Two independent random signals X and Y are known to be Gaussian with mean values x0 and y0 and variance _x^2and _y^2. A signal Z = X - Y is obtained from them. The mean z0, variance _z^2and p.d.f. p(z) of the signal Z are given by:

x_0 - y_0, _x^2 + _y^2,Gaussian

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Signal Processing

Two independent random signals X and Y are known to be Gaussian with mean values x₀ and y₀ and variance $$\sigma _{\text{x}}^2$$ and $$\sigma _{\text{y}}^2.$$ A signal Z = X - Y is obtained from them. The mean z₀, variance $$\sigma _{\text{z}}^2$$ and p.d.f. p(z) of the signal Z are given by:

A) $${{\text{x}}_0} - {{\text{y}}_0},\,\sigma _{\text{x}}^2 - \sigma _{\text{y}}^2,\,{\text{Gaussian}}$$ B) $${{\text{x}}_0} + {{\text{y}}_0},\,\sigma _{\text{x}}^2 + \sigma _{\text{y}}^2,\,{\text{Rayleigh}}$$ C) $${{\text{y}}_0} - {{\text{x}}_0},\,\sigma _{\text{y}}^2 - \sigma _{\text{x}}^2,\,{\text{Uniform}}$$ D) $${{\text{x}}_0} - {{\text{y}}_0},\,\sigma _{\text{x}}^2 + \sigma _{\text{y}}^2,\,{\text{Gaussian}}$$

Answer & Solution

Correct Answer: Option D

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Two independent random signals X and Y are known to be...

Two independent random signals X and Y are known to be Gaussian with mean values x0 and y0 and variance $$\sigma _{\text{x}}^2$$ and $$\sigma _{\text{y}}^2.$$ A signal Z = X - Y is obtained from them. The mean z0, variance $$\sigma _{\text{z}}^2$$ and p.d.f. p(z) of the signal Z are given by:

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Two independent random signals X and Y are known to be Gaussian with mean values x₀ and y₀ and variance $$\sigma _{\text{x}}^2$$ and $$\sigma _{\text{y}}^2.$$ A signal Z = X - Y is obtained from them. The mean z₀, variance $$\sigma _{\text{z}}^2$$ and p.d.f. p(z) of the signal Z are given by: