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I want to add a noise signal to a signal which is a combination of three sinusoidal signals with different amplitude, frequency and phase. How to add this noise signal to the sinusoidal signal so that the Signal-to-Noise ratio will be 10 dB?? and how to pass this resulting signal through an averaging filter (low pass filter system)??

joshua
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  • i know @knedlsepp i saw that post, but i want the signal to noise ratio be specified and pass the resulting signal through a filter. so it's quite different that's why i posted it :) – joshua Dec 27 '14 at 17:50
  • No, it's not different at all. You are asking A+B, whereas the linked question gives you A, and there's probably lots of other questions about filtering, which will give you B. – knedlsepp Dec 27 '14 at 17:58

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For sinusoid with amplitude A : SignalPower=0.5*A^2 For white gaussian noise with STDV=q and Bandwidth=BW: NoisePower=BW*q^2

So for your signal: SNR=(0.5*A1^2+0.5*A2^2+0.5*A3^2)/(BW*q^2)

In matlab you create gaussian white noise with sigma=q:

Noise=q*randn(1,SignalLength);
Mendi Barel
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  • thanks for your answer dude, but i didn't really get it. i have to combine three sinusoidal signals as below: a - first signal, Amplitude = 10, frequency = 200 Hz, phase = pi/4, b - second signal, Amplitude = 15, frequency = 2000 Hz, phase = pi/8, c - Third signal, Amplitude = 25, frequency = 2800 Hz, phase = pi/2, i have to add the noise to the resulting signal of these three signals. so what will be the "q" and "BW" in this case?? thank you again – joshua Dec 27 '14 at 14:54