Signal-Noise-ratio weird observation?

Question

I generated a signal X that contains 100 values and each value varies from 0 to 63. After that, I inserted a noise to the signal with SNR=25dB using awgn function provided by Matlab. The graph of signal and (signal + noise) is shown in Fig. 1.

I then added each value of X an offset of 150. As a result, each value of X now ranges from 150 (0+150) to 213 (150+63). I also inserted the same noise to this new signal using awgn function. The graph of new signal and (new signal + noise) is shown in Fig. 2

It seems to me that the noise increased significantly. I then recalculated the SNR, and I found that the SNR value is unchanged, 25 dB. However, the amplitude difference obviously changed, which affected the results of the next system. My question therefore is why the difference between the new signal and (new signal + noise) increase.

I am grateful if someone can explain it. Thank you.

Answer 1

"The noise increased significantly." That depends on how you evaluate noise. The variance increased, yes, but the SNR didn't. The SNR depends also on the signal strength. Adding a constant to your signal increased its strength. Thus the variance of the noise must increase also to keep the same SNR.

SNR stands for Signal to Noise Ratio. It's a ratio of power of signal to power of noise.