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Given polynomials: P(x) = 4x3 + 5x2 -2x + 3 Q(x) = 2x3 -3x2 + x + 1 Calculate the product PQ(x) in the following three ways.   Use standard algebraic polynomial multiplication (“big-FOIL” ) . Use Discrete Fourier Transform : Evaluate both P(x) and Q(x) at the eighth roots of unity. (check your notes if you don’t remember, but basically z = cos 45 + i sin 45, and all its “powers” in radical form!! Multiply the values for the above to generate 8 points, (z, PQ(z) ) for all powers of z.

Given polynomials: P(x) = 4x3 + 5x2 -2x + 3 Q(x) = 2x3 -3x2 + x + 1 Calculate the product PQ(x) in the following three ways.   Use standard algebraic polynomial multiplication (“big-FOIL” ) . Use Discrete Fourier Transform : Evaluate both P(x) and Q(x) at the eighth roots of unity. (check your notes if you don’t remember, but basically z = cos 45 + i sin 45, and all its “powers” in radical form!! Multiply the values for the above to generate 8 points, (z, PQ(z) ) for all powers of z.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Given polynomials:

P(x) = 4x3 + 5x2 -2x + 3
Q(x) = 2x3 -3x2 + x + 1

Calculate the product PQ(x) in the following three ways.

 

  1. Use standard algebraic polynomial multiplication (“big-FOIL” ) .
  2. Use Discrete Fourier Transform :

Evaluate both P(x) and Q(x) at the eighth roots of unity. (check your notes if you don’t remember, but basically z = cos 45 + i sin 45, and all its “powers” in radical form!!

Multiply the values for the above to generate 8 points, (z, PQ(z) ) for all powers of z.

Use Iterpolation to find the polynomial PQ(x).

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