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Narrow-band Gaussian white noise is demodulated coherently by dsb, and its output power is several times that of input power.
Narrow-band Gaussian white noise is coherently demodulated by dsb, and its output power is 0.5 times of the input power, because the system gain of DSB modulation system is 2. This shows that the demodulator of DSB signal has doubled the signal-to-noise ratio. This is because synchronous demodulation is used to suppress the orthogonal components in noise, thus reducing the noise power by half.

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