Radio and Aliasing

If the carrier is 150K, you can AM modulate it with signals from DC to (the limiting case, just a hair under) 150 KHz. In that case, the modulated sidebands extend from 0 to 300K, and the original signal can be perfectly recovered. Any higher than 150K signal frequency, the lower sidebands will fold over at zero and create false recovered signals: modulate a 150k carrier with a 160k signal and you'll demodulate a false 10KHz line. Of course, no antenna would allow you to actually broadcast a spectrum from 0 to 300 KHz.

There's no limit on how wideband a signal you can SSB modulate/recover using a 150 KHz carrier, USB of course.

John

Why? The spectrum would still have only 3 lines: the carrier at 150, the lower sideband at 50, and the upper sideband at 250. That's really no different from modulating at, say, 1 KHz, where the three lines would be at 149, 150, and 151.

It's only when the modulating signal exceeds 150 KHz that spurious spectral lines are created.

The Nyquist criterion doesn't apply here, as this isn't a sampled-data system. AM multiplies the signal by a sinewave carrier, and that carrier has a single spectral component. A sampling system multiplies the signal by an impulse train, which has infinitely more spectral lines and, specifically, the 2nd one at 300 KHz creates nasties.

John

Except that you modulated with 100 kHz not 50 kHz! The 50 KHz IS the result of the aliasing.

It's not an alias, it's a proper, normal AM lower sideband, no different from the 149 khz sideband you get when you modulate at 1 KHz.

the USB is at 150+100 = 250 KHz

the LSB is at 150-100 = 50 KHz

both of which are perfectly fine.

John

It does not, since AM is not a sampled-data system. I explained that in another post.

John

How can it be fine when it is not the same signal you started with? You put in 100 KHz and got out 50 KHz. You are right that they are normal sidebands but the location of the sidebands the fact that they are not representing the signal frequency is the result of aliasing.

With these sidebands you simply could not recover the original 100 KHz signal.

If you looked at the sidebands as you increased signal frequency you would expect the sidebands to get farther from the carrier. In fact, when you pass Fc/2 the sidebands "fold back" and start getting closer to the carrier. If you want to call it something else, I'm game but in my book this is aliasing.

I wish we could have this discussion in person ... could be fun for the both of us.

Greg

All AM modulation produces sidebands. The carrier amplitude is constant, so without the sidebands there's nothing *but* the carrier, and you sure can't recover any signals from a pure carrier. 1 KHz AM modulated onto a 150 KHz carrier produces a carrier line at 150 and sidebands at 149 and 151, none of which is the signal you started with. You don't *want* it to be identical, which is the whole point of modulation.

The foldback starts at a modulation frequency equal to Fc, not Fc/2. That's because modulation produces sidebands of Fc +- Fs, and you get in trouble whan the lower sideband frequency goes negative, namely when Fs > Fc. As long as Fc-Fs is positive, the AM thing still works.

Beer and napkins would certainly help. But really, I had all this stuff drilled into me in my undergrad Signals and Systems course, and a grad-level course on communications theory, which I somehow managed to pass[1]. The lower sideband is plain vanilla until its frequency passes through zero and goes negative, at which time it sort of reflects off zero and comes back to bitecha.

John

generated.

Whoops: Sorry, I read this wrong. I thought the difference in your example was

It may be possible to SEND the modulated signal but ..

The typical demodulation process is a sampling system sampling at Fc and that you cannot recover data if Fm > Fc/2.

As of right now I believe that though you MAY BE correct in the transmission side of things (I'm not certain that what you are describing is modulation as opposed to mixing) but you still could not demodulate the signal using a typical AM detector.

But many of your posts on this topic are wrong. And if the modulation signal isn't "sampled" by the (sinusoidal or digital) carrier what do you think is going on?

Don

Sidebands do not represent the carrier used in the process. They are a product of the carrier and modulation frequency.

Perhaps you would explain what you had in mind?

