conquistadore
Forum Moderator
Joined: 03 Aug 2004
Posts: 514
|
| Sampling Theory |
 |
|
Hi,
could someone explain the Nyquist Sampling Theory?
thanks so much
conquistadore |
Sat Mar 05, 2005 9:05 am |
|
|
AUdIoCoUrSeS
Joined: 31 Oct 2002
Posts: 2014
|
| Harry Nyquist |
|
|
Imagine a grid is placed over the waveform which then gives us a discrete number over time (horizontal axis) and a discrete number for level (vertical axis). The vertical grid levels are know as the
quantization levels
and the horizontal grid levels are know as the
sampling periods
.
Harry Nyquist discovered that for any waveform (any at all) we only need two sampling measurements on a given waveform, over a known period, to determine its frequency.
We can determine the frequency by the
steepness of the slope
over a known time period, the steeper the slope the greater the frequency. - you can see this in your digital audio editor very clearly.
Therefore to capture all of the audio spectrum accurately we only need to use a sampling rate of twice the highest frequency we wish to capture. - this is known as the
Nyquist rate
.
As the human audio range extends to 20,000 Hertz (20k) we only need to have a sampling rate of 40k, hence the 44.1k CD standard. (the extra bandwidth is for processing tasks etc)
Does that help?
_________________
It's all in the ears. - Learn the concepts not the software.
Audio Courses is a way into the music business for you
|
|
Sat Mar 05, 2005 11:02 am |
|
|
|
|
conquistadore
Forum Moderator
Joined: 03 Aug 2004
Posts: 514
|
| Nyquist Rate |
|
|
hi,
that did help...much better than some of the stuff i found on the net!
a few clarifications though...
are quantization levels dependent on frequency, i.e, does it increase with frequency?
and by steepness of the slope do u mean the mathematical slope - dx/dy?
so say i record a piece of music and the highest frequency is 10k, then a sampling rate of around 22k would do, right? (and the other 12k is for the processing tasks?)
thanks again,
conquistadore |
|
Sat Mar 05, 2005 12:49 pm |
|
|
AUdIoCoUrSeS
Joined: 31 Oct 2002
Posts: 2014
|
| 16 bits |
|
|
Good questions.
quote:
are quantization levels dependent on frequency, i.e, does it increase with frequency?
No quantization is dependent on bit length. So with say 16 bits you can have a possible 65536 levels.. (lots huh) and with 24 bits you have ...
16 bits means 16 "ones and noughts" to carry the message, so:
0000000000000000 = 0 (silence)
1111111111111111 = 65536 (loud)
That's a very crude way to explain it, but it serves a purpose.
The more bits, the better the dynamics ..
quote:
so say i record a piece of music and the highest frequency is 10k, then a sampling rate of around 22k would do, right? (and the other 12k is for the processing tasks?)
Yes that is correct, twice the highest audio frequency is enough to capture it. The processing tasks I mention is all about making it a little easier to calculate, a little room.
Try an experiemnt, record the same thing at different sampling rates, you'll start noticing the "top-end" dissapear with each reduction.
_________________
It's all in the ears. - Learn the concepts not the software.
Audio Courses is a way into the music business for you
|
|
Sat Mar 05, 2005 2:39 pm |
|
|
|
|
conquistadore
Forum Moderator
Joined: 03 Aug 2004
Posts: 514
|
| Re: Nyquist Rate |
|
|
quote:
Originally posted by conquistadore
and by steepness of the slope do u mean the mathematical slope - dx/dy?
so, quantization levels/sampling periods = frequency?
why are cd's written at 16 bits? wouldn't it be 'better' if it was at a higher bit rate (more levels)? or is it written at 16bits because cd's are designed that way?
and when dithering is done...say from 24bits to 16 bits, information is lost. so why is 'noise' added? shouldnt it be added to 'fill up space'. but here there is 'loss of space'. i hope you get what im trying to say.
thanks..
conquistadore |
|
Sat Mar 05, 2005 11:48 pm |
|
|
AUdIoCoUrSeS
Joined: 31 Oct 2002
Posts: 2014
|
| Sampling |
|
|
quote:
so, quantization levels/sampling periods = frequency?
No do not confuse them, they are two different things.
1. quantization = the wordlength (AMOUNT OF BITS).... i.e. 8, 12, 16, 24 etc..
2. sampling = the frequency i.e. 44.1kHz, 96kHz, etc.. (THIS IS HOW MANY TIMES A SECOND THE AUDIO IS PHOTOGRAPHED or MEASURED)
Both are necessary in order to convert audio to digital information. It just so happens we use the term "sampling" to mean capturing the audio in a digital way. I suppose a more correct term might be "samplization". The point being if you take a sample of the audio at a certain point you must then quantize its level at that point.
quote:
why are cd's written at 16 bits?
Because that is how they are designed to work, the CD format utilises 16 bit codes.
quote:
and when dithering is done...say from 24bits to 16 bits, information is lost. so why is 'noise' added? shouldnt it be added to 'fill up space'. but here there is 'loss of space'.
Here is an explanation of [url=http://www.audiocourses.com/ftopict-1353-dither.html]
Dither
[/url]
Make sense?
_________________
It's all in the ears. - Learn the concepts not the software.
Audio Courses is a way into the music business for you
Last edited by AUdIoCoUrSeS on Sun Mar 06, 2005 10:42 am; edited 1 time in total |
|
Sun Mar 06, 2005 8:52 am |
|
|
|
|
conquistadore
Forum Moderator
Joined: 03 Aug 2004
Posts: 514
|
hi,
thanks so much....its a whole lot clearer now! makes a lot of sense!
conquistadore |
|
Sun Mar 06, 2005 10:39 am |
|
|
 
|
|
All times are GMT. The time now is Fri May 16, 2008 3:11 pm
|
|
|
|
| |
