Why we do that in AM demodulation?

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Discussion Overview

The discussion revolves around the methods of synchronous demodulation in amplitude modulation (AM) and the reasoning behind using multiplication instead of division in the demodulation process. Participants explore the implications of both approaches, considering practical implementation challenges and theoretical underpinnings.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions why division by cos(wt) is not used in AM synchronous demodulation, suggesting it seems more intuitive and easier than multiplication.
  • Professor 1 argues that division requires precise knowledge of the transmitter frequency, which can drift, complicating the recovery of the signal.
  • Professor 2 presents two reasons against division: noise amplification when dividing by cos(wt) and the risk of dividing by zero, leading to circuit saturation.
  • Another participant notes that multiplication effectively brings the modulated signal down to baseband, leveraging trigonometric identities to remove modulation frequency.
  • Concerns are raised about the practicality of implementing a "divide by function" circuit, particularly at high frequencies and in analog systems.
  • Some participants suggest that while digital signal processing could theoretically handle division, it complicates the design and may not provide advantages over multiplication.
  • Discussion includes the potential for increased signal power to mitigate noise issues when using division, but questions the overall efficacy of such an approach.
  • Historical context is provided, indicating that synchronous detection was traditionally implemented with analog circuitry, where multiplication is straightforward.

Areas of Agreement / Disagreement

Participants express differing views on the practicality and theoretical justification for using multiplication versus division in AM demodulation. There is no consensus on which method is superior, and multiple competing perspectives remain throughout the discussion.

Contextual Notes

Participants highlight limitations related to the precision of frequency knowledge, noise handling, and the challenges of implementing division in both analog and digital domains. The discussion reflects unresolved technical considerations and varying assumptions about signal processing methods.

  • #31
jim hardy said:
I woke up in the middle of the night thinking about this thread.
old jim

OMG Jim. you're taking your work home with you again!
Aren't you supposed to be retired? :wink:
 
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  • #32
sophiecentaur said:
OMG Jim. you're taking your work home with you again!
Aren't you supposed to be retired? :wink:

Yes, old firehorse syndrome i guess ...

thouht maybe i'd learn something new !

old jim
 
  • #33
idmond dantes said:
why there will be noise at only the carrier frequency and it's harmonics, assuming that the noise added by the channel is a white noise?

Imagine the 1/cos function. Those spikes are terrible! And you multiply your function with it. If there is any signal at all there due to white or whatever noise, it will produce a giant signal. So you will see the same spikes again after dividing your signal. These spikes have twice the period of your carrier so they will be full of harmonics of the carrier frequency.

And finally we have the answer why this stuff isn't done. Three things will kill the scheme:

1) Noise. If your signal is f(t)cos(kt)+e(t) where e is noise, you will have divergences in the spikes of the 1/cos function, because e(t) is surely not zero at the crossings. As I said: you amplify your signal infinitely in the region with the worst signal to noise ratio.

2) Phase and frequency. If your local oscillator is not perfectly phase and frequency locked against the sending oscillator, the zero crossings will be off, the spikes will not get canceled and will dominate whatever comes out

3) Offset voltages. It is pretty much impossible to have components without any offset voltage. So even if your frequency and phase would match perfectly, your zero crossings will be off again producing spikes.

Infinite spikes are simply a bad idea. This type of problem happens also in the Wiener deconvolution, where you also divide the blurring of the signal away, but due to the same signal to noise problems you need to dampen the method at the frequencies were the noise is large compared to the signal.
 
  • #34
0xDEADBEEF said:
You substitute the multiplication with cos(x) by a multiplication with 1/cos(x).
That is a very clear-eyed way of expressing it.

Multiplying by cos x looks much smoother than multiplying by this:

attachment.php?attachmentid=56263.png
 

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