2. Find the inverse DTFT of each trasform specified below, for-π < Ω < p -i,...
Find the DTFT of x[n] = δ[n-2] and plot the |X(Ω)| for -π < Ω <π. If you use a property please state it.
If X and Y have a joint probability density function specified by 2-(+2y) find P(X <Y).
function Ckek osrs4 be a density 4. Let f(x)=3 otherwise Find: i) k = 24] P(-2<x<2)
Problem 3.12 Find the DTFT of the following time-domain signals: (b) x[n] = alu. lal < 1 11:32 AM Wed 25 Mar '< ! Q 0 O Untitled Notebook (12) 5 * Untitled Notebook (12) W X hw3A_s2020.pdf Untitled Problem 3.14 Find the FT of the following signals: continuous la aperiodic (b) X(t) = e te n(jw) t 120
2. Given x[n]— 1-ae-ja' find the DTFT of: (a) y[n] = nx[n],(b) z[n] = (n − 1)x[n] dX(92) Hint: nx[n]< > ; dΩ
6. Let X(e2) be the DTFT of a signal nl which is known to be zero for n < 0 and n > 3. We know X(eim) for four values of N as follows X (ejm)0, X(en/2) X(eT/2)5 5j, X(ej0) 10, 55j = = = (a) Find n. (Hint: Compute the IDFT) (b) Find X(ei?)
5. (4 pts) Let X(ej) be the DTFT of a signal x[n] which is known to be zero for n < 0 and n > 3. We know X(eja) for four values of N as follows. X(@j0) = 10, X(eja/2) = 5 – 5j, X(ejt) = 0, X(ej37/2) = 5 + 5j (a) (3 pts) Find x[n]. (Hint: Compute the IDFT) (b) (1 pts) Find X(ej?).
1. problem 2. and 3. as follows Find the inverse Laplace transforms of the following function: 2w7 F(s) = s($2 + 2Cwns + wa) "US 25 (0<5<1) Solve the following differential equation: * + 2wni+wn?x=0, (0) = a, (0) = b where a and b are constants, and 0 << < 1. Solve the following differential equation: ö + 3 + 40 = 2 sint, x(0) = 0, 0) = 0
find the inverse z transform X(z) = 1-2-3 with [2]<1
Suppose that a random variable X has the following pdf: 8px+2(1-P) 0<x<0.5., JxX;P) = *; where 0 Sp Si 0 otherwise where p is simply a constant that has yet to be specified in other words, p is a parameter). For now, we will leave the parameter p an unspecified constant ► Find P(X>0.3) = Note: your answer will be an expression containing p. Suppose that k> 0 is also a constant (not yet specified). Find the expected value of...