A bad assumption on my part. 2.000001X isn't Hz; it needs to be normalized. The result is not a million seconds, but a million sample times. That's still a long time. Most of the time, there's pretty good resolution at half that, in this case, 500,000 sample times.
I don't see what you mean. Could you explain with an equation or two?
Jerry
If course, and for other things too. Even if you can be certain that there is no signal energy above Fmax, you need to sample faster than
2Fmax in real situations. As it says on traffic a summons in Boston, "Fail ye not thereof at your peril."Jerry
"robert bristow-johnson" wrote in news: snipped-for-privacy@i3g2000cwc.googlegroups.com:
Robert--
CommitteeSize = CommitteeSize + 1 ; %!!!!!
I think what's missing is a demonstration that multiplication with the Dirac train in time pairs with convolution with the scaled Dirac in frequency. Without a good figure showing that, the figures under the "aliasing" subtitle lack some meaning.
As an aside, I'm interested in the analogs in AM. By the book, the carrier needs to be twice as fast as the highest signal component, but for Hilbert demodulation, all I can find is the specification that the signal and carrier not overlap. Is this because the transform essentially throws out the negative frequencies, so you don't have to worry about positive/negative overlap? Alternatively, am I just wrong, and the carrier needs to be twice the highest frequency, even for Hilbert demod??
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Yes I am, and this discussion is great.
--
Tim Wescott Wescott Design Services
Posting from Google? See
"Applied Control Theory for Embedded Systems" came out in April. See details at
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Mostly I'm assuming that things need to be done in the real world, with real equipment that can be bought for real amounts of money. Given those assumptions I think I'm on track.
Yes I am. That's a direct consequence of assuming a real system that is only turned on for a finite period of time.
Yes I am. That's a direct consequence of assuming that you don't want to wait an infinite amount of time for your filter's output.
Falling significantly short of that, I'm staying aware of just how much you have to pay for a filter that's 'practically' brick wall, whatever that means for your particular application.
Most other old timers who are pitching in here seem to understand.
That's true. The problem comes about when newbies who have forgotten all of the addenda, exceptions and quid-pro-quos* assume that Nyquist is a design guideline instead of a theoretical limit.
Can you post a link to an example schematic?
I don't think you missed anything. First, a switch mode power supply isn't a sampled data system, really. It's certainly time-varying and shares some aspects of a sampled-time system (including the fact that you can use the z transform to improve the accuracy of the analysis if you're a masochist), but it isn't really sampled. Second, while the switching action may alias all sorts of higher-frequency components of the control voltage into the baseband, that doesn't keep the baseband component of the control voltage from being passed through just fine.
gives m:n ratio of fft overlap
multiply to give correlation
as fast mul done by FFT like thing, so i understand?
then not FFT infered, possibility!
whats up doc?
No, once it's aliased it's indistinguishable.
Do you mean where the signal has been resampled at each step?
Much of the paper is going to be the explanation necessary for me to make just that assertion -- plus explaining what "effectively disappeared" might mean in different systems.
Or to put it another way: for Fs = (2 + epsilon)F your observation interval is something like
1 t = --------- F*epsilon(more or less -- there's probably a factor of 2 in here that I'm missing). The closer epsilon gets to zero the longer you have to wait. How patient are you?
Bingo. Yes. I'll be making just that point.
Can english write? maybe (not)
Actually designing for the sin x / x rolloff isn't too bad as long as you keep your eyes open -- in older digital video systems it was just done with a peaky 2nd-order LC circuit (in newer digital video systems the sampling rate is way higher than the effective resolution of the phosphor, which simplifies things).
But you can't avoid the issue of providing sufficiently steep skirts on your filters, both in and out. As you get closer and closer to Nyquist in a 'simple' system your filter complexity goes through the roof, as does the difficulty of actually realizing the filters in analog hardware. This is why many systems that must store or transmit data at close to Nyquist (like music on a CD) have A/D and D/A sample rates that are significantly higher than the internal transmission rate, with digital decimation and interpolation coupled with simplified analog anti-alias and reconstruction filters.
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IIRC the sin x / x business only applies to sample and hold filtering. The impulse function avoids that. A further point is that the thing that counts in an end to end system, such as telephony, is the net transfer function. You can distribute this in various way with compensating input and output filters. This is generally known as equalization.
Somewhere in the Nyquist discussion, you might mention that Nyquist didn't attend MIT or Stafford. He went to a small obscure school in North Dakota.
Robert, Did I miss anything?
-- Al Clark Danville Signal Processing, Inc.
-------------------------------------------------------------------- Purveyors of Fine DSP Hardware and other Cool Stuff Available at
FOAD. It was a short, to-the-point comment. The only possible rational argument that can be made to his post is that he didn't trim the quoted text.
Tim
-- Deep Fryer: a very philosophical monk. Website:
HIO4?
Tim
well, then maybe they should be moved the the "mathematical basis", then. you don't need the convolution with the Dirac comb in the frequency domain thingie if you can show by some other means (i think simpler means) that the spectrum is copied and shifted at all multiples of the sampling frequency. we can show that by showing that the Dirac comb is a periodic function with identical coefficients (all 1 if you scale it right) and then using the frequency shifting theorem.
i think so. this kind of AM modulation is called SSB. at least that's what we called it when i was a ham radio kid 38 years ago.
duh, i dunno. i think, if you do it the Hilbert way (we didn't have DSP in them olden days of the Heathkit HW100) you can have a carrier frequency of whatever you want. you can separate the positive and negative parts of the original baseband signal and move the positive up or down any amount with the negative part doing the mirror image and moving down or up the opposite amount.
r b-j
I'm not an expert in this area, so maybe you can clarify something. Does the system handle multiple carrier frequencies? If the carrier frequency is fixed, I would expect that the bandwidth of the PLL would be narrow enough to exclude the aliased frequencies.
True, but the "information" on a periodic waveform will be all garnered one helluva lot quicker at 2.1x than at 2.000000001x
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