Radio and Aliasing

[John O'Flaherty]

Hi:

Lets say there is an AM station with a carrier frequency of 150 KHz.
What is the highest frequency of modulation that it can handle?

I think it depends on a bandwidth, and the exact limits, not a single
frequency. You could modulate a band extending from, say, 100 kHz to
120 kHz, with a 150 kHz carrier, producing a modulated band from 30 kHz
to 50 kHz. Then you could recover the original band at a receiver with
a local oscillator of 150 kHz. As long as there is no overlap of
frequency bands, there's no ambiguity or aliasing. This assumes the
frequency bands produced can be isolated with filters, which they can
in the case mentioned.
On the other hand, if you modulated a band from 20 Hz to 120 kHz with
a 150 kHz carrier, there would be no way to distinguish, and separate
by filters, all the frequencies coming out of the modulator. For
example, an input signal of 76 kHz in the input band would be present
in the output as 76 kHz (itself) and 74 kHz. A 74 kHz input would
likewise be present as 76 kHz and 74 kHz, and there would be no way to
separate the two signals.

In digital audio, the sample rate must be at least 2x the highest
frequency. What is the equivalent in analog AM radio?

You could go to just under 75 kHz, theoretically, but that's well
above audio in any case.

 

[John Larkin]

Bob Myers wrote:
Hi:

Lets say there is an AM station with a carrier frequency of 150 KHz.
What is the highest frequency of modulation that it can handle?

Legally, 5 kHz (well, OK, I can't say that for a 150 kHz
transmitter; I'm talking about the legal limits on radio
stations in the AM broadcast band, 535 - 1705 kHz).

Sorry. I meant to ask what is the highest audio frequency that can
[physically] be broadcasted through a 150 Khz carrier.

Errr.......... 150kHz maybe ? Maybe SSB can do better ?

Graham

Uh.. Nope.

Regulations aside, the highest modulating frequency you should use with a
150 kHz carrier is 60 kHz. Anything higher will be garbage.

Don

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

 

[John Larkin]

Right ... Aliasing will happen anytime the audio signal exceeds 1/2 the
carrier frequency so it would also happen for 100 kHz audio on a 150 kHz
carrier.

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

 

[G. Schindler]

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.

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

 

[John Larkin]

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

 

[John Larkin]

Nyquist does apply to AM modulation

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

John

 

[G. Schindler]

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

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

 

[John Larkin]

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.

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.

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.

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.

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

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

[1] the undergrad school gave grades from A to F, but the grad school
jumped from F to B-, no C's or D's. Since I was the only undergrad in
the class of three students, and they didn't have the heart to flunk
me, so I got a B-. The math was ghastly.

 

[G. Schindler]

Whoops:
Sorry, I read this wrong. I thought the difference in your example was
50 KHz not 100 Khz which is why I said you couldn't recover the 100 KHz
data.

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.

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.

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.

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.

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.

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

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

[1] the undergrad school gave grades from A to F, but the grad school
jumped from F to B-, no C's or D's. Since I was the only undergrad in
the class of three students, and they didn't have the heart to flunk
me, so I got a B-. The math was ghastly.

 

[Don Bowey]

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

John

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

 

[Don Bowey]

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.

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?

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

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.

 

[Tim Williams]

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?

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

 

[Bob Myers]

Someone seems to be misreading the question (conceivably, it could be me).

Because of the reference to sampling I believe the question is meant ask
the highest modulation frequency that can be transmitted over a 150 kHz
AM broadcast. The answer here is 75 kHz due to Nyquist Criteria. Nyquist
Criteria is the reason for limiting the Digital Audio data to one half the
sampling rate.

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.

 

[Bob Myers]

Isn't Nyquist Criteria for digital data only? AM radio is analog.

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.)

Can aliasing occur in analog AM radio?

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.

 

[Alan B]

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

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

 

[Bob Myers]

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.

 

[John Larkin]

But many of your posts on this topic are wrong.

You might be more specific.

And if the modulation
signal isn't "sampled" by the (sinusoidal or digital) carrier what do you
think is going on?

Don

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

 

[Radium]

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??

 

[Radium]

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?

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

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 station can contain a modulation signal of 300 khz.

Which should I believe??

 

[Alan B]

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.

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.