By using Fourier transform analysis equation we get the solution.
7. Let h(T) =T,IT <1 (and equal to zero otherwise) be an impulse response function of...
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6 Impulse Response Let h(t) denote the response of a system for which the input signal is the unit-impulse t 0: he(t) = t [a(t) _ u(t-1)] + 2a(t-2), for t > 0.
5. Let ffx)= cx for 1 < x< c0, zero otherwise be the pdf for the random variable X. a) Find c b) Find F(x). c) Find P(X> 3.2). d) Find E(X).
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t) = 〉 1 0 < t < 1 0 t>1 Find the output y(t) of this system if the input is given by a) x(t) = 1 + cos(2nt) b) x(t)-cos(Tt) c) x(t) sin (t )l d) x(t) = 1 0 < t < 10 0 t 10 e) x(t) = δ(t-2)-5(t-4) f) a(t)-etu(t) Problem 2: For the same LTI system in Problem 1,...
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
4. Let S be a linear, time-invariant, and causal system whose input x(t) and corresponding output y(t) are shown below: r(t) Page 1 of 2 Please go to next page... y(t) ? (a) Find the impulse response function h(t) of ? (b) Find the output of S when its input is e*, t<0, t2, t20
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...
Exercise 5. Let X(t) be a WSS process with correlation function 1-Irl, if-1-1S1 0,otherwise. Rx(T) = It is known that when X (t) is input to a system with transfer function H(), the system output Y(t) has a correlation function Ry(T) sin TT = =-TT Find the transfer function H(u
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An LTI system has the impulse response h(T) = 1 for 0 <T<T and is zero otherwise. If continuous-time white noise with ACF ru(T) = (No/2)8(T) is input to the system, what is the PSD of the output random process? Sketch the PSD.
BC:9.4 A LTI discrete time system has an impulse response h[n] = (-0.8)"u[n] + (0.65)"u[n-1] Find the transfer function, #(eo), in the normalized frequency domain. Use Matlab to plot the magni- tude and phase (in degrees) of H(eo) in the range of-? < ? < ?. Attach your Matlab source code with the plots. 1212 AM ^???4/4/2013
Find the Laplace transform of the given function. f(t) = {et, Ost<2 lo, t> 2 | F(s) =