4. Find and the autocorrelation function R (t) of the following signal : x( Find the...
151 4.8 Problems 4.17 The autocorrelation function Txx(t) of a real analog signal x (t) is defined by xx(t) x(t)x (r-t) dt, (4.73) obtained from Eq. (4.70) by replacing y(t) with x (t). Thus the function is a cross-correlation of x(t) with itself. One application of the autocorrelation function is to detect the period of a periodic signal that has been corrupted by noise. Show that rxx(t) is an even function of r.
151 4.8 Problems 4.17 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).
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...
1.12. The Fourier transform of a signal x(t) is defined by X(f) = sincf, where the sinc func- tion is as defined in Equation (1.39). Find the autocorrelation function, R.(T), of the signal x(t).
1.12. The Fourier transform of a signal x(t) is defined by X(f) = sincf, where the sinc func- tion is as defined in Equation (1.39). Find the autocorrelation function, R.(T), of the signal x(t).
answer comepltely and clearly
1. For which of the following is R(T) an appropriate autocorrelation function? If R(T) is not a valid autocorrelation, state why not; otherwise, find the power spectral density S(f) and the total power. (a) R(T) = sinc(2nfor) (d) R(T) In G) - 1–12, 1131 (0, |-|> 1 -2 -1 _ſ1 - IT, IT 31 (c) R(T) = (1 + IT, IT > 1
Determine and plot the autocorrelation function rxx[l] of the
signal 1, 0≤n≤N−1
x[n] = 0, otherwise .
Determine and plot the autocorrelation function r] of the signal x[n] = 0, otherwise
x(t)=exp(-at) u(t), u(t) is unit step function what is x(t) autocorrelation function? energy spectral density? energy? bandwidth?
A random signal with autocorrelation function is filtered by a filter with transfer function H(f) = What is the autocorrelation function of the output signal?
1.2-4 For an energy signal x(t) with energy Ex, show that the energy of any one of the signals –x(t), X(-t), and x(t - T) is Ex. Show also that the energy of x(at) as well as x(at - b) is Ex/a, but the energy of ax(t) is a Ex. This shows that time inversion and time shifting do not affect signal energy. On the other hand, time compression of a signal (a > 1) reduces the energy, and time...
4- Find the auto-correlation function of the signal g(t) = e-at
u(t). From this determine the energy
spectrum density of g(t).
4 Find the auto-correlation function of the signal g(t) = e-at u(t). From this determine the energy spectrum density of g(t).