The Optimal Sample Rate for Quality Audio

[Miska]

What part of what Dan says do you disagree with? The thing about the timing resolution is pretty much basic sampling theory and is well supported by people working in the field

 

Due to filter ringing features, I've defined optimal sampling rate such where:

- you can fit anti-alias/imaging filter's impulse response into half-wave of 20 kHz sine

- frequency response in pass-band must be within 0.01 dB

- phase reponse in pass-band must be within 1 degree

- final re-constructed analog signal must also have all alias/images attenuated at least by 144 dBFS

[Miska]

So what figures does that give us in practice?

 

Of course it depends on specifics of particular design. But I've concluded that I can reach it in practice at 352.8 ~ 384 kHz.

[Miska]

A fair amount of academic researchers have expressed concerns about Kunchur's work.

 

How about Oohashi & co brain imaging results when sound with ultrasonics produces different brain responses than sound without ultrasonics?

[Miska]

he has begun to talk about human ability to sense sharper amplitude rise times than occur in sound waves at the highest audible range. He has referred to this ability with the descriptor "ultrasonic,"

 

I believe this and Oohashi's work match quite well, and also with my own experience on passive sonar and such. It's not about hearing ultrasonic sine waves alone, it's about sensing waveform shapes and changes steeper than "audible" (as continuous sines) frequencies. I believe hearing is closer to wavelet analysis filter banks than Fourier frequency breakdown. (I've spent quite some time on WVD analysis and etc, perfectly matching these)

[Miska]

With infinite processing power, you can definitely avoid ringing, but most of us don't like the idea of a supercomputer bolted on to our DACs.

 

No you can't, if the ratio of passband vs Nyquist frequency is too small. I've spent enormous time to optimize filter to be as short as possible while still being "perfect", however it's just about math and it's impossible to optimize the filter to 1-tap and make the transition band with 144 dBFS attenuation to fit into 20 - 22.05 kHz band.

[Miska]

allow massive oversampling and a practically-endless number of taps (both for filtering and for compensation)

 

Massive number of taps means massive amount of ringing. Art is to minimize taps while maximizing filter performance.

 

Ringing is introduced when you decimate the oversampled ADC into RedBook rates. That's where the constrains are introduced. With "apodizing" upsampling you can modify the ringing behavior, but the constraints are already defined by the lowest sampling rate in the chain...

[Miska]

So? The ESS SABRE³² Reference ES9018 chip can upsample 24-bit 192 kHz material to no less than 1536 kHz, even (...and it uses a 32-bit internal data path to go with that).

 

Is that something special? I already support the same with 64-bit floating point internal data path and 32-bit integer output. Or alternatively up to 24.576 MHz 1-bit Delta-Sigma.

[Miska]

A very good point, Chris. Red book only needs 1.4 Mbit/s, while 384/24 requires 18.5 Mbit/s - pretty serious transmission speeds.

 

Quite pathetic speed, goes just fine even over WLAN transmission link. Or easily at eight channels over gigabit ethernet.

 

Another issue is disk space - a red book CD is 0.6 GB, the same album in 384/24 is 8 GB. Yes, disk capacities are constantly increasing, and prices are decreasing, but still... Again, perhaps justifiable if those extra bits actually contain real information, but if the music is just upsampled, it is just fluff - better do the upsampling at the DAC instead of wasting bandwidth and disk space.

 

Why would it ever go to disk? I'm performing upsampling on the fly during playback. Doesn't go to disk ever, and I can change and update the upsampler at any time. If it's built into DAC, then it's mostly literally carved into stone. And with DACs typically becomes performance limitations due to heat, power consumption, etc...

[Miska]

Of course it isn't. That was actually my point, even my $1K DAC (which I consider relatively cheap) can do it.

 

And I do it for about tenth of the price...

 

Yeah but IMO that's overkill if your DAC is connected directly to your power amp, using no EQ nor preamp nor analog attenuation. The theoretical 144 dB of dynamic range you'll get with just 24-bit integer output already provides sufficient headroom due to thermal noise kicking in at around -120 dB, and 32-bit float internal data path ought to be just as good as 64-bit float internal data path for just upsampling 24-bit 192 kHz material. Or am I wrong?

 

Of course I'm also doing also room EQ etc at the same time. For 24-bit output it is possible to achieve same sample values with some of the upsamplers using 32-bit floats (not for all). But for the newer 32-bit DACs it makes a difference.

[Miska]

Theory demands a perfect “reconstruction tool” filter. In practice, real world filters require sampling a little faster than twice the audio bandwidth. For 20 KHz audio bandwidth, the theory requires at least 40 KHz sample rate. The 44.1 KHz standard provides 4.1 KHz margin. The margin for the filter (from the theoretical filter) is 100*(44.1KHz-2*20KHz)/(2*20KHz) = 10.25%

 

What is often ignored, here too, is affect of length (steepness) of the filter to perceived sound. IOW, length of pre- and post-ringing.

 

As I've stated earlier, IMO, optimal sampling rate is such where you can fit entire impulse response of the reconstruction filter into half-wave of 20 kHz sine while having stop-band attenuation of 2^bits at all image bands (all frequencies above fs/2). At 8x rate you thus have about 8 FIR-taps to spend.

 

But of course those kind of documents tend to conveniently ignore things that don't fit into point of view of the presenter.

[Miska]

...and in addition higher rates allow better linearization through use of heavier noise shaping and also pushing down noise in the audio band...

 

(I'm getting extremely good performance from my high rate converter designs.)