# Talk:Amplitude modulation

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## Formulas

I am not sure, but as far as I remmber the formulas should be ${\displaystyle c(t)=C\cos(\omega _{c}t)\,}$ and ${\displaystyle m(t)=M\cos(\omega _{m}t+\phi )\,}$ so ${\displaystyle \ X_{AM}(t)=[C+M(t)]\cos(\omega _{c}t)=[C+M\cos(\omega _{m}t+\phi )]\cos(\omega _{c}t)}$, i.e., ${\displaystyle \ X_{AM}(t)=C\cos(\omega _{c}t)+{M \over 2}[\cos(\phi +(\omega _{m}+\omega _{c})t)+\cos(\phi +(\omega _{m}-\omega _{c})t)]}$, thus, ${\displaystyle \ X_{AM}(t)=C[1+m_{a}\cos(\omega _{m}t)]\cos(\omega _{c}t)}$ while ${\displaystyle m_{a}={M \over C}}$. The first formulas, here in this article, include sines but only the last one include cosines. I scammed the other Wikipedias and I found cosines in every forgin Wikipedia I checked. Am I mistaken? --Shimonnaim 13:25, 31 March 2007 (UTC)

## Image

The FM article uses Image:Frequency-modulation.png as a static image showing the waveform. It seems like it would wise to include the equivalent image for AM on this page: Image:Amplitude-modulation.png. Thoughts? Tacvek 18:20, 29 June 2007 (UTC)

## 'Telephone' example

I don't think that the telephone is a good example. We can't consider a baseband medium 'modulated', even with DC bias, IMO. A better example is needed. Or am I missing a historical AM telephone? --Ktims 07:28, 31 August 2007 (UTC)

I am inclined to agree. But I will play devil's advocate for a moment. Rather than looking at it as "DC bias" or "transmission medium", the implication is that it is a 0 Hz "carrier", with a measureable power level of its own. Without that power source, the telephone apparently doesn't work.
In contrast, consider acoustic transmission of the same voice signal through air. The air provides no energy. It is truly just a medium. The only measureable power comes from the information source itself.
But I agree that the distinction is unnecessarily subtle.
--Bob K 14:17, 31 August 2007 (UTC)

## amplitude modulation index

I don't think the amplitude modulation index is correctly explained.

See http://www.rfcafe.com/references/electrical/amplitude_modulation.htm —Preceding unsigned comment added by 192.91.172.36 (talk) 02:08, 2 October 2007 (UTC)

I agree the calculation for the modulation index is obviously wrong because earlier it the article it is explained that A=0 is used for carrier suppression. This equation therefore implies that m = M/0 = infinity when the carrier is suppressed.

Kris —Preceding unsigned comment added by 203.97.235.82 (talk) 07:49, 8 February 2008 (UTC)

Yes the modulation index is wrong here. If we are using the same definitions as in this article for the carrier wave and the modulation waveform, the modulation index is actually M.

## Merge?

It seems to me this article is very similar or identical in purpose and scope to the Modulation article. Could/should they be merged? --166.70.188.26 (talk) 17:43, 30 June 2008 (UTC)

They are not in any way similar in purpose or scope! Modulation is an introduction to "all" modulation schemes. This article covers the maths, theory and application of one specific modulation scheme. Oli Filth(talk) 19:34, 30 June 2008 (UTC)

## Fig.1 is wrong

The depiction of the FM signal is wrong in Fig.1 image (it does not follow the modulating signal). —Preceding unsigned comment added by Gyll (talkcontribs) 16:54, 6 August 2008 (UTC)

Looks ok to me. Oli Filth(talk|contribs) 17:06, 6 August 2008 (UTC)

## Too many animations

See discussion at Talk:Frequency modulation#Too many animations

## The idea of Heterodyning

This process is known as heterodyning.

This is a small stub gleaned from the original article which suggests that the AM carrier and its two sidebands are merged in a process known as heterodyning. This is a false statement. The sidebands occur as a modulation product just as they do in FM. FM has theoretically infinite sidebands but are of little use other than consuming spectrum space than AM. Actually the process of heterodyning takes place in the radio receiver circuitry. The local oscillator frequency is fed to a circuit called a mixer along with the received signal from the antenna after a preamplifier. This "mixing" of signals is known as heterodyning and produces sums and differences of the received signal and the signal from the local oscillator. Heterodyning has nothing to do with an AM carrier and its adjacent sidebands in a pure sense since the sidebands, carrier or both can be heterodyned with a local oscillator frequency then fed to an IF filter and once again mixed and then finally output to an amplifier for audio with everything except the modulating signal removed. The final ouput from an AM superheterodyne receiver has to be absolutely linear in that the received signal has to be exactly reproduced at the output. FM receivers are much more forgiving since only the frequency has to be preserved, so sloppy, non linear circuits can be used. --Skywalker45 (talk) 19:15, 11 November 2010 (UTC)

