Homework Answers
![n = 2.5500 Þ(n) = $(2.5 soo) = $(2). (ssoo) = 1x S5oo _5499 = 5499 [s.] o(mm) = 4(m). do $(pk)= pk pkey = 4 x 5499 in this gr](http://img.homeworklib.com/questions/c5a05a00-2233-11eb-9da6-4d2f73cfa786.png?x-oss-process=image/resize,w_560)
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Con Consider the group (Z*,·), where n = 2 · 5500. Use the properties of the...
(2) For an integer n, let Z/nZ denote the set of equivalence classes [k) tez: k -é is divisible by n (a) Prove that the set Z/nZ has n elements. (b) Find a minimal set of representatives for these...
(2) For an integer n, let Z/nZ denote the set of equivalence classes [k) tez: k -é is divisible by n (a) Prove that the set Z/nZ has n elements. (b) Find a minimal set of representatives for these n elements. (c) Prove that the operation gives a well-defined addition on Z/nZ Hint: The operution should not depend on the choice of coset representatives Verify that this gives Z/n2 the structure of an ahelian group. Be sure to verify all...
5. (22+2=4") Topic: The z-transform, z-transform properties Use the z-transform properties to determine the z-transform the...
5. (22+2=4") Topic: The z-transform, z-transform properties Use the z-transform properties to determine the z-transform the following signal and specify the region of convergence. x[n]=(1)"u[n]*2":[-n-1]+)?[n-2]
2-Use tables and properties to determine z-transform of the following signal x[n] = (+)*u[n] – (3)...
2-Use tables and properties to determine z-transform of the following signal x[n] = (+)*u[n] – (3) "u[n]
Part 15A and 15B (15) Let n E Z+,and let d be a positive divisor of...
Part 15A and 15B
(15) Let n E Z+,and let d be a positive divisor of n. Theorem 23.7 tells us that Zn contains exactly one subgroup of order d, but not how many elements Z has of order d. We will determine that number in this exercise. (a) Determine the number of elements in Z12 of each order d. Fill in the table below to compare your answers to the number of integers between 1 and d that are...
We consider the generalized linear phase filter defined by H(z) = 0.4 +0.6z-1 +0.77-2 – 0.77-3...
We consider the generalized linear phase filter defined by H(z) = 0.4 +0.6z-1 +0.77-2 – 0.77-3 – 0.6z-4 – 0.4z-5 1. Find the order N and the group delay T of H. 2. Compute the amplitude A(W) of H. HINT: factor out the phase, e-jwN/2, and use Euler formula to create terms of the form sin(w/2), sin(3w/2), ....
2. Use Lagrange's theorem to prove the Euler-Fermat Theorem: If n E Z+ and (a, n)...
2. Use Lagrange's theorem to prove the Euler-Fermat Theorem: If n E Z+ and (a, n) = 1, then ap(n)-1 mod n.
Problem 3. Consider the general linear group GL2 = (M2,*) of 2 x 2 invertible matrices...
Problem 3. Consider the general linear group GL2 = (M2,*) of 2 x 2 invertible matrices under matrix multiplication. In Homework Problem 9 of Investigation 6, you showed that Pow G 1-( )z is isomorphic to the group Z. Prove that the group (Pow 1 i
8. Let n be a positive integer. The n-th cyclotomic polynomial Ф,a(z) E Z[2] is defined recursively in the following way: 1. Ф1(x)-x-1. 2. If n > 1, then Фп(x)- , (where in the product in the...
8. Let n be a positive integer. The n-th cyclotomic polynomial Ф,a(z) E Z[2] is defined recursively in the following way: 1. Ф1(x)-x-1. 2. If n > 1, then Фп(x)- , (where in the product in the denomina- tor, d runs through all divisors of n less than n). . A. Calculate Ф2(x), Ф4(x) and Ф8(z): . B. n(x) is the minimal polynomial for the primitive n-th root of unity over Q. Let f(x) = "8-1 E Q[a] and ω...
MATLAB HELP 3. Consider the equation y′ = y2 − 3x, where y(0) = 1. USE THE EULER AND RUNGE-KUTTA APPROXIMATION SCRIPTS...
