. Consider an impulse response h[n] such that h[n] = 0 for n < 0 and n > M, and h[n] =−h[M − n] for 0 ≤ n ≤ M where M is an odd integer. a) Express the Fourier transform of h[n] in the form H(ejω) = ejf(ω)A(ω) , where f(ω) and A(ω) are real-valued functions of ω. Determine f(ω) and A(ω). b) Provide an example of such an impulse response h[n] for M = 7 and find the corresponding f(ω) and A(ω).

\Question No.2 Find f(1), f(2), S (3), and f(4) if s(n) is defined recur- sively by f(0) = 1 and for n 0, 1, 2, ... a) S(n + 1) = f(n) + 2. b) f(n + 1) -3/ (п). c) f(n + 1) = 2/W). d) S(n + 1) = (n)2 + S(n) + 1. Find f(1), f(2), f (3), f (4), and f (5) if f (n) is defined recursively by f (0) = 3 and for n =0, 1, 2, ... a) f(n + 1) = -2 (n). b) f (n + 1) = 3/ (n) +7. c) f(n + 1) = / (n)2 - 25 (n) – 2. d) f(n + 1) = 3/(m)/3. %3D Find f (2), f(3), f(4), and f(5) if f is defined recur- sively by f(0) =-1, S(1) = 2, and for n= 1, 2, ... a) f(n + 1) = S(n) + 35 (n – 1). b) f(n + 1) = f (n)?f (n – 1). c) f(n + 1) = 3/ (n)2 – 4f (n - 1)2. d) f (n + 1) = (n - 1)/S(n). Find f(2), S(3), (4), and f(5) if f is defined recur- sively by f(0) = (1) 1 and for n= 1, 2, ... a) S(n + 1) = f (n) - S(n – 1). b) f (n + 1) = f (n)/ (n - 1). c) f(n + 1) = / (n)2 + S(n – 1). d) f(n + 1) = r (n)/S(n - 1).

Question 21. Please help

Please do not give solution in image format thanku :Given two non-negative valued functions f(n) and g(n), is it possible that neither is big-Oh of the other; i.e., can we have both f(n) ̸= O(g(n)) and g(n) ̸= O(f(n))? Argue.

1. Let f(n) and g(n) be asymptotically positive functions. Prove or disprove the follow- ing conjectures: (a) f(n) + g(n) = 0(min(f(n), g(n))). (b) f(n) + w(f(n)) = ©(f(n)).

Q10/the minimum sum- of- products for the following function isF(A,B,C,D,E)=[m(0,3,5,7,9)+d(2,4,6,10,15) using Quine - McClusky method : A'BC'D'E+A'B'E'+A'B'D+A'B'C O Option 6 A'B'E'+A'B'D+A'B'C+A'CDE O None of them O A'B'E+A'B'E'+A'B'D+A'B'C O A'CDE+A'BC'D'E+A'B'E'+A'B'D+A'B'C

Big-Oh. For each function f in the left column of the following table,choose one expression O(g) from the following list:O(1/n),O(1),O(log2 n),O(n),O(n log2 n),O(n2),O(n10),O(2n),O(10n),O(nn)such that f ∈ O(g). Use each expression only once.

Please answer question.

Q10/the minimum sum- of- products for the following function is F(A,B,C,D,E)=Em(0,3,5,7,9)+Ed( 2,4,6,10,15)using Quine - McClusky method : * ΑB'ΕAΒ'D+A'B'C+A'CDE A'BC'D'E+A'B'E'+A'B'D+A'B'c None of them O A'CDE+A'BC'D'E+A'B'E'+A'B'D+A'B'C 'Β'Ε'+Α'Β'Ε'+A'B' D+AB'C

The complement of the function F(A,B ,C, D) = E (2, 4, 7. 10, 12, 14) is F =7 (0,1.3.5,6,8,9,11,13.15) F =E (0,1,3,5,6,8,9.11.13.15) O Other