The questions about modulation of sine waves near the Nyquist limit seem to be common and repeated. The image URL here has a plot that, I think, explains how the "beating" comes about due to adding in frequencies that are solely above the Nyquist limit, and thus how filtering them out removes any "beating" one observes in raw, unfiltered data from a DAC (before the anti-imaging filter).Start at the BOTTOM. That's the waveform you see at the DAC output, before the anti-imaging (reconstruction) filter. In this example, the beating is quite obvious.
Now, going from top down, let us see how this staircase wave was constructed. In the TOP graph, we see the original sine wave (cyan) and the first two images. (magenta and yellow). The black waveform is the SUM of the three. You notice how already, at this point, we have a lot of "beating" happening, and that also, we've very carefully and quite specifically added ONLY sine waves ABOVE the anti-imaging filter cutoff.
The middle three rows add more of the images, adding 2 sets (4 total sine waves) each time. (c,m,y,g in order, lowest to highest image)
The final row is the sum of the first 1000 images. I didn't bother to show the other 900+ very high frequency sine waves.
So, very clearly, shown in simple pictures, the result is clear, the waveform that shows the modulations at the output of the DAC arises from OUT OF BAND signals.
The graph, btw, is Copyright J. Johnston, 1999, 2000.
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Topic - A Graphical Explanation involving Sampling - jj 09:25:41 02/17/00 (43)
- Re: A Graphical Explanation involving Sampling - Rod M 19:33:54 02/17/00 (20)
- RodM. . . - patentguy 08:11:23 02/18/00 (19)
- Re: RodM. . . - Rod M 13:50:12 02/18/00 (15)
- Re: RodM. . . - Mart 09:43:02 02/19/00 (14)
- You mean, "it can" - jj 14:04:41 02/19/00 (13)
- Re: You mean, "it can" - Mart 14:08:05 02/19/00 (12)
- There's no such THING, Mart. That's where you err. - jj 14:18:54 02/19/00 (11)
- so by infinite duration - Mart 14:35:10 02/19/00 (10)
- The example is not recursive... - jj 14:42:47 02/19/00 (9)
- care to design one? - Mart 14:56:17 02/19/00 (8)
- Design what? - jj 15:55:09 02/19/00 (7)
- Re: Design what? - Mart 18:39:24 02/19/00 (6)
- Ahhh.... - jj 19:35:44 02/19/00 (5)
- who doesn't cheap out? - Mart 22:42:19 02/19/00 (4)
- Sorry, I never name specific equipment - jj 10:10:14 02/20/00 (3)
- Re: Sorry, I never name specific equipment - Mart 18:34:57 02/20/00 (2)
- Hmm.... - jj 19:39:17 02/20/00 (1)
- very true... - Mart 20:46:42 02/20/00 (0)
- in all modesty - petew 10:44:17 02/18/00 (1)
- Thank you for sharing (nt) - jj 11:35:33 02/18/00 (0)
- I wouldn't feel bad about this... - jj 09:38:46 02/18/00 (0)
- Phase Preservation. - jj 13:08:43 02/17/00 (0)
- Great info, jj! - Spike 10:15:10 02/17/00 (0)
- Re: A Graphical Explaination involving Sampling - Werner 09:53:29 02/17/00 (19)
- Interesting idea, that. - jj 09:56:24 02/17/00 (18)
- I've never got around to learning MatLab ... - Mart 21:33:31 02/17/00 (17)
- That presents a bit of a problem. - jj 11:27:42 02/18/00 (9)
- now I know how a hamster feels ... - Mart 11:55:32 02/18/00 (8)
- Well, the point is... - jj 12:57:52 02/18/00 (7)
- Well, the REAL point is... - Mart 09:10:37 02/19/00 (6)
- No, it doesn't migrate down to audible frequencies - jj 14:06:49 02/19/00 (5)
- Re: No, it doesn't migrate down to audible frequencies - Mart 14:20:15 02/19/00 (4)
- Please see above... You're making some odd assumptions - jj 14:35:16 02/19/00 (3)
- oops, typo ... analogy -> use an analog - Mart 14:52:53 02/19/00 (2)
- Ah, now at least that comment computes :-) - jj 15:59:21 02/19/00 (1)
- Re: Ah, now at least that comment computes :-) - Mart 18:29:42 02/19/00 (0)
- oversampling - Werner 23:32:11 02/17/00 (6)
- Re: oversampling - Mart 00:52:51 02/18/00 (5)
- Re: oversampling - Werner 01:42:01 02/18/00 (4)
- Re: oversampling - JoeII-K 11:49:09 02/18/00 (2)
- care to expound on pros & cons of upsampling? - Mart 09:28:57 02/19/00 (1)
- Re: care to expound on pros & cons of upsampling? - JoeII-K 12:24:36 02/19/00 (0)
- I'm sorry I took too much for granted - Mart 04:58:04 02/18/00 (0)