Fft algorithm, Mathematics

(a) Using interpolation, give a polynomial f ∈ F11[x] of degree at most 3 satisfying f(0) = 2; f(2) = 3; f(3) = 1; f(7) = 6

(b) What are all the polynomials in F11[x] which satisfy f(0) = 2, f(2) = 3, f(3) = 1, f(7) = 6?

(2) Hand in your completed worksheets from labs \Fast Multiplication" and \Fast Multiplication II". Hand it in to me by saving the worksheet to a le (after making sure all the cells you want are evaluated) and then emailing it to me.

(3) Let F be a eld and a(x) ∈ F[x] be a polynomial of degree n - 1 = 3k - 1.

(a) Show that a(x) can be decomposed into

a(x) = b(x3 ) + x . c(x3) + x2. d(x3);

where b(x), c(x) and d(x) are polynomials in F[x] of degree at most n/3 - 1 = 3k - 1 - 1.

(b) Show that if ω ∈ F is a primitive nth root of unity, then a(x) can be evaluated at all the powers of ! by recursively evaluating b(x), c(x) and d(x) at the powers of ω3.

(c) Put all of this together into an algorithm similar to FFT for evaluating a(x) at the powers of ω.

(d) What are the number of additions and number of multiplications in F that this algorithm does on input size n?

(e) The set S = {1, ω, ω2n -1} has some special properties that make this "3-ary" FFT (and the "binary" FFT from class) work. What properties does a set S need to be used in this way (or in the original FFT algorithm)? Can you fi nd any other sets that have these properties?

 

Posted Date: 2/26/2013 12:53:47 AM | Location : United States







Related Discussions:- Fft algorithm, Assignment Help, Ask Question on Fft algorithm, Get Answer, Expert's Help, Fft algorithm Discussions

Write discussion on Fft algorithm
Your posts are moderated
Related Questions
Lindy has 48 chocolate chip cookies and 64 vanilla wafer cookies. How many bags can Lindy fill if she puts the chocolate chip cookies and the vanilla wafers in the same bag? She pl


A valid identifier in the programming language FORTAN contains a string of one to six alphanumeric characters (the 36 characters A, B,...., Z, 0, 1,...9) starting with a letter. De

Given the vectors u = 3 i - 2 j + k ,   v = i + 2 j - 4 k ,    w = -2 i + 4 j - 5 k use vector methods to answer the following: (a) Prove u , v and w can form

what is the remainder when 75 is divided by 4

how can you memorise you times facts

Lines EF and GH are graphed on this coordinate plane. Which point is the intersection of lines EF and GH?

what is the importance of solid mensuration?

The Geometric Index or Industrial Share index The Geometric Index or Industrial Share index is an index of 30 selected top industrial companies. This is calculated by taking a

What percent of the figure below is shaded? Break the rectangle into eighths as shown below. The shaded part is 6/8 or 3/4 ; 3/4 is 75%.