What would be the purpose of denoting the noise as single-sided? It seems that if we consider the noise as double-sided with power spectral density $\frac{N_0}{2}$, noise power is still $\sigma^2=\mathbb{E}\{n^2(t)\}=N_0W$ since we have to integrate over the negative frequencies and the positive frequencies. The term "red noise" comes from the "white noise"/"white light" analogy; red noise is strong in longer wavelengths, similar to the red end of the visible spectrum. Strictly, Brownian motion has a Gaussian probability distribution, but "red noise" could apply to any signal with the 1/f 2 frequency spectrum. Power spectrum Gaussian Distribution of Noise Amplitude. Since the rms value of a noise source is equal to δ, to assure that a signal is within peak-to-peak limits 99.7% of the time, multiply the rms value by 6(+3δ−(−3δ)): Erms 6 = Epp. For more or less assurance, use values between 4(95.4%) and × 6.8(99.94%). SNRdb = 10 ∗log10 Psignal Pnoise S N R d b = 10 ∗ log 10 P s i g n a l P n o i s e. Your gaussian noise function generates the noise based on a scaling factor k of the signal max amplitude. Since you want to scale the amplitude of the noise based on your signal, i believe you want a relationship of: k = Anoise Asignal k = A n o i s e A s i Generate white noise (technically this should be converted to the frequency domain, but the frequency domain is also white noise so the step can be skipped (i.e. consider the generated white noise to be the spectrum of another set of generated white noise) The initial circular Gaussian curve is shown in the top image, and the cosine White noise (at least in all the meanings ice come across) means normal random variables with mean 0 and variance 1 and are iid. So yes, I guess you could think of white noise as a specific type of iid random variables. This was sent on my phone sorry for any spelling/grammar errors! There's an important clarification embedded in this. .

white noise vs gaussian noise