Noise with uniform power spectral density of N₀ W/Hz is passed through a filter H(ω ) = 2exp (-jωt_d) followed by an ideal low pass filter of bandwidth B Hz. The output noise power in Watts is

A 1 mW video signal having a bandwidth of 100 MHz is transmitted to a receiver through a cable that has 40 dB loss. If the effective one-sided noise spectral density at the receiver is 10^-20 Watt/Hz, then the signal-to-noise ratio at the receiver is

If the variance $$\sigma _d^2$$ of d(n) = x(n - 1) is one-tenth the variance $$\sigma _x^2$$ of a stationary zero-mean discrete-time signal x(n), then the normalized autocorrelation function $${R_{xx}}\,(k)\,/\,\,\sigma _x^2\,at\,\,k\,\, = \,1$$ is

For a random variable 'X' following the probability density function, p (x), shown in figure, the mean and the variance are, respectively.