The carrier is 150 kHz and the modulating frequency is 100 kHz. You will recover the 100 kHz sideband using the transmitted 150 kHz carrier as the reference in a envelope detector, or insert a substitute reference frequency at a multiplier demodulator.

Well gee, AM is a multiplication. If you divide out the carrier, you get the signal back ...period.

AM is typically demodulated with a switch on the signal peaks, which is indeed sampling. But that only messes with the peaks... Tell me, the dV/dt around zero crossing changes in proportion with the amplitude, no? 'Tis information completely disregarded by a diode (or sampling) detector, but it's there nonetheless, in all its subtlety. You can't go and tell me it doesn't represent something now...

(Or if you don't like my case for dV/dt inbetween peaks, take absolutely anything else about the overall shape of the waveform, outside of the peaks themselves.)

Tim

Sorry, no - it's 150 kHz. If you want to approach AM from the standpoint of sampling theory, you have to realize that there are two "samples" per cycle of the carrier.

Bob M.

While the Nyquist sampling criteria is most often used in digital systems these days, the theorem itself actually does not care whether the final result is conveyed in digital form or analog. All it really is is a mathematical analysis of how rapidly you must sample a time-varying function in order to capture all of the information that waveform has to provide. (Actually, it's not limited to temporal sampling - the Nyquist criteria also applies to spatial sampling, as comes into play in image processing theory.)

Of course. It can occur in any sampled system, and again AM CAN be treated as sampling - you just have to be careful to look at it correctly.

Bob M.

On Sat, 09 Sep 2006 20:04:56 GMT, in message , "G. Schindler" scribed:

Well, I'm in the Pacific Northwest. If there's some way we could all get together, I'd by the first round.

Wrong. "Aliasing" in this case (AM radio) occurs when the bandwidth of the modulating signal exceeds that of the carrier, not 1/2 the carrier - the reason being that the effective "sample rate" (if you're going to consider AM radio to be a sampling system) is twice the carrier frequency.

John also missed the boat a little bit, in saying:

Actually, Nyquist DOES apply here, you just have to look at the "samples" as occuring at the peak (and trough) of each carrier cycle (which of course define the amplitude "envelope" of the modulated carrier. It's a bit odd to look at AM radio in this manner, but the basic criteria DOES hold true here and the aliasing occurs if the rates aren't right, just as Nyquist predicts.

Bob M.

You might be more specific.

AM is the time-domain multiplication of a signal with a sinusoidal carrier. Sampling is the multiplication of a signal with a train of unit impulses. These things look very different in the frequency domain, since the transform of the sinusoidal carrier is a single Fourier line, but the transform of the impulse train is an infinite series of lines. A sine times a sine gives two products, or sidebands, in the frequency domain. A sine times an impulse train gives an infinite number of product frequencies.

That's the mathematics, and the math doesn't care about your verbal descriptions... it always works the same.

I'm surprised I have to explain simple stuff like this.

John

The responses I've received have confused me.

What is the highest frequency that can be received on a 150 khz AM radio receiver? Is it 150 khz, 300 khz, 75 khz, or 60 khz?

Some of the responses have told me that Nyquist theorem means that the frequency of the station must be at least 2x [and due to physical limitations, at least 2.5x] that of the highest frequency of the modulation [audio] signal. Other responses have said different. Some have said 150 khz can contain a modulation signal of 300 khz.

Which should I believe??

Sorry. I meant to say what is that highest modulation frequency...

On Sat, 09 Sep 2006 17:15:12 -0700, in message , John Larkin scribed:

That's what I love about electronics. The proof is in the math. Bullshit doesn't walk.

Well in all fairness, it *is* sci.electronics.BASICS. I suggest you have a little more patience. Not everyone who asks a question or posts a response is trying to be perfect, or otherwise infallible. This discussion is having an immense impact on my orientation into my new career, so let's keep it civil, folks! So far, so good.