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Mackers Guide to Sample Rates, Bit Depths and more...
Macker
PostPosted: 05 February 2009 - 03:32:52 (189)  Reply with quote
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Mackers Guide to Sample Rates, Bit Depths, Aliasing, Dither & Jitter

If you’ve been producing for long enough, you’ll have heard all of these terms banded around quite a lot, and will most probably have a fairly decent grounding on some of them too. Some of you however may not, and what I’m trying to do in this is not tell you “this is the preset you must use” but rather give some guidance & information on the science behind these terms and let you make your own educated decisions on how to go about using them. I'm shit at proof reading too, so I appologise in advance for any mistakes & or ommisions I've made.

Sample rates

A common term that most of us producers understand fairly well, but what does it all actually mean, and how does it affect my audio? What are the benefits & drawbacks of using high sample rates?

Well, I suppose I’d better start with the fundamentals; All sound is a vibration of matter, specifically it’s the vibration of air that we percieve as sound. The human hearing range is widely stated to be 20Hz to 20kHz, though typically for adults it is more likely to go upto around 16kHz. So, to make a good recording we need to capture all of the human hearing range – and this is where sample rates come into play.

In the audio world an analogue signal is recorded as a change/fluctuation in voltage levels over time, however the digital process is very different. In the digital world samples of the voltage are taken over very short spaces of time and converted into binary data for storage or reproduction. So the sample rate is the speed at which these samples are taken, so for example if 1,000 samples are taken per second, this means that our sample rate will be 1,000Hz (1kHz). So, how does that affect our audio..?

The Nyquist Shannon sampling theorem states that to record a signal, the sample rate must be at least double the frequency you wish to record. What does this mean for our 1kHz sample rate then? Well, it means that the highest frequency we would be able to record with it would be 500Hz – yes, it is that simple…or is it?

As I’m sure you’re aware, CD’s are recorded at a sample rate of 44.1kHz – yep, the analogue to digital converter is taking a measurement of the voltage 44,100 times every single second! So, again what does this mean for our audio? Well if we put into practice the nyquist theorem again we’ll be able to work out that the highest frequency we can record is 22,050Hz – well in excess of even the most critical of ears (human ones, I hasten to add!).

So why then do we ever need to go higher than 44.1 if we can’t hear any of the extra recorded material? It’s all down to Aliasing.

Aliasing
So, we’ve got our sample rate set at 44.1kHz and are ready to record our sound whatever it may be. So, the maximum frequency we are going to be able to record (also known as the Nyquist frequency) is 22,050Hz. So then, what happens if something over that frequency gets into our signal chain & into the recording?

This is where it gets a little more complicated because if left unattenuated, these frequencies will cause aliasing artifacts. Aliasing is caused by a signal over the nyquist frequency being recorded; it is essentially “mirrored” about the Nyquist frequency, creating an “alias” of itself within the audible spectrum of sound. Let’s try an example, and simplify the math a little to make it easier to grasp…

Our sample rate is 10Hz, therefore the Nyquist frequency is 5Hz; so no audio must go above this, otherwise it will be aliased. A tone of 7.5Hz is recorded, and thus an alias is created (mirrored at the nyquist frequency) at 2.5Hz. It’s probably worth taking a look at this image to get a more clear idea of what I am trying to explain;



Sorry for the poor image quality, I'll make a homemade one sometime but this will have to suffice for now.

So, this is what aliasing is; how do we prevent it? Antialias filters!

As producers you've almost certainly used a low pass filter; an antialias filter is no different, it removes all of the audio above the Nyquist frequency (if it's a well designed antialias filter, of course). By the time the audio gets to the nyquist frequency, the filter should have attenuated it sufficiently for it to not be recorded at all.

But this still doesn't explain why we need high sample rates. Well, sadly not all antialiasing filters are as perfect as they should be in theory, and thus aliasing is a very real problem. So by upsampling your audio to a higher sample rate, you can greatly reduce the risk of aliasing artifacts in your audio, and make the job of the antialias filter much easier.

Bit Depth

Bit depth is something that was a mystery to me for quite some time. Bit depth is essentially the number of discrete steps that can be sampled, also known as quantization. You remember how the sample rate states how many samples are being taken per second? Of course you do, I just explained it. Well, that doesn’t state how accurate each of those samples are – this is what bit depth is all about.

Quantisation is the representation of the amplitude of the signal (which in the analogue domain is continuous); unlike sample rate. It is this part of the process that determines what value each of the 44,100 samples taken every second should be.