MATLAB HELP 3. Consider the equation y′ = y2 − 3x, where y(0) =
1. USE THE EULER AND RUNGE-KUTTA APPROXIMATION SCRIPTS
PROVIDED IN THE PICTURES
a. Use a Euler approximation with a step size of 0.25 to
approximate y(2).
b. Use a Runge-Kutta approximation with a step size of 0.25 to
approximate y(2).
c. Graph both approximation functions in the same window as a
slope field for the differential equation.
d. Find a formula for the actual solution (not...
A transform of auto-correlation n Consider two sequences 1[n] and 2 n] with their transform where,...
A transform of auto-correlation n Consider two sequences 1[n] and 2 n] with their transform where, x1 n] has M + 1 elements from index 0 to Ni and likewise for 2n (i) Define Y(z) , (z)X2(z), and let Y(z)-ΣMoy서z-k, express M in terms of N, and N2 Syntax: type in Ni as 'N_1', and N2 as 'N_2' (ii) Which of the following is the right expression for yl y[1]-(No answer given) ' a. z11 202 10 b. 10202111 c....
(2) For an integer n, let Z/nZ denote the set of equivalence classes [k) tez: k -é is divisible by n (a) Prove that the set Z/nZ has n elements. (b) Find a minimal set of representatives for these n elements. (c) Prove that the operation gives a well-defined addition on Z/nZ Hint: The operution should not depend on the choice of coset representatives Verify that this gives Z/n2 the structure of an ahelian group. Be sure to verify all...
5. (22+2=4") Topic: The z-transform, z-transform properties Use the z-transform properties to determine the z-transform the following signal and specify the region of convergence. x[n]=(1)"u[n]*2":[-n-1]+)?[n-2]
2-Use tables and properties to determine z-transform of the following signal x[n] = (+)*u[n] – (3) "u[n]
Part 15A and 15B
(15) Let n E Z+,and let d be a positive divisor of n. Theorem 23.7 tells us that Zn contains exactly one subgroup of order d, but not how many elements Z has of order d. We will determine that number in this exercise. (a) Determine the number of elements in Z12 of each order d. Fill in the table below to compare your answers to the number of integers between 1 and d that are...
We consider the generalized linear phase filter defined by H(z) = 0.4 +0.6z-1 +0.77-2 – 0.77-3 – 0.6z-4 – 0.4z-5 1. Find the order N and the group delay T of H. 2. Compute the amplitude A(W) of H. HINT: factor out the phase, e-jwN/2, and use Euler formula to create terms of the form sin(w/2), sin(3w/2), ....
2. Use Lagrange's theorem to prove the Euler-Fermat Theorem: If n E Z+ and (a, n) = 1, then ap(n)-1 mod n.
Problem 3. Consider the general linear group GL2 = (M2,*) of 2 x 2 invertible matrices under matrix multiplication. In Homework Problem 9 of Investigation 6, you showed that Pow G 1-( )z is isomorphic to the group Z. Prove that the group (Pow 1 i
8. Let n be a positive integer. The n-th cyclotomic polynomial Ф,a(z) E Z[2] is defined recursively in the following way: 1. Ф1(x)-x-1. 2. If n > 1, then Фп(x)- , (where in the product in the denomina- tor, d runs through all divisors of n less than n). . A. Calculate Ф2(x), Ф4(x) and Ф8(z): . B. n(x) is the minimal polynomial for the primitive n-th root of unity over Q. Let f(x) = "8-1 E Q[a] and ω...
MATLAB HELP 3. Consider the equation y′ = y2 − 3x, where y(0) =
1. USE THE EULER AND RUNGE-KUTTA APPROXIMATION SCRIPTS
PROVIDED IN THE PICTURES
a. Use a Euler approximation with a step size of 0.25 to
approximate y(2).
b. Use a Runge-Kutta approximation with a step size of 0.25 to
approximate y(2).
c. Graph both approximation functions in the same window as a
slope field for the differential equation.
d. Find a formula for the actual solution (not...
A transform of auto-correlation n Consider two sequences 1[n] and 2 n] with their transform where, x1 n] has M + 1 elements from index 0 to Ni and likewise for 2n (i) Define Y(z) , (z)X2(z), and let Y(z)-ΣMoy서z-k, express M in terms of N, and N2 Syntax: type in Ni as 'N_1', and N2 as 'N_2' (ii) Which of the following is the right expression for yl y[1]-(No answer given) ' a. z11 202 10 b. 10202111 c....
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