Consider an optimal Huffman code for the following set of frequencies, based on the Fibonacci numbers, that is, a:1 b:1 c:2 d:3...... and so on. What will be the maximum number of bits required for the first 9 characters?
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- The Fibonacci function f is usually defined as follows. f (0) = 0; f(1) = 1; for every n e N>1, f (n) = f(n – 1) + f(n – 2). Here we need to give both the values f(0) and f(1) in the first part of the definition, and for each larger n, f(n) is defined using both f(n - 1) and f(n- 2). Use induction to show that for every neN, f(n) 1; checking the case n = 1 separately is comparable to performing a second basis step.)Let N = {0, 1, 2, . . .} be the set of Natural Numbers. Given an n ∈ N, which of the followingconditions are necessary, and which of these conditions are sufficient, for the Natural Number,n, to be a factor of 10.(a) 1 is a factor of n.(b) 1 is a factor of 2n.(c) −n is a factor of 10.(d) 10 is a multiple of n.(e) n is divisible by 2.(f) n^2 is divisible of 5.(g) n = 10.Consider the following continuous-time sinusoidal signal: x. (1) = sin(27F1), -oFor each set of cubes in terms of variables (a, b, c, d] obtain the minimized version for boolean fuction f(a, b, c, d) (00X1, 0XX1, 1000, 1100, 1010, 1110} {1XX0, 10XX, 11XX, 00XX} ✓ {00XX, 01XX, 0XXX, 01X1} (0100, 1010, 1XX1, XXXX, 0001} {0001, 0011, 0101, 0111, 1101, 1111, 1001, 1011} ✓ {000X, 010X, 1X00, 1X01} A f(a, b, c, d) = 1 B. f(a, b, c, d) = d C. f(a, b, c, d) = ē D. f(a, b, c, d) = a + a b Ef(a, b, c, d) = a F. f(a, b, c, d) = a dConsider the following continuous-time sinusoidal signal: x. (t) = sin(27F1), -oConsider the following continuous-time sinusoidal signal: x. (1) = sin(27F1), -∞Prove that the following shows LHS = RHS : (+ 2 1 ) = 3 Given: 1=λf.λy.f y 2=λf.λy.f(f y) 3=λf.λy.f(f(f y)) M+N=λx.λy.(M x)((N x)y)Considering the function f(x) = x – cos(x), what is the value of x7 after performing fixed point iteration. Assume an initial guess of 1. Use the equation form that will seem fit according to the choices provided.Group of answer choices 0.72210 0.71537 0.76396 0.722361. 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 formH(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).You are given a sequence of integers A1, A2,..., AN and an integer M. For any valid integers p, q, let's define F(p,q) as the dot product of the subsequences Ap, Ap+1, . .., Ap+M–1 and Aq, Aq+1, . .., Aq+M–1, İ.e. F(p, q) = Eo Apti · Aqti- ¬M-1 You should process Q queries. In each query: • You are given two integers pos and val. Change the value of Apos to val. • Then, find the sum S = N-M+1N-M+1 Li=1 Lj=1 F(i, j). %3D Develop a python code that prints a single line containing one integer S % 999000000 Sample Input: 321 321 32 Output: 49You are given a sequence of integers A1, A2,..., AN and an integer M. For any valid integers p, q, let's define F(p,q) as the dot product of the subsequences Ap, Ap+1, . .., Ap+M–1 and Aq, Aq+1, ..., Aq+M–1, i.e. F(p, q) = Eo Apti · Aqti- ¬M-1 You should process Q queries. In each query: • You are given two integers pos and val. Change the value of Apos to val. • Then, find the sum S = SN-M+1N-M+1 Li=1 Lj=1 F(i, j). %3D Develop a python code that prints a single line containing one integer S % 999000000 Sample Input: 321 321 32 Output: 49Given f(x) = 2x2+3x+1 and g(x) = 3x−2.Compute (a) (f◦g)(x) =SEE MORE QUESTIONSRecommended textbooks for youDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill EducationDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education