![(50 points) The input X(t) in the circuit shown in the following figure is a stochastic process with EIX(t)]-0 and Rx(t)-626(](http://img.homeworklib.com/images/675b9914-a460-427a-975a-8f0644e41c58.png?x-oss-process=image/resize,w_560)
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(50 points) The input X(t) in the circuit shown in the following figure is a stochastic process w...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t)...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t)...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Q.2 ICO2]10 Marks] The signal g(t) forms the input to the LPF circuit shown in the figure, where R l,and y(Dis the output. If the power spectral density (PSD) of the signal ge) is (a) The autoc...
Q.2 ICO2]10 Marks] The signal g(t) forms the input to the LPF circuit shown in the figure, where R l,and y(Dis the output. If the power spectral density (PSD) of the signal ge) is (a) The autocorrelation of g(t) (b) The 3-dB bandwidth of the LPF (c) The power of g(t) and y(t) (d) Based on your answers above, will it be better if the signal has more or less bandwith? (e) If a white noise of PSD No/2 is...
Find the power of the signal conponent of a P is the Fourice t of s,(0)(2.5 points) edf,where S.f density of pu nose (2.5 points) . Consider the RL circuit shown below. Assume that R-10 and L-IN....
Find the power of the signal conponent of a P is the Fourice t of s,(0)(2.5 points) edf,where S.f density of pu nose (2.5 points) . Consider the RL circuit shown below. Assume that R-10 and L-IN. Hint : Use Parseval's relationship if necessary i(t) e. What is the input signal-o-oise (SNR,ratio, defined as: SNR, 1olog..C)as polnts d. Find the output power spectral density of noise N,00 N,( HP, where HU) is the frequency response of the circuit, and N,(n)...
Q1) Let X(t) be a zero-mean WSS process with X(t) is input to an LTI system with Let Y(t) be the output. a) Find the mean of Y(t) b) Find the PSD of the output SY(f) c) Find RY(0) -----------------...
Q1) Let X(t) be a zero-mean WSS process with X(t) is input to an LTI system with Let Y(t) be the output. a) Find the mean of Y(t) b) Find the PSD of the output SY(f) c) Find RY(0) ------------------------------------------------------------------------------------------------------------------------- Q2) The random process X(t) is called a white Gaussian noise process if X(t) is a stationary Gaussian random process with zero mean, and flat power spectral density, Let X(t) be a white Gaussian noise process that is input to...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the...
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function of Y(t)
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
11.8 A linear system has a transfer function given by H(W) + 15w+50 Determine the power...
11.8 A linear system has a transfer function given by H(W) + 15w+50 Determine the power spectral density of the output when the input function is a. a stationary random process X(t) with an autocorrelation function, Rxx(t)=10e ! b. white noise that has a mean-square value of 1.2 V/Hz
A stochastic process X() is defined by where A is a Gaussian-distributed random variable of zero ...
A stochastic process X() is defined by where A is a Gaussian-distributed random variable of zero mean and variance σ·The process Xt) is applied to an ideal integrator, producing the output YO)X(r) dr a. Determine the probability density function of the output Y) at a particular time t b. Determine whether or not Y) is strictly stationary Continuing with Problem 4.3, detemine whether or not the integrator output YC) produced in response to the input process Xit) is ergodic.
A...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Q.2 ICO2]10 Marks] The signal g(t) forms the input to the LPF circuit shown in the figure, where R l,and y(Dis the output. If the power spectral density (PSD) of the signal ge) is (a) The autocorrelation of g(t) (b) The 3-dB bandwidth of the LPF (c) The power of g(t) and y(t) (d) Based on your answers above, will it be better if the signal has more or less bandwith? (e) If a white noise of PSD No/2 is...
Find the power of the signal conponent of a P is the Fourice t of s,(0)(2.5 points) edf,where S.f density of pu nose (2.5 points) . Consider the RL circuit shown below. Assume that R-10 and L-IN. Hint : Use Parseval's relationship if necessary i(t) e. What is the input signal-o-oise (SNR,ratio, defined as: SNR, 1olog..C)as polnts d. Find the output power spectral density of noise N,00 N,( HP, where HU) is the frequency response of the circuit, and N,(n)...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function of Y(t)
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
11.8 A linear system has a transfer function given by H(W) + 15w+50 Determine the power spectral density of the output when the input function is a. a stationary random process X(t) with an autocorrelation function, Rxx(t)=10e ! b. white noise that has a mean-square value of 1.2 V/Hz
A stochastic process X() is defined by where A is a Gaussian-distributed random variable of zero mean and variance σ·The process Xt) is applied to an ideal integrator, producing the output YO)X(r) dr a. Determine the probability density function of the output Y) at a particular time t b. Determine whether or not Y) is strictly stationary Continuing with Problem 4.3, detemine whether or not the integrator output YC) produced in response to the input process Xit) is ergodic.
A...
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