Heterodyne, modulate, and mix, are three words that mean exactly the same thing. We generally don't use heterodyne when we talk about modulators, but we are heterodyning. We take an audio frequency signal and a radio frequency signal, put them together, and end up with the original signals and the sum and difference of the two signals. The sidebands are the sum and the difference. When I read the article, the word heterodyne startled me, but it is technically correct. wa6bjh (talk) 20:57, 24 December 2010 (UTC)
The meanings overlap, but they're not exactly the same. Mixing is probably most general, as it means nonlinearly combining two signals (in audio it means linearly, but that's different). AM modulating is bilinear mixing a baseband signal with a carrier oscillator signal. Heterodyning is mixing an RF signal with a local oscillator signal of a frequency different from the RF carrier frequency. Homodyning is mixing an RF signal with a local oscillator signal of same frequency as the RF. Dicklyon (talk) 23:08, 24 December 2010 (UTC)
"When multiplication of two signals takes place, as opposed to their simple addition, mixing is involved. The result is multiple signals, including the sum and difference of the AF and RF frequencies. These two "products" will appear as sidebands alongside what was the original RF frequency. Mixing, modulation, detection, demodulation, and heterodyning all refer to this multiplication process and can all be analyzed by the same mathematical treatment." American Radio Relay League, Handbook for Radio Communications, 2008, p. 9.26. wa6bjh (talk) 23:54, 2 January 2011 (UTC)
Are you saying we should ignore subtle differences in meaning, just because this one sourced sentence does? Dicklyon (talk) 02:51, 3 January 2011 (UTC)
This discussion started because someone wrote that "heterodyning has nothing to do with an AM carrier and its adjacent sidebands..." I pointed out that all of those things are the same, and they are. It's important to understand that all of those things are the same, regardless of what you call them. I don't like heterodyning for the AM modulation process, and I wouldn't use the word, but I wouldn't change the article, because it's technically correct. In the 1950s, a single diode mixer was common in VHF receivers. I owned one in the 70s. The strong local oscillator (heterodyne oscillator) and the weaker VHF signal were both applied to the cathode of a diode. The filter after the diode selected the signal you wanted for the IF. We call this circuit a mixer. But when we take a diode in a crystal radio and we apply a strong carrier and weaker sidebands to the cathode, and select the resulting audio signal, we call this a detector or a demodulator. But it does the same thing as a the VHF mixer, except that we select an AF signal instead of an RF signal. The process is the same regardless of what we call it. In the 1920s people spoke of condensers and capacity, but now we say capacitor and capacitance. People may have once used homodyne, but the term now is direct conversion. They mean the same thing. There are some problems with this article and the modulation article, and we need to fix them so people understand the process.wa6bjh (talk) 01:36, 5 January 2011 (UTC)
What it said was "In its basic form, amplitude modulation produces a signal with power concentrated at the carrier frequency and in two adjacent sidebands. This process is known as heterodyning." I don't believe that this process of modulation has ever been called heterodyning. Do you know of a source where it is? Dicklyon (talk) 02:20, 5 January 2011 (UTC)
You're correct, modulation usually isn't called heterodyning. And I must admit that I've never seen that anywhere. But I have seen this: When describing what we would call heterodyning--mixing an RF signal with a local oscillator to produce an IF--the author called the products upper and lower sidebands instead of the usual sum and difference frequencies. I think it was in Experimental Methods of RF Design, but I'll look. I don't like heterodyne for modulation and I don't like upper and lower sidebands for sum and difference frequencies in a mixer. But they're really all the same. On a slightly different point, I prefer a modulation description that talks only about sidebands, because then you're well on your way to understanding single sideband. I don't like the time domain thing that's in figure 1, because that's not what's happening. wa6bjh (talk) 02:12, 7 January 2011 (UTC)
Why don't you like the time-domain view? It looks correct to me. And what's wrong with calling the products upper and lower sidebands, when they are not discrete frequencies? Or do you mean that at the mixer to IF, both sidebands get translated via sum and difference to two complete two-sideband images? Actually, there's nothing there about an mixer to IF, so I guess it's moot. Dicklyon (talk) 03:51, 7 January 2011 (UTC)
Here are some sources that heterodyning is the process behind amplitude modulation:
I think the issue is a POV problem. The word "heterodyne" is mostly used in the description of the superheterodyne reception process. It would be confusing to explain to students that the sidebands of the transmitted signal are also themselves heterodynes, created by the modulation process. So in elementary explanations of radio the word heterodyne is not used for AM modulation or sidebands. From the POV of elementary telecommunications, the word heterodyne is restricted to mean shifting of (modulated) signals from one frequency to another, using mixers and local oscillators.
However from the POV of the electrical engineer, heterodyning, the mixing of two frequencies in a nonlinear device to create new frequencies, is the common principle behind AM modulation, demodulation, mixing and frequency conversion, as the above sources show. I think it is important that this point be in the article. --ChetvornoTALK 23:17, 28 September 2013 (UTC)

