There's no reason to output analog audio at more than 16 bit PCM (delivery format) but there are good reasons to process (raw audio from high-res sensors) digital analog data at greater resolution (production format). 16-bits covers what audible to humans (usually) but it doesn't cover IMO the needed dynamic range of high quality audio equipment to reproduce the entire characteristic of the audio signal including the phase of common audio signals in multi-channel systems during processing.

16 or 24 bit usually doesn't matter for home listening anyway as most people spend a huge amount of money on electronics/speakers and then setup the system in a room with dismal acoustic dimensions, no base traps, wall treatments, speaker placement for only looks and then expect a magical EQ button to fix all that.

 

A very basic reason for capturing and processing the audio at >16 bit depth is because you ARE processing it and, therefore, suffering roundoff errors that can accumulate. As long as they don't accumulate into the high 16 bits, you are golden. But if you START with just 16 bits ....

 

But since we're accommodating the number of samples to best match a a waveform with a maximum frequency of about 40 Khz, then that "chop" (is it the same as "clipping"?) will be negligible. Am I making sense?

Using a fast sampling rate to improve accuracy makes sense. But what baffles me is shown in the video at about 4:50 to 7:30, particularly towards the end. A perfect sine wave is reconstructed from just a few samples per cycle. I understand how that works for a perfect sine wave. The DAC finds the one sine wave that fits the sample data, and interpolates the missing points. But how does it fit real sample data that is NOT from a known wave shape? If he had mixed a handful of sine waves and could still reconstruct it, I'd be more impressed.

 

How does this DAC "find" a since wave? The DAC is getting fed a stream of sample values and it is producing an output for the most recent sample it has been given. At the very least, it has no idea what sample values are coming up.

He DID should a single that was a mix of sine waves -- it was called a band-limited square wave.

 

If he had mixed a handful of sine waves and could still reconstruct it, I'd be more impressed.

Watch it to the end, he does just that with 10 sine waves starting at 17:24

 

Most of these types of sine wave examples are at the max (Nyquist limit) frequency of the sampling (Nyquist) rate with an implied anti-alias filter. This is the fastest the superposition of any energy at 'that' frequency can change for a faithful reconstruction. Without a filter and higher frequency energy you have this question


Lower frequency energy will have more samples to reconstruct its contribution to the sampled waveform.
https://www.maximintegrated.com/en/app-notes/index.mvp/id/928

 

Watch it to the end, he does just that with 10 sine waves starting at 17:24

I must have missed that. I saw him work with a bandlimited squarewave (which I thought was pretty impressive, particularly some of the more subtle points he demonstrated in conjunction with it).

I'll have to go back and rewatch the portion I missed.

 

One thing to note is the low pass filter or some other thing is not doing a linear interpolation or some other function to pull out the original signal: the original signal is contained within the digital samples in it's total and complete form.

I saw a proof of this in a communication systems class where we typically worked in the frequency domain, but first a digression.

Consider an AM modulated signal. The "baseband" signal is bandwidth limited to fm, and is impressed on a carried of frequency fc. The resultant AM signal is a carrier frequency of fc with side bands from (fc - fw) to (fc + fw).

It looks like so:

And of course you AM modulate a signal by multiplying it with the carrier.

Now think of an analog to digital converter. First it must sample the analog, and one way to think of that is to imagine a special signal. The special signal will have frequency fs of the sampling rate, and a value of 1 for a very short (ideally zero) length of time. If you then multiply the "baseband" signal by this special signal you get the digital samples.

These *are* the digital samples, not the "numbers" counted in bits. That is the next step an important step too, but eventually they will be converted back to these samples.

But what are these samples like? First, there are two things to recognize about the special signal: One, it is periodic and two, it has a DC value. Periodic because it repeats exactly at the sampling rate. It has a DC value because the value of 1 has a DC (or constant) value

If it is periodic then it may be decomposed into a series of sinewaves at frequency fc, 2fc, 3fc, and so on. Each of these frequencies acts as the carrier signal for an AM signal, just as the above figure shows, if you allow for many many additional carrier waves. Actually the higher frequency components don't matter much, as I'll show.

Now take that DC value of the sampling rate and multiply the baseband by it and you get... the very same baseband signal differing only by amplitude.

That is why all you need to convert back is a low pass filter: the signal is already right there.

