adding noise to a signal

Hello everyone,
I am confused about a thing. If I wanna add white noise with a variance of 0.0625, are the following are correct?
I am stuck whether I need to use 0.0625 or sqrt of it.

Besides, is it OK to write the following:
so that I can make a relationship between SNR and variance therefore everytime I change SNR, the noise_sig will change according to the variance.

Thanks a lot.

vHi
v
it should be
noise_sig = original_sig + sqrt(0.0625)*randn(size(original_sig)) ;

assuming zero-mean AWGN.

be definition SNR=S/N, now the energy of N for AWGN is equal to the variance, the you need to set the signal energy S to a certain level for an specific SNR.

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Sal

Hi leony,

Whether you can use the equation depends on the signal you are using.

SNR = (Signal Power)/(Noise power)

Signal power = V²/2 for sinusoid RMS value
Noise power = σ² for N(0,σ²)

so for sinusoid SNR (dB) = 10 log(V²/2σ²)

You may rearrange this for you use as you had done. Be sure to change the signal power for any other signal.

Hope this helps.

BRM

Hi
About your first question, if x is a normal random variable(0 mean and variance 1), if you want to make a another gaussian random variable with meam 0 and variance sigma2, you should make it from x by sigma*x

Added after 16 minutes:

Hi
About your 2nd question.
White noise is confusing, specially in simulations.
brmadhukar is right. Noise power = sigma2 for N(0,sigma2). But what is sigma2 ?
Be careful, power spectral density(PSD) of white noise is flat. so power of white noise is infinite. If some filters are used, power become finite. If PSD of white noise is flat with amp N0/2, then after filtering, its power become N0*B and B is bandwidth of filter. so sigma2 = N0*B.
If u dont like to work with bandwidth, just make a normal random variable and multiply it by sigma.
see MATLAB help about AWGN and SNR, it hase some good points.