## Spectrum section

While I'm no mathematician (which is putting it mildly), I know a little about radio—which I presume this article is trying to address, although it has far too many formulas IMO—and can't get my head around this section. The assertion that each sideband has the same carrier-plus-sidebands as the "fundamental" frequency confuses this concept with DSB-AM and its variants and since the whole negative-frequency thing is speculative to begin with, it just muddies the waters.--Miniapolis (talk) 20:22, 26 October 2011 (UTC)

## Modulation

Modulation is a technique by which we can transfer our information at a distance . Science only amplitude phase and frequency of the wave can be changed so we have three basic type of modulation 1.) Amplitude Modulation 2.) Frequency Modulation 3.) Phase Modulation. 1.) Amplitude Modulation : Here the amplitude of the carrier is varied w.r.t variation of the amplitude of the signal wave or original data. 2.) Frequency Modulation : Here the Frequency of the carrier is varied w.r.t variation of the amplitude of the signal wave or original data. 3.) Phase Modulation : Here the phase of the carrier is varied w.r.t variation of the amplitude of the signal wave or original data — Preceding unsigned comment added by 122.173.247.34 (talk) 05:07, 13 July 2012 (UTC)

## Carrier-suppressed DSB is 100 percent power-efficient?

Is it correct to say Suppressed-carrier AM is 100 percent power-efficient?

Seems to me that since the information is transmitted twice (two sidebands) it's more like 50% efficient.

Mike (talk) —Preceding undated comment added 19:58, 2 April 2013 (UTC)

It depends how you define efficiency. If you demodulate DSB using a USB or LSB receiver, you are losing 50% of the power that goes into the other sideband. However, if you have an optimal DSB receiver, it combines the power in the two sidebands, and nothing is lost -- 100% efficiency. I.e., all the transmitted power goes into "useful" modulation with nothing "lost" to a carrier.--Albany45 (talk) 00:43, 3 April 2013 (UTC)

I have made a few changes that hopefully will address the question Mike raises and not add other confusion. I agree with Albany45s comments, but have extended the logic to include all receiver types. The main point being that if you match the transmitted signal to the receiver type, all three systems (AM, DSB, SSB)are 100% efficient, defined as every part of the transmitted signal being useful. Note however that for DSB to be 100% efficient as a system, the sidebands must demodulate coherently so as to add. For AM to be 100% efficient as a system, we must assume an envelope detector.JNRSTANLEY (talk) 18:15, 18 April 2013 (UTC)

As far as I know, this question mostly comes up in the case of the final amplifier for a transmitter. A lot of power is supplied by the amplifier, and then transmitted. Now, compare to the DSB-SC used for the stereo subcarrier in FM broadcast radio. You couldn't add an AM carrier, and still stay within the other limits for FM. On the other hand, adding a DSB-SC (left-right) subcarrier to a baseband (left+right) gives the same result as switching between (left) and (right) at 38kHz. The pilot carrier at 19kHz is needed to demodulate it. Could one have a broadcast system based on DSB-SC with 10% pilot carriers at half the frequency? Or could one define a broadcasting system that transmitted the carrier at reduced (maybe 10%) power? Given modern digital technology, there are many more efficient ways to broadcast audio signals. Receivers that are many years old are still out there, and all would be useless. For broadcast radio, with many receivers, the power cost per receiver is pretty low. Gah4 (talk) 23:06, 13 October 2016 (UTC)

