Let the sequence: x[n]= { (a^n)*sin(nw), a>0 known constant, n ∈ N0 else x[n]=0 Find with...
Let the sequence:
x[n]= { (a^n)*sin(nw), a>0 known constant, n ∈ N0 else x[n]=0
Find with a direct calculation (without using the transformation
matrix Z) the transform Z of x [n], its convergence pass, the
roots (zeroes) and its poles.
Homework Answers
![{ a sio nwj o ANS neNO xin]- thansformation metaix a(-x a (-x a Sin nw Sol- n a -asiaw) (-asinw) 2 0 2n a asinw nt Sinw o a](http://img.homeworklib.com/images/d48e1471-d4dc-44b8-980e-43886c874b55.png?x-oss-process=image/resize,w_560)
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Let the sequence:
x[n]= { (a^n)*sin(nw), a>0 known constant, n ∈ N0
else x[n]=0
Find with...
please answer them indetail. thanks 4. Let x(n) be a causal sequence. a) b) what conclusion...
please answer them indetail. thanks
4. Let x(n) be a causal sequence. a) b) what conclusion can you draw about the value of its z-transform x(z) at z 00, Use the result in part (a) to check which of the following transforms cannot be associated with a causal sequence (z-1* (z (1-^2-1)- i, x(z) = 321) iii, x(z) = A causal pole-zero system is BIBO stable if its poles are inside the unit circle. Consider now a pole- zero system...
Exercise 9.2. Let Z~ N(0, 1). Find the variance of Z2 and Z3 N0 1) Find...
Exercise 9.2. Let Z~ N(0, 1). Find the variance of Z2 and Z3 N0 1) Find the density of . Is the density bounded?
Let x[n] ←→ X(z) and let x[n] = αnu[n]. Let x1[n] ←→X(z3). Find x1[n] without computing...
Let x[n] ←→ X(z) and let x[n] = αnu[n]. Let x1[n] ←→X(z3). Find x1[n] without computing X(z) or using properties of the z-transform.
x[n] = { Consider the discrete sequence S (0.5)" 0<n<N-1 otherwise a) Determine the z-transform X(2)!...
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!
1. Let Z = (Z1, Z2, Z3) be a vector with i.i.d. N(0, 1) components. Let...
1. Let Z = (Z1, Z2, Z3) be a vector with i.i.d. N(0, 1) components. Let r be a constant with 0 < r < 1. Define X1 = √ rZ1 + √ 1 − rZ2 and X2 = √ rZ1 + √ 1 − rZ3. (a) Give the distribution of X1 and the distribution of X2. Find Cov(X1, X2). (b) Give the matrix A so that the vector X = (X1, X2) is a transform X = AZ. Give...
(4) Let(an}n=o be a sequence in C. Define R-i-lim suplanlì/n. Recall that R e [0,x] o0 is the rad...
(4) Let(an}n=o be a sequence in C. Define R-i-lim suplanlì/n. Recall that R e [0,x] o0 is the radius of convergence of the power series Σ a (z 20)" Assume that R > 0 (a) Prove that if 0 < ρ < R, then the power series converges uniformly on the closed (b) Prove that the power series converges uniformly on any compact subset of the disk Ix - xo< R
(4) Let(an}n=o be a sequence in C. Define R-i-lim...
4. Let X have the following PDF: sin(x) , 0 < x < π , otherwise...
4. Let X have the following PDF: sin(x) , 0 < x < π , otherwise Ix(x) = 0 Find the CDF of X Using the Probability Integral Transformation Theorem, describe the process of generating values from the density of X Using R, generate 1,000 values using your process in part b. Produce a histogram of these generated values, and overlay the density curve of X over top. (Hint: in R, the function acos calculates the inverse cosine function.) Using...
Let Xn = a sin(bn+Z), where n ∈ Z, a, b ∈ [0, ∞) are constant, and Z has a continuous uniform distribution on [−π, π] (i...
