x(t)=exp(-at) u(t), u(t) is unit step function what is x(t) autocorrelation function? energy spectral density? energy?...
1.x(t) =Aexp((-t^2)/T^2) (T>0) (a) Energy Spectral Density (b)Autocorrelation Function y(t)=x(t)cos(2m/t) (1) Energy spectral Density 1.x(t) =Aexp((-t^2)/T^2) (T>0) (a) Energy Spectral Density (b)Autocorrelation Function y(t)=x(t)cos(2m/t) (1) Energy spectral Density
Use your knowledge of the relationship between spectral density and autocorrelation function in order to answer the following questions. Show your work for full credit. Determine the spectral density of a process with autocorrelation function Rx(t) = 3e-2t a) Determine the spectral density of a process with autocorrelation function Rx(t)-2 sinc(0.51) b) c) Determine the autocorrelation function of a process with spectral density Sx (f) 2 sinc2(f/2) 12 Determine the autocorrelation function ofa process with spectral density Sx(a)-A+ d) Use...
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...
Q.6 Determine the autocorrelation function and power spectral density of the random process olt)= m(t) cos(21f t+), where m(t) is wide sense stationary random process, and is uniformly distributed over (0,2%) and independent of m(t).
2. Let Y(t) = (x(0)+)(\pi) where X(t) is a Poisson process with autocorrelation function Rxx(t1, tz) = tīta + min(tı, tz), and 6 ~ U(0,2%) is independent of X(t). a. Is X(t) W.S.S.? b. If so, find its power spectral density. [25]
2. Let Y(t) = ei(x(0)+o)(\pi) where X(t) is a Poisson process with autocorrelation function Rxx(t1, tz) = tīta + min(tı, tz), and 6 ~ U(0,2") is independent of X(t). a. Is Y(t) W.S.S.? b. If so, find its power spectral density. [25]
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...
I. The autocorrelation function of a random signal is R(r) !-ⓞrect rect a. Find the power spectral density of the signal. b. Plot the amplitude of the power spectral density with Matlab (Let Ts -2) c. Find the null-to-null bandpass bandwidth, and the 0-to-null baseband bandwidth (in terms of Ts).
Please do all parts please. thank you Exercise 3. Let u(t) denote the unit step function u(t)= { 0, t<0, u(t)={ 1, ost. Show that A) (exp(at) u(t)) * (exp(Bt) u(t)) = ex (+)_exp(at) - exp(Bt) 8t) u(t), for a #B (1) a-B B) (exp(at)u(t)) * (exp(at)u(t))=texp(at)u(t) exp(Bt) - exp(at)+(a-B)texp(at)u(t), for a #B C) (t exp(at) u(t))*(exp(Bt) u(t))= (a - )2 D) (t exp(at)u(t)) * (exp(at)u(t)) =žt? exp(at)u(t) E) (t exp(at)u(t)) * (t exp(at)u(t)) = tº exp(at)u(t) (at)u(-t) +exp(Bt) u(t)...
Calculate the energy and the energy-spectral-density for the signal x(t) 100 sine(200 π t)cos (1400mt)