Consider $s(t)$ as the signal, $w(t)$ as the noise, and $y(t)$ as the captured signal. Usage of additive noise model, that is $y(t)=s(t)+w(t)$, is quite wide spread, example in speech and audio signal enhancement, and is also physically convincing to hypothesize. The convolutive noise model,that is $y(t)=s(t)\star w(t)$, where, delayed copies of the signal overlap together is another widespread model. A physically relevant scenario for this is reverberation modelling.

My question is - Is there a physical motivation to model noisy signal using multiplicative noise model, that is $y(t)=s(t)w(t)$? I am unable to think about any convincing physical domain examples where this happens in reality.

  • $\begingroup$ Useful link 1, useful link 2 $\endgroup$ – Gilles Aug 19 '16 at 10:43
  • $\begingroup$ well, remember what a frequency mixer is: a mutliplicator. Now, what happens when you feed in additive-noisy signals to that? $\endgroup$ – Marcus Müller Aug 19 '16 at 11:01
  • $\begingroup$ Thank you @MarcusMüller Yes, frequency mixer can be interpreted as a modulation - shifting the baseband frequency content. My question is where do we encounter such modulation (or frequency mixing) happening directly in the signal model before the signal is acquired. $\endgroup$ – Neeks Aug 19 '16 at 11:23
  • $\begingroup$ @Gilles Thank you for the link. However, enough physical domain examples are not available there. I see that, channel delay in analog demodulation can result in a multiplicative noise (a constant factor), and this may also be time-varying. Are there any more examples for 1-D signals (not images)? $\endgroup$ – Neeks Aug 19 '16 at 11:27
  • $\begingroup$ @Neeks , you're welcome. Here is another useful link. $\endgroup$ – Gilles Aug 19 '16 at 11:30

In communications, a very important multiplicative model is a flat fading channel where the received signal can be modeled as

$$y(t)=h(t)\cdot s(t)+n(t)\tag{1}$$

where $h(t)$ is the time-varying attenuation caused by the channel, and $n(t)$ is additive noise.

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