Let Xn = a sin(bn+Z), where n ∈ Z, a, b ∈ [0, ∞) are constant,
and Z has a continuous uniform distribution on [−π, π] (i.e. Z ∼
U([−π, π])). Show that Xn is stationary. (Hint: sin(x) sin(y) = 1 2
(cos(x − y) − cos(x + y)) may be helpful).
l. Let Xn-a sin(bn+ Z), where n є z, a, b є lo,00) are constant, and Z has a continuous uniform distribution on [-π, π] (i.e. Z ~...
number 4 1. Find the limit of the following sequences (find lim an) n n a.)...
number 4
1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series cos(x) (2n)! (-« <...
13.1.11. Problem. Let f(x) = x and g(x) = 0 for all x ∈ [0,1]. Find...
13.1.11. Problem. Let f(x) = x and g(x) = 0 for all x ∈ [0,1].
Find a function h in B([0,1]) such that
du(f,h) = du(f,g) = du(g,h).
(3 problems)
13.2.6. Problem. Given in each of the following is the nth term of a sequence of real valued functions defined on (0, 1]. Which of these converge pointwise on (0, 1]? For which is the convergence uniform? (a) a z" (b) z+ nr. (c) a+ re-na 13.2.7. Problem. Given in...
please answer them indetail. thanks
4. Let x(n) be a causal sequence. a) b) what conclusion can you draw about the value of its z-transform x(z) at z 00, Use the result in part (a) to check which of the following transforms cannot be associated with a causal sequence (z-1* (z (1-^2-1)- i, x(z) = 321) iii, x(z) = A causal pole-zero system is BIBO stable if its poles are inside the unit circle. Consider now a pole- zero system...
Exercise 9.2. Let Z~ N(0, 1). Find the variance of Z2 and Z3 N0 1) Find the density of . Is the density bounded?
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!
(4) Let(an}n=o be a sequence in C. Define R-i-lim suplanlì/n. Recall that R e [0,x] o0 is the radius of convergence of the power series Σ a (z 20)" Assume that R > 0 (a) Prove that if 0 < ρ < R, then the power series converges uniformly on the closed (b) Prove that the power series converges uniformly on any compact subset of the disk Ix - xo< R
(4) Let(an}n=o be a sequence in C. Define R-i-lim...
4. Let X have the following PDF: sin(x) , 0 < x < π , otherwise Ix(x) = 0 Find the CDF of X Using the Probability Integral Transformation Theorem, describe the process of generating values from the density of X Using R, generate 1,000 values using your process in part b. Produce a histogram of these generated values, and overlay the density curve of X over top. (Hint: in R, the function acos calculates the inverse cosine function.) Using...
Let Xn = a sin(bn+Z), where n ∈ Z, a, b ∈ [0, ∞) are constant,
and Z has a continuous uniform distribution on [−π, π] (i.e. Z ∼
U([−π, π])). Show that Xn is stationary. (Hint: sin(x) sin(y) = 1 2
(cos(x − y) − cos(x + y)) may be helpful).
l. Let Xn-a sin(bn+ Z), where n є z, a, b є lo,00) are constant, and Z has a continuous uniform distribution on [-π, π] (i.e. Z ~...
number 4
1. Find the limit of the following sequences (find lim an) n n a.) an = n +3 b.) an = V35n n- 2. Determine whether the following series converge or diverge. -3 (n + 2)n + 5 b.) tan-'(n) n2 + 1 a.) 5 nel 3. Determine the radius of convergence and the interval of convergence of the series 2" (x – 3)" n n=1 n=0 (-1)", 2n 4. Using the power series cos(x) (2n)! (-« <...
13.1.11. Problem. Let f(x) = x and g(x) = 0 for all x ∈ [0,1].
Find a function h in B([0,1]) such that
du(f,h) = du(f,g) = du(g,h).
(3 problems)
13.2.6. Problem. Given in each of the following is the nth term of a sequence of real valued functions defined on (0, 1]. Which of these converge pointwise on (0, 1]? For which is the convergence uniform? (a) a z" (b) z+ nr. (c) a+ re-na 13.2.7. Problem. Given in...
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