Gah4 asks "Could one have a broadcast system based on DSB-SC with 10% pilot carriers at half the frequency? Or could one define a broadcasting system that transmitted the carrier at reduced (maybe 10%) power?" Having a pilot carrier at half the frequency works for FM stereo where the entire spectrum from DC to the maximum baseband frequency is continuously available, but in over the air broadcasting would be impossible both for frequency allocation reasons and for propagation reasons. DSB-RC with a pilot carrier does save power but requires a complicated receiving setup. It would have been a viable system for communications but not so attractive for broadcasting due to the legacy receiver issue. SSB-RC has been used in broadcasting. With 6 dB carrier reduction the program is intelligible but distorted, and with a phase locked receiver sounds terrific. HCJB used this system for about 10 years on one frequency, 21.455 MHz, a couple of decades ago JNRSTANLEY (talk) 14:26, 15 October 2016 (UTC)

Thanks. It was a little bit idle thoughts, wondering what might be possible, in theory. I was ignoring the allocation problem, as that is only a practical problem. The propagation concern is interesting. Legacy receiver issue is a problem, but note that it didn't get in the way of the digital television transition. Though I suppose people replace television sets more often than AM radios, especially with the transition away from CRT sets. In the case of broadcast radio, the power is amortized over a large number of listeners, so the cost isn't all that high. Gah4 (talk) 20:27, 15 October 2016 (UTC)

## More details on high level generation

There are quite a few more methods of generating an AM signal at high power levels, at least six of them I have used in my broadcast engineering career, not counting obsolete methods. I would like to expand this section quite a bit, but wonder if this is something that would merit a page of its own, perhaps under "AM transmitters" or "AM broadcast transmitters". It seems that this section is a subset of "Radio Transmitter Design", which is also quite limited and out of date in its coverage of AM transmitters. Perhaps best to expand under that subject and then modify this presentation a bit with a link to that. I am open to suggestions. JNRSTANLEY (talk) 18:46, 18 April 2013 (UTC)

Since the article isn't so long, it seems to me that this could be an interesting addition. I suspect you shouldn't go too far into engineering details, though. Can you hint as to what you would say? Gah4 (talk) 22:39, 13 October 2016 (UTC)

This was some time ago, but as well as I can remember, I have already added the material I had in mind. JNRSTANLEY (talk) 14:11, 15 October 2016 (UTC)

## Changed [t+m(1)] to m(t+1).

The formula for modulation presented in the "Simplified Example" is incorrect. The equation states that ${\displaystyle y(t)=[m(t)+1]*c(t)}$, when the equation is actually ${\displaystyle y(t)=m(t+1)*c(t)}$. The original equation does not produce a correctly modulated line, but one that is only ever on one side of the x-axis per wave packet. (See https://www.desmos.com/calculator/40yzkqufin, the top graph is the original equation, the bottom graph is the correct one) I took the liberty of fixing it, but I'm not sure quite how to update the Prosthaphaeresi version, so that is probably now incorrect. If somebody knows how to fix the Prosthaphaeresi version or my edit is incorrect, please fix it yourself and/or let me know. Skylord a52 (talk) 21:08, 6 May 2015 (UTC)

I believe the original is correct and I have restored it while the issue is discussed. I don't feel like doing whatever is necessary to examine the link you gave, but reading the section in question shows that m is a function of time (say an audio signal) and m(t+1) does not make sense (why add 1 to t?), and the math is correct. In the original, the 1 represents the carrier component and the m represents the variation in carrier amplitude, which can go up or down by an amount up to the carrier amplitude. Johnuniq (talk) 01:50, 7 May 2015 (UTC)
The reason I was confused was because the original equation doesn't graph a traditional looking modulated wave, one where the group waves appear as full ellipses. The original equation looks something like a sine wave with the area closest to the x-axis "filled in," it only has waves on one side of the axis at a time, and as M decreases, the more it appears like a normal sine wave. The other version looks like the AM wave in fig 1, so that's why I thought that that was correct. The +1 in my version is unnecessary, I put that there because I thought that the original was a typo and I wasn't sure what the +1 was for. I would very much appreciate if you took a look at the graph I linked, and verify which equation is correct.
Skylord a52 (talk) 19:43, 8 May 2015 (UTC)
The original equation was correct. Here are some sources: [1], Eq.3.1, [2] Eq.4-1-1, [3] Eq.77.6. I'm not sure what problem you had (your app won't load in my browser) but as ${\displaystyle \scriptstyle m}$ decreases to zero it is supposed to look like a "normal sine wave". The idea of amplitude modulation is that with no modulating signal ${\displaystyle \scriptstyle m(t)\;=\;0}$ the modulated signal ${\displaystyle \scriptstyle y(t)}$ is a sine wave of a certain amplitude. On the positive half cycles of the modulation signal ${\displaystyle \scriptstyle m(t)\;>\;0}$ the amplitude of the sine wave increases, while on the negative half cycles ${\displaystyle \scriptstyle m(t)\;<\;0}$ the amplitude of the sine wave decreases. The "1" in the formula ${\displaystyle \scriptstyle m(t)\;+\;1}$ is necessary so that ${\displaystyle \scriptstyle m(t)\;+\;1}$ is always positive so it acts as a scaling factor. In your equation the amplitude of the output sine wave ${\displaystyle \scriptstyle y(t)}$ increases on both the negative and the positive half-cycles. --ChetvornoTALK 21:22, 8 May 2015 (UTC)
Okay, I see what I was doing wrong. (Thanks for providing the sources) I'm sorry to waste your time Skylord a52 (talk) 04:19, 12 May 2015 (UTC)

