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norm

P-norm of filter

Syntax

l = norm(hd)
l = norm(hd,pnorm)

Description

All of the variants of norm return the filter p-norm for the object in the syntax, a digital filter. When you omit the pnorm argument, norm returns the L2-norm for the object.

Note that by Parseval's theorem, the L2-norm of a filter is equal to the l2 norm. This equality is not true for the other norm variants.

For dfilt Objects

l = norm(hd) returns the L2-norm of a discrete-time filter.

l = norm(hd,pnorm) includes input argument pnorm that lets you specify the norm returned. pnorm can be either

  • Frequency-domain norms specified by one of L1, L2, or Linf

  • Discrete-time domain norms specified by one of l1, l2, or linf

By Parseval's theorem, the L2-norm of a filter is equal to the l2 norm. This equality is not true for the other norm variants.

IIR filters respond slightly differently to norm. When you compute the l2, linf, L1, and L2 norms for an IIR filter, norm(...,L2,tol) lets you specify the tolerance for the accuracy in the computation. For l1, l2, L2, and linf, norm uses the tolerance to truncate the infinite impulse response that it uses to calculate the norm. For L1, norm passes the tolerance to the numerical integration algorithm. Refer to Examples to see this in use. You cannot specify Linf for the norm and include the tol option.

Examples

collapse all

This example shows how to compute the L2 norm of an IIR filter. A tolerance of 1e-10 is used.

spec = fdesign.lowpass('n,fc',5,0.4);
filter = butter(spec);
filternorm = norm(filter,'l2',1e-10)
filternorm =

    0.6336

See Also

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Introduced in R2011a

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