Uncultured audio tourist swine question: Aren't all the daws and samplers doing sinc interpolation automatically these days? The very first Kontakt versions had issues with aliasing, but I always thought anything regarding aliasing is now a thing of the past.

 

This is what I tell my friends all the time when they are spending thousands of dollars on analog guitar gear and they can't answer that

 

I believe you are not realising at this point that you are in fact not looking at what comes out of your DAC (analog) at all. You are looking at what digitally goes into your computer. A set of digitised samples taken from your DAC's analog waveform. This is the fundamental flaw in your logic. You are not looking at your DAC's output. You need to stop for a second if you didn't realise this yet. You are not looking at your DAC's output. The visual representation of the samples going into your computer is entirely up to the software you're using and has no bearing whatsoever on what comes out of your DAC. You are not looking at your DAC's output.

Samples are discrete numbers, they are not connected by lines, curves or loops. The connections are drawn by your software and only your software. Your DAC doesn't have a 'create straight lines between samples' mode, your software's visual rendition does. You are not looking at your DAC's output.

I strongly suggest Akash Murthy's intro to sampling, it's understandable regardless of prior knowledge and covers the entirety of this thread.

Not necessarily pertaining to the post above, but a couple general pointers if people want to understand this stuff better:

- Start by refreshing your knowledge on the sine, cosine and sinc function and pi and how those relate to circles. There are *excellent* very short visualisers on YouTube, start with those. It'll be eye-opening.

- Briefly read up on Shannon-Whittaker and why we've known for the past 120 years that wave reconstruction is perfect as long as the signal is bandlimited.

- I recommend both of Akash Murthy's playlists on the topic. They are all very visual and simpler than books.

 

TBH, I'm a bit confused. What is this all about? I provided a description of how DA conversion works yesterday until I realized that @pratyahara seemed to be talking about waveform rendering in the DAW, so I edited my post. @saccamano on the other hand says you can see the "steps" in the waveform at the output of the DAC if you zoom in enough. I was so confused by this statement that I actually tested it. I connected the signal generator of my oscilloscope to the input of my ADC and the output of my DAC to the input of the oscilloscope. Do you know what I see there? A perfect sine wave. No matter how small I set the window and zoom in. No steps!

Then there is talk here of samples being connected by square waves. No, samples are not connected by anything. Samples are samples. Nothing exists between them. Unless new samples are inserted. Zeros, for example. And then you have completely different problems if you don't remove these zeros again or compensate in some other way. But you still won't get rectangles or "steps".
What @saccamano shows here instead is a software waveform render. It doesn't matter how the software displays the waveform. S&H, rectangle, linear, spline... does not matter. It is just a graphical representation. In digital audio there are only samples. And there are no samples on the analog output, but voltage - or current.

 

Last edited: Apr 22, 2024

I am confused, too. There are different conversions going on. I am coming from a user perspective and waveform rendering is the part that is relevant to me and don't understand why this a topic anymore. I might be just talking from the wrong orifice, because of my lack of understanding. But thank you very much for taking the time to explain the nitty gritty.

 

the sine waves samples connected by square waves was a new concept really ground breaking to me, yesterday.
but today i read xorome's comment and here i am with my ground exactly as it was, today.
this tread is confusing af

 

The examples given were for illustrative purposes. The point made is accurate enough. You're simply inserting more fog into an already clouded situation. The concept of digital sampling of analog audio is NOT ROCKET SCIENCE and the fact that you're attempting to make it so is nonsensical.

Of course that's NOT the "output of my DAC" and was it not stated anywhere that it was. I do not believe that the OP who I was replying to was looking at the "output of their DAC" either. The principles illustrated by my example are sound and accurate enough. Simply stated if the output of the resampled signal looked legitimately "rounder" (as was originally stated) at the DSP stage, that kind of radical anomaly would be shown in the rendered waveform. I equate the word "rounder" to mean distorted in this case which would mean the result was not an accurate representation of the original signal - a fault of Digital Signal Processing at that point. If you wish to favor the conversation with actual sampled captures of your DAC please feel free.

 

Last edited: Apr 22, 2024

EDIT: deleted because... Since the post I was replying to was changed while I was writing the reply, there is no meaningful connection between the quote and my reply.

 

Last edited: Apr 23, 2024

The elementary principles of digital audio have been the same since the beginning. The only thing that has changed is the quality of components and the improvement in the tech and electronic support surrounding the whole medium. Your understanding of it is correct. The member post talking about the actual "output of the digital to analog converter" of an audio interface is correct. Unless one is using a complete piece of junk for an audio interface the signals appearing at the "analog out" of your interface should appear as a reasonable facsimile of the analog input signal (sans the "stair-steps and the lines") - otherwise the entire exercise is moot. There is considerable processing and filtering that happens to the digital signal internally in the audio interface before it is squirted out the back of the analog output. My examples illustrate what happens at the DSP stage not the output stage.

 

Last edited: Apr 22, 2024

...and back to perma-ignore for you...

