously varying signals at all. In fact, for a high fidelity reconstuction you need to sample at at least 5x and preferably 10x the highest frequency present in the signal.
@@nicksterj Thanks for your reply. If we look at that quote in more detail (p34 of Shannon's classic paper) we firstly see that we are assuming an infinite number of samples: Xn = [ ... , s_-2, s_-1, s_0, s_1 s_2, ...] We also see that the reconstruction is based on summing together an infinite set of sinc functions, with each one centred on a sample point and scaled using the value of f(t) at that point. This is the classic sinc reconstruction. We further see that f(t) is itself implicitly assumed to be equal to the sum of a set of sinusoids (which, by definition, means that f(t) is periodic with a period, T, defined by the LCM of the periods of the constituent sinusoids). As for the condition that the separation between adjacent samples must be less than half the period of the highest frequency component present in f(t) then this arises from the basis functions chosen for the reconstruction which are all zero at the sample points and have peak values halfway between the sample points: if f(t) contained sinusoids that had a half-wave duration that was less then the sample separation then the sinc functions - which do not have zeros between sample points - would not be usable. It’s worth pointing out that the sinc functions chosen are not special and could be replaced by piecewise parabolic functions or even triangle functions: because the reconstruction is based on an infinite set then all that is required of that set is that all unique pairs of functions are orthogonal and each basis function is equal to zero at all sample points, other than the one upon which it is centered. But in a practical case - where we have N samples, N reconstruction functions and are dealing with non-periodic signals - then the Nyquist limit is a crude guide at best. If one conducts some precise simulations with a test function that is composed of a finite set of sinusoids of different amplitudes, frequencies and phases (where we know for sure what the highest frequency component is) then sampling at the Nyquist limit, Sr == f_max. will definitely result in substantial reconstruction errors between samples.
@@nicksterj In the field electrical engineering probably the most feared topic is digital signal processing (DSP). This is because deeply understanding what’s really going on requires a pretty decent level of competence with linear algebra, basis functions, trigonometry, calculus, matrices, complex numbers, Fourier analysis, probability and statistics, differential equations - as well as, these days, competence with coding and computational methods. It gets harder if you’re trying to do fancy things on an embedded system. It’s probably not surprising that the field is replete with misconceptions and misunderstandings - for instance we are told that in order to perform a DFT you need to use complex numbers and matrices. This is wrong: you can manage perfectly well without using any complex numbers at all. Most practising engineers simply don’t have the time or energy to really go deep. But if you do then one will find many nuances and insights which serve to keep the subject endlessly fascinating. Returning to the point I recall when the CD first came out the analog crows maintained that the digitisation at 44.1k samples per sec was somehow not a faithful way to represent music which (very optimistically) contains frequency components up to 20kHz. They were mostly unable to articulate why but they were right all along. I find that pretty amusing!
Interpolation happens any time the software has to make an educated guess about what is happening between the samples. This might happen if you are stretching or re-pitching audio, or just resampling a 44.1k clip into a 48k project.
@@DavidMacDonald thanks, but it’s hard to find which sinc formula is better to make that “guess” with and i’ve seen some linear interpolations that add samples to the file.
@@elijahjflowers interpolation always adds samples to the file. That’s its job. It isn’t ever going to be perfect and different algorithms will give different results in different circumstances. You just have to experiment.
I was assigned to watch this for my college audio-editing class, and I found this quite an informative video! I have learned several new terms today: sample rate, bit depth, and bit rate, as well as some other terms.
Thanks for the video! I'll subscribe!
Thanks so much for the comment! Would you mind sharing what college? I'm just curious!
The best explanation on youtube. Thanks Bro
Thanks a ton for explain things to me. Really appreciate it!
very clear and concise thank you for the wisdom
This deserves a lot more views.
Dude… thanks for the info. 🖤
I would add that not all WAV files are uncompressed, although most of them are. The exceptions are WAV files using ADPCM compression.
@nicksterj Yes, although I had to look that one up. 😊 I have only worked with LPCM and ADPCM in real products.
Yes exactly, wav is only a container and its "codec" (if you can call it that) is usually PCM.
The wav container can hold almost any other codec actually but most devices/ software won't know what to do with it 😂
This is a good video going over some stuff that's tough to explain, but the analogy of digital images is a little bit misleading. Because it's not possible for us to create a mathematical function that describes the image coming from the sensors in our camera, our only option for making the digital copy closer to the analog equivalent is to reduce the amount of information lost at the sensor (increasing the resolution and bit depth). But audio is not like this - it actually is possible for us to create a mathematically perfect description of the analog signal such that it can be perfectly recreated again (much like lossless compression), and that's what the sampling theorem is all about. As long as you stick to the rules (fourier transform of 0 above Fmax / 2, constantly spaced samples etc), the digital signal is perfectly describing the analog input wave, and the reconstructed wave will sound identical to the input wave (ignoring aliasing filter slope and time domain distortion caused by it). This means that (again, with an ideal aliasing filter), there is literally 0 audible difference in the audible range between 44.1KHz, 48KHz, 96KHz, etc. Obviously this isn't true with photos, because you will always get something positive out of increasing the resolution! In this sense, a better analogy to audio is vector images, like SVG or PDFs. These use mathematical descriptions of the images, such that you can zoom in infinitely without degredation, and they perfectly represent the continous nature of the shapes despite being stored as a long discrete string of numbers.
