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In Reply to: I'm not following you posted by Charles Hansen on May 20, 2006 at 21:14:38:
Generate a 15kHz sine wave at 44.1k sampling rate.You will a complete waveform is represented by only 3 samples (44.1/15).
However, the three samples are enough because mathematically, after Nyquist filtering, the original 15kHz waveform is reconstructed perfectly - so says theory anyway, and generally most DACs will come very close.
Now, as an experiment, move each sample slightly in the time domain (simulating jitter) or slightly in the amplitude domain (simulating quantization error).
You will find the reconstructed waveform is no longer a perfect 15kHz sine wave, illustrating the effect of jitter and quantization error. The higher the frequency, the greater the deviation in the reconstructed waveform.
Now, imagine the waveform wasn't a constant 15kHz waveform, but one that changes in amplitude as well as frequency. Ie. over exactly the same time period (1/15k of a second), the wave changes from 15kHz to 20kHz and the amplitude changes from 0dB to -10dB.
Now try and reconstruct the waveform. You will find that 44.1/16 is not enough resolution to reconstruct the waveform perfectly even in the absence of jitter and quantization error.
However, what is worse is that if you now move the samples around to simulate jitter and quantization error, the reconstructed waveform now bear little resemblance to the original intended signal.
In the worse possible case - where the frequencies are close to Nyquist (say around 20kHz) but are also rapidly modulated in both amplitude and frequency, the reconstructed waveform can be completely different in phase and amplitude, based on some reasonable assumptions about jitter magnitude and amplitude accuracy.
Anyway, that should be enough information for you to replicate my observations. You should be able to do it in Excel, but the calculations required to reconstruct a waveform can be a bit tedious to implement (I would suggest implementing the equivalent of a digital filter in a VBA script callable from Excel).
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Follow Ups
- I'll try and explain it as simply as I can, but it is a lot easier if i can draw a picture - Christine Tham 22:01:19 05/20/06 (1)
- Re: I'll try and explain it as simply as I can, but it is a lot easier if i can draw a picture - Frank.. 11:30:45 05/22/06 (0)
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