How to apply SNR to Guassian White Noise?

[djnotes]

I have an exercise that requires applying a guassian white noise with signal to noise ratio of 10 dB on a sine signal with amp=1, sampling rate=1 Hz, duration=1 and freq=3 Hz.
The question then requests application of some filtering with cut-off and moving average.

The guassian noise implementation in thinkdsp does not take a SNR parameter. I didn't find anything signal to noise ratio in the book. Is it possible to solve this problem using thinkdsp and Python?

noise = thinkdsp.UncorrelatedGaussianNoise()

[AllenDowney]

Should be doable. You can generate a signal with the SNR you want by generating a sine signal as specified and then adding white noise with the power ratio you want. For SNR=10 dB, the power of the white noise should be one tenth the power of the sine signal. Is that enough to go on?

[djnotes]

Still a bit confused. Does this mean?

sinSig = ... # the sine signal
noise = 1/10 * thinkdsp.UncorrelatedGaussianNoise()
mix = sinSig + noise

[AllenDowney]

Yes, but you'll need to use UGN to generate a Wave with the same length as your signal. And dividing the amplitude by 10 divides the power by 100. Also, you might want to compute the power of both Waves before to check whether they have the same power before you divide.