I disagree with your statement that vector graphics are a useful analogy. The ability to create a function to “perfectly” is very similar to vector graphics, but that’s not what’s happening when audio is recorded. Using FFTs and related techniques to model a sound is like vectorizing a bitmap, it’s a separate thing from the bitmap itself. Most audio is _never_ represented by a mathematical model. What you described is like a vector, but that’s not what I described in the video.
@@lyntedrockley7295it is very much not like vector graphics in the way the data is stored digitally. Vector graphics would be more analogous to basic synthesis from unit generators.
great video, thank you so much!
It is a common misconception that the Nyquist Limit allows accurate reconstruction of analog signal. It does not. The source of the Nyquist Limit comes from two papers pubished in 1928 and 1948 (Nyquist and Shannon, respectrively) and those papers are focused on digital communication. These papers do not deal with continuiously varying signals at all. In fact, for a high fidelity reconstuction you need to sample at at least 5x and preferably 10x the highest frequency present in the signal.
@@nicksterj Thanks for your reply.
If we look at that quote in more detail (p34 of Shannon's classic paper) we firstly see that we are assuming an infinite number of samples:
Xn = [ ... , s_-2, s_-1, s_0, s_1 s_2, ...]
We also see that the reconstruction is based on summing together an infinite set of sinc functions, with each one centred on a sample point and scaled using the value of f(t) at that point.
This is the classic sinc reconstruction.
We further see that f(t) is itself implicitly assumed to be equal to the sum of a set of sinusoids (which, by definition, means that f(t) is periodic with a period, T, defined by the LCM of the periods of the constituent sinusoids).
As for the condition that the separation between adjacent samples must be less than half the period of the highest frequency component present in f(t) then this arises from the basis functions chosen for the reconstruction which are all zero at the sample points and have peak values halfway between the sample points: if f(t) contained sinusoids that had a half-wave duration that was less then the sample separation then the sinc functions - which do not have zeros between sample points - would not be usable.
It’s worth pointing out that the sinc functions chosen are not special and could be replaced by piecewise parabolic functions or even triangle functions: because the reconstruction is based on an infinite set then all that is required of that set is that all unique pairs of functions are orthogonal and each basis function is equal to zero at all sample points, other than the one upon which it is centered.
But in a practical case - where we have N samples, N reconstruction functions and are dealing with non-periodic signals - then the Nyquist limit is a crude guide at best.
If one conducts some precise simulations with a test function that is composed of a finite set of sinusoids of different amplitudes, frequencies and phases (where we know for sure what the highest frequency component is) then sampling at the Nyquist limit, Sr == f_max. will definitely result in substantial reconstruction errors between samples.
@@nicksterj In the field electrical engineering probably the most feared topic is digital signal processing (DSP). This is because deeply understanding what’s really going on requires a pretty decent level of competence with linear algebra, basis functions, trigonometry, calculus, matrices, complex numbers, Fourier analysis, probability and statistics, differential equations - as well as, these days, competence with coding and computational methods. It gets harder if you’re trying to do fancy things on an embedded system.
It’s probably not surprising that the field is replete with misconceptions and misunderstandings - for instance we are told that in order to perform a DFT you need to use complex numbers and matrices. This is wrong: you can manage perfectly well without using any complex numbers at all.
Most practising engineers simply don’t have the time or energy to really go deep. But if you do then one will find many nuances and insights which serve to keep the subject endlessly fascinating.
Returning to the point I recall when the CD first came out the analog crows maintained that the digitisation at 44.1k samples per sec was somehow not a faithful way to represent music which (very optimistically) contains frequency components up to 20kHz. They were mostly unable to articulate why but they were right all along. I find that pretty amusing!
Thanks.
thanks, do you have any tips for understanding audio interpolation?
Interpolation happens any time the software has to make an educated guess about what is happening between the samples. This might happen if you are stretching or re-pitching audio, or just resampling a 44.1k clip into a 48k project.
@@DavidMacDonald thanks, but it’s hard to find which sinc formula is better to make that “guess” with and i’ve seen some linear interpolations that add samples to the file.
@@elijahjflowers interpolation always adds samples to the file. That’s its job. It isn’t ever going to be perfect and different algorithms will give different results in different circumstances. You just have to experiment.
thank you
You're welcome