2-norm or infinity-norm of digital filter
A typical use for filter norms is in digital filter scaling to reduce quantization effects. Scaling often improves the signal-to-noise ratio of the filter without resulting in data overflow. You, also, can use the 2-norm to compute the energy of the impulse response of a filter.
filternorm(b,a,2,tol) computes the 2-norm of an IIR filter with the specified tolerance, tol. The tolerance can be specified only for IIR 2-norm computations. pnorm in this case must be 2. If tol is not specified, it defaults to 1e-8.
Compute the 2-norm with a tolerance of 1e-10 of an IIR filter:
[b,a]=butter(5,.5); L2=filternorm(b,a,2,1e-10) L2 = 0.7071
Compute the inf-norm of an FIR filter:
b=firpm(30,[.1 .9],[1 1],'Hilbert'); Linf=filternorm(b,1,inf) Linf = 1.0028
 Jackson, L.B., Digital Filters and Signal Processing, Third Edition, Kluwer Academic Publishers, 1996, Chapter 11.