 

Last edited: Apr 23, 2024

Digital recording is a mediation between analog input and analog output. With the analog technique, there is no such mediation. Any assumption that one can achieve a state of analog output as if that mediation had never existed assumes that it is possible to erase all traces of it, which is theoretically not possible due to the fundamental ontological difference between discrete and continuous. Calculus doesn't necessarily bridge the fundamental gap between discrete and continuous. By taking infinitely smaller discrete steps, calculus can approximate the behavior of a continuous system. However, results obtained through calculus are approximations; they don't perfectly capture the underlying discreteness. Thus, calculus doesn't eliminate the distinction between discrete and continuous.

 

Last edited by a moderator: Apr 23, 2024

That's exactly my point. Without inherent distortion, processing or filtering isn't possible, and they can't eliminate all digital artifacts either.

 

Hopefully non-confusing micro summary for real world sampling applications with some minor headroom:

Ignoring gear imperfections and faults, to capture an audio signal spanning the human hearing range (and no more), one has to sample at about 48kHz. No amount of additional samples can possibly improve the capture's quality. All higher sampling frequencies will always result in the same reconstruction by your DAC as the 48kHz capture. Not kind of the same, but perfectly the same. The math and physics have the same result for 48kHz and all sampling frequencies above.

Hope that helps!

If somebody tells you otherwise, they "did their own research" and got it wrong at some point.

Then why are we on page 4/5 of this thread with people being uncertain if digital means square and analog means round? This keeps coming up again and again and this forum is no exception. People just don't get that a sample is just a number and not square, round, straight, curved, looped or anything more than that at all.

 

Good, then why didn't you say so in the first place?
That would have saved a lot of confusion in an already confusing thread where several topics are going on under and over each other.

Yes, the direct output in the conversion chain from a discrete digital signal to an analog one is a ZOH function output (which, by the way, does not correspond to the representation in your illustration), and yes, ZOH generates harmonics. But who cares? Just one step further down the chain, there are no steps at all. If this direct output were measured in analog, it would not be stepped or rectangular, but noisy. It would look something like this when viewed on an oscilloscope:



And after the reconstruction filter, we get our reconstructed waveform in all its beauty.

So, you think analog signals are superior because they have continuous parameters and have infinite resolution for all variables, right?

Wrong! Analog signals have exactly the same problems as digital: noise and bandwidth.
The noise in analog signals makes it difficult to measure the amplitude of the waveform, just like the quantization noise in digital signals. And the ability to separate closely spaced events in an analog signal depends on the highest frequency allowed in the waveform. Imagine you have an analog signal with two impulses that are very close together. If you pass this signal through a low-pass filter, these impulses blur into one.
An analog signal consisting of frequencies between DC and 10 kHz therefore has exactly the same resolution as a digital signal sampled at 20 kHz. And that's a good thing, because the sampling theorem guarantees that both signals contain the same information.

 

Last edited: Apr 23, 2024

Hogwash.

I think you might be the one who needs to brush up on their digital sampling basics. If what you say above is true, then there has NEVER EVER been any need for any audio gear that samples analog signals at anything higher than 48Khz? Sure buddy. Your arguments are just quibbling over semantics and illustration methods. However, to say that a resultant analog signal sampled at 48Khz rate is as good as a signal sampled at 192khz is simply untrue. The higher the resolution (i.e. sampling rate) the better chance you have of exactly reproducing the analog input. This is the proven theory and the physics of digital audio which is as true now as it was when digital audio was first introduced.

Every single digital audio theory book I have ever seen (as well as audio processing software) illustrates digital audio in the form of the stair stepped signal because it is the best way to ILLUSTRATE the nature of the technology and what goes on inside a digital audio interface. We know that in reality those "stair steps" are actually binary number values assigned to a portion of an analog input signal in computer memory or storage.

I believe this entire conversation is now entering the realm of bozo-land so I am done here... good luck amigo's..

 

Human hearing is bandwidth limited, so even for youngest people, 44.1 kHz resulting in 22 kHz upper limit is perfectly fine for properly encoded final audio files. Everyone complaining about stepped waves and so on, please do your home work. Also a dynamic range of 90 dB in most cases is perfectly fine, unless you need to power a 120dB SPL PA system and want to keep it silent during pauses, and this is easily achieved with 16 bits and proper noise shaped dithering.

Capturing and processing audio with non linear algorithms like distortion is a whole different thing, oversampling and filtering is needed to avoid aliasing artifacts.

That's basically everything you need to know and understand about digital audio.

 

sampling means transposition means SRC.

it is an issue, but it is not an issue "analog vs digital".

 

So theoretically audio wouldn't work in outter space or on the moon. Someone correct me if I'm wrong.

 

I put fairly tight constraints in my statement that you ignored or didn't understand.

If at some point you decide to transition from looking at those illustrations to also reading the accompanying text, we can pick up where we left off. The offer is genuine and I meant no snark. But for now, there's simply no point in continuing until you dig yourself out of your (paraphrasing your posts) 'it's not rocket science/it's common sense/did my own research/drew my own conclusions' hole.