Consider the discrete-time signal given below. Ş ()", n20 X = 0 n < 0 where...
Consider a discrete-time LTI system with impulse response hn on-un-1), where jal < 1. Find the output y[n] of the system to the input x[n] = un +1].
Consider a discrete-time system with frequency response given by HO OSN< -<N<0 Determine the unit pulse response of this system, showing all your workings.
x[n] = { Consider the discrete sequence S (0.5)" 0<n<N-1 otherwise a) Determine the z-transform X(2)! b) Determine and plot the poles and zeros of X(2) when N = 8!
Compute and sketch the convlution of y[n] = x[n]*h[n] using the
graphical method for discrete signal where
x[n] =
h[n] =
2.-1<n<3 0, other wise
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
1. Discrete Fourier Analysis. Given the following periodic function: 50. 0<t<2s a) Find discrete time rot and amplitude y(rSi) values for y(t). Find time values t1, t2, ..tN with ot-0.2 s over the interval -2.0 to 1.8 s, amplitudes yl, y2, y3,.. .,yN. and N.
2+z-1 1. The Z-transform of a signal x[n] is given as X(z) = }</21 < a) Find the signal x[n] [7] b) Draw the pole – zero plot of the z-transform .[3] c) Is x[n] causal or not? Justify your answer [2]
1. Convolution of Discrete Time Signals Analytically determine the convolutions: (a) Find yn]-nun], where un] is the unit step (b) Find yln] z[n] when, where 131 <1
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.
Consider the probability density function 0 ifr <0 8.77 if 0 < x <1 0 if > 1 Find the median. Enter your answer to 3 decimal places. Answer: