Understanding Sample Rate

[jhwalker]

Just now, mansr said:

No, I said that part is correct.

 

Exactly.  But the second statement is INCORRECT because increasing the frequency of sampling is only effective up to double the audio frequency you wish to sample and, in any case, increasing the sampling rate does not lead to a "smoother" sound - it simply allows you to sample higher frequencies.

 

PS - I used to believe the same (i.e., the higher the sampling rate, the "smoother" the curve produced) - after all, it's just "common sense", right?  But after additional study, I discovered I was wrong. 

[jhwalker]

The math really comes down to this - to reconstruct a sine wave / curve, you only need a certain number of samples; i.e., at least twice the frequency of the wave.  

 

There is one (and only one) wave that fits into a given set of coordinates - which is why in the diagram above the two curves are IDENTICAL even though there are more samples "defining" one than the other.

 

This was the "aha" moment for me.  I agree it's not "intuitive" and that big companies like Sony and Phillips, etc., have made it confusing by dumbing down the idea of sampling for the masses.  But the math is right.

[jhwalker]

1 hour ago, beerandmusic said:

 

No one will change my mind, and i am not willing to take the amount of study time that would make me understand where i may believe i am mistaken

 

 

This is as succinct a statement of the "my belief is just as good as your facts" problem I've seen

[jhwalker]

45 minutes ago, buonassi said:

 

 I'll be sure and watch it all and report back later.  On the surface, I'm having trouble grasping that time resolution could be partially a function of amplitude and not purely based on sample rate.  One is about "loudness" of a sample (not time), the other is more obviously about the rate (in time).  But perhaps the video will help me grasp that better.  And my noob brain just needs to go a little deeper! 

 

 

 

Think again about the nature of a wave - frequency is the horizontal axis (the higher the frequency, the steeper the slope), amplitude is the vertical axis (likewise).  The wave is sampled 44,000 / second, and both X and Y change each time.  So, as others have pointed out, you're not limited to accuracy along the horizontal axis, but the horizontal TIMES the vertical axis (i.e., sampling rate times amplitude / bit depth) TIMES the formula for the curve, which allows an extremely fine resolution.

[jhwalker]

8 minutes ago, Don Hills said:

In theory then, it's an argument for 24 bit sampling.

In practice, 55 picoseconds ought to be "close enough for rock'n'roll".

As a thought exercise, what is the accepted minimum time resolution for human hearing? From that, we can work out how many bits are required to encode it.

 

Exactly - if I'm doing my math correctly (always a shaky proposition for me!), 48/24 sampling would be 279x more sensitive in time discrimination than 44/16 - down to an incredible 198 femtoseconds! 

[jhwalker]

10 hours ago, mansr said:

I must correct you guys on one important thing regarding this calculation. The time accuracy depends on the frequency of the signal, not the sample rate. Instead of 44100 Hz in your formula, you must use the frequency of the signal. At 22050 Hz, 16-bit sampling gives an accuracy of 110 ps. At 1 kHz, it is about 2.5 ns. Another way of looking at it is that the sample precision determines the minimum detectable phase shift regardless of frequency. At higher frequencies, the same phase shift corresponds to a shorter time.

 

Thank you - of course.