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
How will you use the Gantt chart for solving the sequencing problem?

Circle Well, let's recall just what a circle is. A circle is all the points which are the similar distance, r - called the radius, from a point, ( h, k ) - called the center. I


Trapezoid Rule - Approximating Definite Integrals For this rule we will do similar set up as for the Midpoint Rule. We will break up the interval [a, b] into n subintervals of


Q. How to Convert decimals to fractions? Ans. Note: This tutorial covers only terminating decimals.

Proof of: if f(x) > g(x) for a x b then a ∫ b  f(x) dx > g(x). Because we get f(x) ≥ g(x) then we knows that f(x) - g(x) ≥ 0 on a ≤ x ≤ b and therefore by Prop


Q. Draw Grouped Frequency Tables? Ans. Grouped frequency tables are often used when there are many different values. In these tables, the values are grouped into classes

You''ve decided you want a plant for your room. At the gardening store, there are 444 different kinds of plants (tulip, fern, cactus, and ficus) and 444 different kinds of pots to