Gaussian noise will form narrowband Gaussian noise when it passes through a narrowband system with central angular frequency. The characteristic of narrow-band Gaussian noise is that its frequency spectrum is limited in a narrow frequency range nearby, and its envelope and phase change slowly and randomly. If you observe the waveform with an oscilloscope, it is a sine wave with a frequency of about 0, and its envelope and phase change randomly.
Extended data
The probability density function of narrow-band Gaussian white noise satisfies the statistical characteristics of normal distribution, the power spectral density function is constant, and the frequency band width is much smaller than its central frequency. Its power spectral density function is constant in the whole frequency domain, that is, it obeys uniform distribution. Because it is similar to white light that includes all visible light frequencies in optics.
Gaussian white noise involves two different aspects of noise, namely, the normal distribution of probability density function and the uniformity of power spectral density function, both of which are indispensable.
Reference source: Baidu Encyclopedia-Narrow-band Gaussian White Noise
Reference source: Baidu Encyclopedia-DSB-SC
Reference source: Baidu Encyclopedia -—DSB
Reference source: Baidu Encyclopedia-Gaussian White Noise