The amplitude of modulating signal frequency is constant the carrier signal is varying by time. — Preceding unsigned comment added by 122.169.186.2 (talk) 05:51, 13 May 2015 (UTC)

## Assessment comment

The comment(s) below were originally left at Talk:Amplitude modulation/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

 It is a good article.It is usefull if you add a topic in AM generation showing how to give Class C amplifier output to a tuned circuits yours faithfully shafeeque c220.225.200.154 (talk) 06:41, 17 January 2008 (UTC)

Last edited at 13:31, 10 April 2008 (UTC). Substituted at 07:38, 29 April 2016 (UTC)

## DSB-SC and QAM

I wonder if there should be a reference to modulation methods derived from AM. Specifically, DSB-SC and QAM. There is a {{citation}} related to its use in computer modems. QAM is widely used in computer modems, and DSB-SC for the stereo subcarrier for FM transmission. Both are modifications to AM. I suspect that enough of a description to give people a reason to link to the appropriate page would be right. In the QAM case, the computer modem use could be added there. A discussion for the reason for the difference in demodulation methods between AM and DSB-SC would also be useful. That is, that the carrier isn't a waste. Gah4 (talk) 22:49, 13 October 2016 (UTC)

## Importing and translating content from Czech article

The Czech article seems to include content, particularly in the section cs:Amplitudová_modulace#Typy_amplitudov.C3.BDch_modulac.C3.AD, that could be helpful in understanding the principles of AM and its different types. ZFT (talk) 19:03, 1 January 2017 (UTC)

## Modulation

Modulation is the process of modifying a carrier wave in accordance with an information signal to be transmitted. Changing the amplitude of the carrier produces AM. — Preceding unsigned comment added by Jibon Krishna (talkcontribs) 05:08, 13 March 2017 (UTC)

## Adapter Filter

Wireless communication has become an essential part of life in many parts of the world. With the deployment of communication everywhere, it became very crucial to pay attention to its technological betterment. It is essential to address the problems associated with different types of communication channels and to find out probable solutions. When dealing with multipath fading channels, Intersymbol Interference (ISI) occurs during transmission. It is necessary to know the channel characteristics for solving the problems associated with it. Hence researches on channel equalization and channel estimation have been carried out by many researchers. Different kinds of adaptive filtering are used for channel equalization and estimation. However we developed a new algorithm for estimation of a communication channel. In this thesis, a new adaptive filtering is introduced, where the main goal is to improve the performance of the existing algorithms in terms of convergence speed and filtering performance. It is well known that the LMS algorithm has slow convergence for correlated inputs. Moreover its filtering performance and convergence speed are inversely related through a single parameter, the step size. The GLMS algorithm is one of the modified LMS algorithms, which uses single step size but introduces a smoothing parameter which in turn controls its convergence speed and provide better steady state performance. On the other hand, variable step size is used in the LMS algorithm to achieve both fast convergence and a small ﬁnal excess mean-square estimation error. As a well-studied area, many variations of the LMS algorithm with variable step sizes have been proposed in the literature. A common point in these algorithms is that the step-size computation uses preset control parameters, and sometimes the step size is adapted for every iteration. In this paper, we propose a simple but effective variable step-size adjustment approach, in which only three different step sizes are chosen for filter coefficient adaptation with GLMS algorithm (VSSGLMS). Experiments for the Raised Cosine channel estimation with our proposed VSSGLMS algorithm show the effectiveness in rapidly driving the mean-square estimation error to a small signal steady-state value. We compared our proposed VSSGLMS algorithm with LMS and GLMS algorithms under different parameter settings. From the simulation, we observed that our proposed VSSGLMS algorithm provides better performance in terms of convergence and steady state MSE level. — Preceding unsigned comment added by Jibon Krishna (talkcontribs) 05:11, 13 March 2017 (UTC)