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 rxx[l] of the signal 1, 0≤n≤N−1 x[n] = 0, otherwise...
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...
1. Suppose x(t)-1f 4<t<5 otherwise 0 Determine the absolute time duration of this signal and plot it. 2. Suppose lnlf n 2 otherwise Classify this signal as left-sided, right-sided, two-sided, or time-limited and plot it.
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]
A random process X(t) has an autocorrelation function Rxx (T) = 9 + 2e-1| If X(t) defined in question 11 is the input to a system having an impulse response h(t) = e-stu(t), where is a positive constant Find the mean value of the output process
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]
1. (a) Given function 0t2 x(t) = - - 0, otherwise plot function x(-^t + 2) plot function r+2) (b) For function plot function y[1 -2n].
Section 2.1 I. Suppose 2(t) if 4<t 5 otherwise Determine the absolute time duration of this signal and plot it. 2. Suppose rn]-1 if n 23 otherwise Classify this signal as left-sided, right-sided, two-sided, or time-limited and plot it. Section 2.2 3. Suppose r(t) is as given in Problem 1. Plot and give an expression for y(t) - (^ + ^t). Also determine the turn-on and turn-off times for y(t) 4. Suppose a[n] is as given in Problem 2. Plot...
for the plot, provide the matlab code.
3. Let the input signal x[n] (defined for -<n < oo) to the system be x[n] = 3 cos( 0.05πn) + 4 cos( 0.45πn) + cos( 0.95 n) and the transfer function be 1-re-je a) Plot this signal as a function of n. b) Determine and plot the output y[n] produced by the system due to the input analyzed in part a) of this problem. Do this first with r 0.05 and then...
2.4. Compute and plot y[n] - x[n] * h[n], where x[n] - 0, otherwise 1. 4 sn s 15 0, otherwise h[n] = 2.6. Compute and plot the convolution y[n] - x[n] * h[n], where 2.1. Let x[n] = δ[n] + 2δ[n-1]-δ[n-3] and h[n] = 2δ[n + 1] + 2δ[n-l]. Compute and plot each of the following convolutions: (a) y [n] x[n] * h[n] (c) y3 [n] x[n] * h[n + 2]
3. Consider the periodic signal x(t) = 0 otherwise (a) Plot r(t). (b) What is the period T of x(t)? (c) Find the CTFS coefficients ak for (t).
3. Consider the periodic signal x(t) = 0 otherwise (a) Plot r(t). (b) What is the period T of x(t)? (c) Find the CTFS coefficients ak for (t).