Wavelet Toolbox™

Laurent polynomials constructor

Syntax

• P = laurpoly(C,d)
  P = laurpoly(C,'dmin',d)
  P = laurpoly(C,'dmax',d)
  

Description

P = laurpoly(C,d) returns a Laurent polynomial object. C is a vector whose elements are the coefficients of the polynomial P and d is the highest degree of the monomials of P.

If m is the length of the vector C, P represents the following Laurent polynomial:

• P(z) = C(1)*z^d + C(2)*z^(d-1) + ... + C(m)*z^(d-m+1)
  

P = laurpoly(C,'dmin',d) specifies the lowest degree instead of the highest degree of monomials of P. The corresponding output P represents the following Laurent polynomial:

• P(z) = C(1)*z^(d+m-1) + ... + C(m-1)*z^(d+1) + C(m)*z^d
  

P = laurpoly(C,'dmax',d) is equivalent to P = laurpoly(C,d).

Examples

• % Define Laurent polynomials.
  P = laurpoly([1:3],2);
  P = laurpoly([1:3],'dmax',2)
   
  P(z) = + z^(+2) + 2*z^(+1) + 3
  
  P = laurpoly([1:3],'dmin',2)
   
  P(z) = + z^(+4) + 2*z^(+3) + 3*z^(+2)
  
  % Calculus on Laurent polynomials.
  Z = laurpoly(1,1)
   
  Z(z) = z^(+1)
  
  Q = Z*P
   
  Q(z) = + z^(+5) + 2*z^(+4) + 3*z^(+3)
  
  R = Z^1 - Z^-1
   
  R(z) = + z^(+1) - z^(-1)
  

References

Strang, G.; T. Nguyen (1996), Wavelets and filter banks, Wellesley-Cambridge Press.

Sweldens, W. (1998), "The Lifting Scheme: a Construction of Second Generation of Wavelets," SIAM J. Math. Anal., 29 (2), pp. 511-546.

See Also
laurmat

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