You are here : matlabSignal Processingfilternorm

# filternorm() - Signal Processing

```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.L = filternorm(b,a) computes
the 2-norm of the digital filter defined by the numerator coefficients
in b and denominator coefficients in a.L = filternorm(b,a,pnorm) computes
the 2- or infinity-norm (inf-norm) of the digital filter, where pnorm is
either 2 or inf. L = 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 10–8.```

### Syntax

`L = filternorm(b,a)L = filternorm(b,a,pnorm)L = filternorm(b,a,2,tol)`

### Example

```Filter NormsOpen This Example
Compute the 2-norm of a Butterworth IIR filter with tolerance
. Specify a normalized cutoff frequency of
rad/s and a filter order of 5.
[b,a] = butter(5,0.5);
L2 = filternorm(b,a,2,1e-10)

L2 =

0.7071

Compute the infinity-norm of an FIR Hilbert transformer of order 30 and normalized transition width
rad/s.b = firpm(30,[.1 .9],[1 1],'Hilbert');
Linf = filternorm(b,1,inf)

Linf =

1.0028```