Skip to main content

Notice

Please note that most of the software linked on this forum is likely to be safe to use. If you are unsure, feel free to ask in the relevant topics, or send a private message to an administrator or moderator. To help curb the problems of false positives, or in the event that you do find actual malware, you can contribute through the article linked here.
Topic: Representing frequency of n Hz needs sampling rate >2n Hz, not =2n (Read 30580 times) previous topic - next topic
0 Members and 1 Guest are viewing this topic.

Representing frequency of n Hz needs sampling rate >2n Hz, not =2n

Reply #50
We could pull a ten year old off the street.


I see what you did there. Or just another Freudian slip?

Pull as in pull into a test, or simply replace with poll.  This would be with proper consent; I certainly don't want people to think that I'm suggesting kidnapping.

Representing frequency of n Hz needs sampling rate >2n Hz, not =2n

Reply #51
Well, JAZ, you can theoretically create a tone at Fs/2, but there will be no phase information. Using the DFT to calculate the Nyquist bin, you will get a sum of the samples multiplied by effectively exp(-i*pi*n), which is alternating +1+0i, -1+0i, so a phase of zero. So it's similar to the DC bin.
"I hear it when I see it."

Representing frequency of n Hz needs sampling rate >2n Hz, not =2n

Reply #52
Look, the only way you can do fs/2 is if the signal is infinitely long, which of course does not exist in the real world. Otherwise its bandwidth extends beyond fs/2 well over quantizing levels.

This really isn't rocket science.

-----
J. D. (jj) Johnston

Representing frequency of n Hz needs sampling rate >2n Hz, not =2n

Reply #53
What I'm thinking of and trying to build is a remez-designed filter with a cutoff frequency of 20kHz and a -90dB point of about 20050 (not 22050!) Hz.

Quote

I've been trying this with a remez design of Fp=20000, Fs=20001, and dp=ds=–90dB, which gives a filter around 5 seconds long.


Nothing bad happens AFAICT—I can't ABX it with castanets.


Samples & filter coefficients (@ 44100, 48k, & 96k) are here

if anyone wants to play.



I'd be amused to hear about how you came to use that 24/96 recording, as it seems to be exceptionally similar to some original recorded work I posted on www.pcabx.com back in Y2K.

No complaints and of course its PD as far as I'm concerned, but it appears to be one of my lost children, and I'm always interested in how they come to be used in a worthwhile way.

;-)

Representing frequency of n Hz needs sampling rate >2n Hz, not =2n

Reply #54
jj, well.. it depends on what you mean with 'do'.

If I have a signal of +1, -1, +1, -1 ... then I can simply upsample by inserting zeros, send it off to a D/A converter. If the initial sample rate was 44.01 kHz then we should see a 22.05 kHz tone at the output.

Obviously, there is trickery involved (I leave this to the reader to figure out) and you are right if you respect the sampling theorem. It's also not really useful.
"I hear it when I see it."

Representing frequency of n Hz needs sampling rate >2n Hz, not =2n

Reply #55
jj, well.. it depends on what you mean with 'do'.

If I have a signal of +1, -1, +1, -1 ... then I can simply upsample by inserting zeros, send it off to a D/A converter. If the initial sample rate was 44.01 kHz then we should see a 22.05 kHz tone at the output.

Obviously, there is trickery involved (I leave this to the reader to figure out) and you are right if you respect the sampling theorem. It's also not really useful.


Well, if we're using already sampled data, ...

Which is the flaw of FFT's in this context. You need to consider the Fourier Transform, not a cyclic transform.
-----
J. D. (jj) Johnston

Representing frequency of n Hz needs sampling rate >2n Hz, not =2n

Reply #56
I'd be amused to hear about how you came to use that 24/96 recording, as it seems to be exceptionally similar to some original recorded work I posted on www.pcabx.com back in Y2K.

No complaints and of course its PD as far as I'm concerned, but it appears to be one of my lost children, and I'm always interested in how they come to be used in a worthwhile way.

;-)

Yes, it's castanets-2_2496.wav.  The site (including downloads) is in fact still available: http://web.archive.org/web/20050201005114/http://pcabx.com/

Representing frequency of n Hz needs sampling rate >2n Hz, not =2n

Reply #57
I'd be amused to hear about how you came to use that 24/96 recording, as it seems to be exceptionally similar to some original recorded work I posted on www.pcabx.com back in Y2K.

No complaints and of course its PD as far as I'm concerned, but it appears to be one of my lost children, and I'm always interested in how they come to be used in a worthwhile way.

;-)

Yes, it's castanets-2_2496.wav.  The site (including downloads) is in fact still available: http://web.archive.org/web/20050201005114/http://pcabx.com/



That is a very helpful link and it is about the best we've got, but the image of the site one finds there is incomplete because the original PCABX web site was composed of three separate sites, only one of which was linked by a registered web site name. It in turn linked 2 other unregistered web sites that were accessed only by IP addresses. This was done to minimize operational costs.  Once upon a time I put all three web sites together on one CD and gave out a few copies of it, but I've lost track of it.

Representing frequency of n Hz needs sampling rate >2n Hz, not =2n

Reply #58
OT: The internet archive is one of the most frustrating things in existence. Almost everything I've ever wanted to access has been "partially" archived there. It's not for the reason you suggest Arny. It seems to leave things out almost at random. e.g. some of your samples linked via IP addresses are there, others hosted at the same IP address are not. It often only picks a selection of images, audio files, forum posts. documents etc rather than the whole lot. It seems that its web crawler just doesn't know how to crawl.

Of course if you're really lucky, there's nothing there at all, which makes you thankful for something. The problem is some niave people think "Oh, it's OK, the whole internet is saved there" when it's not. Mostly, our recent on-line history has gone.

As for the whole "web 2.0" dynamic experience, good luck accessing any of that when it's gone offline. I bet already it's impossible to properly experience what facebook looked like just a couple of years ago.

Cheers,
David.