113_1_equations

113_1_equations - . This yields a = 1 3 (3 q-p 2 ) , b = 1...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
EE113: Digital Signal Processing Spring 2008 Prof. Mihaela van der Schaar Prepared by Martin Andersen and Hyunggon Park Solution of general quadratic and cubic equations 1. Any quadratic equation can be reduced to the form ax 2 + bx + c = 0 . The solution of this equation is provided by x = - b ± b 2 - 4 ac 2 a . 2. A general cubic equation y 3 + py 2 + qy + r = 0 may be reduced to the depressed cubic form x 3 + ax + b = 0 by substituting y = x - p 3
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . This yields a = 1 3 (3 q-p 2 ) , b = 1 27 (2 p 3-9 pq + 27 r ) . Now let A = 3 s-b 2 + r b 2 4 + a 3 27 , B = 3 s-b 2-r b 2 4 + a 3 27 . The solution of the depressed cubic is x = A + B, x =-A + B 2 + A-B 2 -3 , x =-A + B 2-A-B 2 -3 , (1) and y = x-p 3 . [Reference: B. P. Lathi, Signal Processing and Linear Systems, 1998.]...
View Full Document

This note was uploaded on 02/09/2011 for the course EE 113 taught by Professor Walker during the Spring '08 term at UCLA.

Ask a homework question - tutors are online