Home |
Search |
Today's Posts |
|
#2
|
|||
|
|||
Gee, I hope Bonnie didn't claim they were original. Certainly it's not
difficult to figure out. More interesting to me is recent work on letting a delta-sigma ADC sample at a rate to serve as a direct IF sampler--up around 5GHz. The practice of getting it to work really right at such frequencies is much more interesting than the formulas for what frequencies work and avoid aliasing. Cheers, Tom |
#3
|
|||
|
|||
Greetings all,
I'm new to the group and find many of the various threads fascinating. I'm currently building a homebrew HF rig. I think undersampling has probably been around nearly as long as sampling itself. This is because samplers are a subset of (RF) mixers, and early engineers fluent in RF mixer skills would have had undersampling in their toolboxes already. As mixers, samplers are modelled as a multipliers with the sampler clock serving as the local oscillator. What makes samplers a subset of mixers are the constraints placed on the LO--in the ideal sampler a Dirac delta function is used. This waveform has the property that all harmonics (including the zeroth or DC and even harmonics) have the same amplitude. Our doubly-balanced RF mixers typically respond to only odd harmonics. Real-World samplers approximate the ideal sampler fairly well over a wide frequency range. Because samplers have a DC response, the baseband signal Fin is passed by the sampler, something RF mixers don't normally do (but can be made to do simply by putting a DC component on the local oscillator). When viewing a sampler as a mixer, aliasing is nothing more or less than the mixing product (LO-Fin) overlapping the baseband signal Fin. Undersampling is nothing more or less than prefiltering the desired band of frequencies and mixing them to baseband with the appropriate harmonic of the local oscillator. I've not found the notion of samplers as mixers in the literature, but probably could if I looked hard enough. Perhaps authors consider the notion either obvious or not useful, but to this old ham viewing samplers as mixers is useful. Bonnie's article contains a fun blunder. She states Nyquist and Shannon developed sampling theory in the 1920's, which would have put Shannon in his teens. Shannon's seminal paper on communication theory was actually published in 1948. I've read that the 'Nyquist rate' should really be called the 'Shannon rate' as he was the first to develop it. Anyone know more? Regards, Glenn Dixon, AC7ZN |
#4
|
|||
|
|||
That's absolutely correct.
Tektronix has produced sampling oscilloscopes from at least the early 60's which have a frequency response of from several to several tens of GHz but sample at rates often below 1 M sample/sec. Aliasing? You betcha! As you pointed out, the aliased signal is the desired one -- a frequency (or time) converted signal. The only requirement is that the signal be repetative, since it takes samples from many cycles to create the time-scaled waveform. Single-shot events, often misunderstood or disregarded by RF engineers, require Nyquist-dictated sampling rates. This is done by most conventional digital oscilloscopes. The Nyquist criterion assumes that you want to recreate a nearly exact replica of the waveform and that it extends down to DC; if you'll settle for a time scaled or frequency shifted one, or one with a limited bandwidth, other options are available. Roy Lewallen, W7EL wrote: Greetings all, I'm new to the group and find many of the various threads fascinating. I'm currently building a homebrew HF rig. I think undersampling has probably been around nearly as long as sampling itself. This is because samplers are a subset of (RF) mixers, and early engineers fluent in RF mixer skills would have had undersampling in their toolboxes already. As mixers, samplers are modelled as a multipliers with the sampler clock serving as the local oscillator. What makes samplers a subset of mixers are the constraints placed on the LO--in the ideal sampler a Dirac delta function is used. This waveform has the property that all harmonics (including the zeroth or DC and even harmonics) have the same amplitude. Our doubly-balanced RF mixers typically respond to only odd harmonics. Real-World samplers approximate the ideal sampler fairly well over a wide frequency range. Because samplers have a DC response, the baseband signal Fin is passed by the sampler, something RF mixers don't normally do (but can be made to do simply by putting a DC component on the local oscillator). When viewing a sampler as a mixer, aliasing is nothing more or less than the mixing product (LO-Fin) overlapping the baseband signal Fin. Undersampling is nothing more or less than prefiltering the desired band of frequencies and mixing them to baseband with the appropriate harmonic of the local oscillator. I've not found the notion of samplers as mixers in the literature, but probably could if I looked hard enough. Perhaps authors consider the notion either obvious or not useful, but to this old ham viewing samplers as mixers is useful. Bonnie's article contains a fun blunder. She states Nyquist and Shannon developed sampling theory in the 1920's, which would have put Shannon in his teens. Shannon's seminal paper on communication theory was actually published in 1948. I've read that the 'Nyquist rate' should really be called the 'Shannon rate' as he was the first to develop it. Anyone know more? Regards, Glenn Dixon, AC7ZN |
#5
|
|||
|
|||
I read Angelo's full article (shoulda done that before I pontificated
the first time) and it answered the Nyquist vs. Shannon question I had. Nyquist had the concept, Shannon proved it mathematically. Thanks, Angelo. Regards, Glenn Dixon, AC7ZN |
Reply |
Thread Tools | Search this Thread |
Display Modes | |
|
|
Similar Threads | ||||
Thread | Forum | |||
eScrew OWNS YOU!!! | CB | |||
eScrew OWNS YOU!!! | Policy | |||
eScrew zen story | Antenna | |||
Unbelievable a My story | Dx |