8 bit audio (rarely used any more) is capable of sampling the amplitude of the signal to an accuracy of 256 encoding steps. This means that any analogue signal that falls in between any of these steps will be truncated/rounded to the nearest figure – and this is known as quantization distortion/error. 16 Bit audio is capable of sampling the amplitude of a signal to an accuracy of 65,536 steps.

Bit depth also dictates the maximum dynamic range of your recordings, and the general rule is;

Dynamic Range = Bit Depth x 6

So, the dynamic range of an 8 bit recording is around 48dB, and the dynamic range of a 16 bit recording is around 96dB. The noise floor (lowest possible value that you can record) of both of these bit depths is sadly less than the signal to noise ratio of any half decent analogue equipment (the SNR of my old E-MU soundcard was 120dB).
24 bit audio therefore gives us a dynamic range of around 144dB, meaning that even if your tracks all peaked at -40dB, the resolution would still be more accurate than that of a 16 bit file.


Dither
Coming soon…

Jitter
Coming soon…


Last edited by Macker on 17 February 2009 - 04:49:15 (242); edited 1 time in total

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Macker Goodbye trance.nu. You shall be missed
Sabre1489
PostPosted: 05 February 2009 - 04:23:37 (224)  Reply with quote
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Awesome stuff thumbsup
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neon chaser
PostPosted: 05 February 2009 - 04:42:20 (237)  Reply with quote
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Excellent worshipping
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mizzar
PostPosted: 05 February 2009 - 06:21:36 (306)  Reply with quote
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keep them coming thumbsup
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pagaille21
PostPosted: 05 February 2009 - 10:21:59 (473)  Reply with quote
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macktastic?

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pagaille21 is back in the country
Halcyon_Rave
PostPosted: 05 February 2009 - 10:45:37 (490)  Reply with quote
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and there's macker again droppin some mad knowledge xD!!!

This shaall become a stickyy! (if it hasn't already lol)
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Halcyon_Rave Slowly creeping back into electronic music... with minimal!
Jezper
PostPosted: 05 February 2009 - 11:30:00 (520)  Reply with quote
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Made sticky. Good stuff!
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R_tan
PostPosted: 05 February 2009 - 12:07:23 (546)  Reply with quote
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Finally something people can use!

Thank you mackah! worshipping cheers

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trancefuric
PostPosted: 05 February 2009 - 12:26:31 (560)  Reply with quote
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I always thought "dither" sounded like a slang term for a sexual act: "This one time in junior high I got so wasted that I dithered my cousin."
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Macker
PostPosted: 05 February 2009 - 15:03:28 (669)  Reply with quote
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Hope you all find it useful in some way. I Finished the bit depth part last night, but because I was up so late doing it - it could all be complete nonsense, so I wont upload it 'til I get home & read what i've written!

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Macker Goodbye trance.nu. You shall be missed
RichardClairemont
PostPosted: 06 February 2009 - 07:28:30 (353)  Reply with quote
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Good grief...I had to struggle to stay awake through most of that, but I'm glad I did. It's very informative! Thanks Macker happy
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RichardClairemont Adios amigos
VoodooChild
PostPosted: 12 February 2009 - 20:39:28 (902)  Reply with quote
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Wow! awesome read. I had one question though; If my final output is in 24bit 96khz sample rate, would aliasing occur when I re-sample it to 44.1kz for CD-audio?
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Atlantis_AR
PostPosted: 13 February 2009 - 15:36:08 (691)  Reply with quote
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VoodooChild wrote:
Wow! awesome read. I had one question though; If my final output is in 24bit 96khz sample rate, would aliasing occur when I re-sample it to 44.1kz for CD-audio?

You need to use an anti-aliasing lowpass filter before resampling. Then afterwards dither it to 16 bit.

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MaartenHercules
PostPosted: 15 February 2009 - 11:32:58 (522)  Reply with quote
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Finally read it, you're good at explaining things mate, well done. Everything is right there and clearly described. Don't worry about the image quality, its fine. Have you read your own bit depth part? Haha

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Macker
PostPosted: 17 February 2009 - 04:46:16 (240)  Reply with quote
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MaartenHercules wrote:
Finally read it, you're good at explaining things mate, well done. Everything is right there and clearly described. Don't worry about the image quality, its fine. Have you read your own bit depth part? Haha


HAH! no, not yet, I really should get round to that! I've been totally side-tracked with other things going on.

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Macker Goodbye trance.nu. You shall be missed
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