Here's another point: to keep that recovered baseband signal clean you want to keep the sample signal out of it. In other words (look back at the figure) you want to make sure that (fc - fm) > fm, or

fc > 2fm

If that looks to you just like the Nyquist sampling frequency then well, now you know why.

You're welcome.

 

I like the video but he does gloss over the fact you need (in practical devices) an anti-imaging filter (analog or digital time-domain Sinc Interpolation) after the DAC signal to reconstruct the original analog signal.
https://en.wikipedia.org/wiki/Reconstruction_filter

 

General Audio myths.

The Led Zeppelin bit (5:20) shows in a very clear way how expectations of 'what' to hear influence what you think you hear in speech and music.

 

I like the video but he does gloss over the fact you need (in practical devices) an anti-imaging filter (analog or digital time-domain Sinc Interpolation) after the DAC signal to reconstruct the original analog signal.
https://en.wikipedia.org/wiki/Reconstruction_filter

All of the signal processing is interesting but so far, the conversation stops there. Once it gets to the speakers, the filtering is benefited by a mechanical limit of the inertia and electromagnetically induced acceleration / deceleration of the cone.

 

All of the signal processing is interesting but so far, the conversation stops there. Once it gets to the speakers, the filtering is benefited by a mechanical limit of the inertia and electromagnetically induced acceleration / deceleration of the cone.

Thinking along the same line here...

 

Watch it to the end, he does just that with 10 sine waves starting at 17:24

Yes, I had to go watch that again. He gets to my puzzlement at 18:50, showing that the output wave is a sum of a limited number of waves. That I get, but I'm wondering how in the world the DAC actually does that. How can it fit all of those parameters on the fly?

 

Yes, I had to go watch that again. He gets to my puzzlement at 18:50, showing that the output wave is a sum of a limited number of waves. That I get, but I'm wondering how in the world the DAC actually does that. How can it fit all of those parameters on the fly?

IT DOESN'T!!

As he stated many times -- that IS the signal. That IS what a band-limited square wave looks like. If you take a square wave from an analog signal generator and pass it through a filter (with sufficiently sharp skirts) that is what you will get. No digitization needed at all.

 

General Audio myths.

The Led Zeppelin bit (5:20) shows in a very clear way how expectations of 'what' to hear influence what you think you hear in speech and music.

This image at 18:47 is the ultimate representation of "audiophool"

 

IT DOESN'T!!

As he stated many times -- that IS the signal. That IS what a band-limited square wave looks like. If you take a square wave from an analog signal generator and pass it through a filter (with sufficiently sharp skirts) that is what you will get. No digitization needed at all.

Well fine, but the exact waveform gets reproduced from a sampling of that waveform. Some how the DAC comes up with a best-fit (or is it an exact analytical) solution?

 

The DAC is braindead. You supply a basic 8-bit unipolar DAC with the value 128 and it will produce an output voltage (assuming it is a voltage-output DAC) that is right about 1/2 of it's reference voltage level. That's what it does. That's all it does. It doesn't know what the shape of the waveform is that that value is a part of. It has not way to figure it out. And it does not care.

 

Well fine, but the exact waveform gets reproduced from a sampling of that waveform. Some how the DAC comes up with a best-fit (or is it an exact analytical) solution?

I think the settling time of the DAC is critical. A DAC intended for audio with a settling time of somewhere between half and 1/4 the sampling rate is fine and will make a sine wave about each sampling point as a sort of natural resonance. I would really like to see the video in the original post re sampled at 100 or 60hz to see if the stair step appears. Or, use a video or other low settling time ADC (5 nSec) to repeat at 1kHz.

 

Well fine, but the exact waveform gets reproduced from a sampling of that waveform. Some how the DAC comes up with a best-fit (or is it an exact analytical) solution?

The reconstruction filter takes the sampled output of the DAC and "fills in" the waveform between the samples. It produces a smooth waveform from the DAC output.

 

The DAC is braindead. You supply a basic 8-bit unipolar DAC with the value 128 and it will produce an output voltage (assuming it is a voltage-output DAC) that is right about 1/2 of it's reference voltage level. That's what it does. That's all it does. It doesn't know what the shape of the waveform is that that value is a part of. It has not way to figure it out. And it does not care.

Nor does it need to know. The original signal is already contained in the digitatized samples. All that needs be done is to filter out the high frequency artifacts of the sampling process.

It is probably impossible to visualize that in the time domain, but dirt simple in the frequency domain.

I need to add a figure to show that in my previous long post.