P-norm of filter

`l = norm(hd)`

l = norm(hd,pnorm)

l = norm(hm)

l = norm(hm,pnorm)

All of the variants of `norm`

return the filter
p-norm for the object in the syntax, either a digital filter, or a
multirate 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.

`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.

`l = norm(hm)`

returns the
L2-norm of a multirate filter.

`l = norm(hm,pnorm)`

includes
argument `pnorm`

to let 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`

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.

To demonstrate the tolerance option used with an IIR filter
(`dfilt`

object), compute the 2-norm of filter `hd`

with
a tolerance of 1e-10.

H =fdesign.lowpass('n,fc',5,0.4); Hd = butter(H); L2=norm(Hd,'l2',1e-10);

In this example, compute the infinity norm of an FIR polyphase
interpolator, which is an `mfilt`

object.

```
Hm = mfilt.firinterp;
Linf = norm(Hm,'linf');
```

`reorder`

| `scale`

| `scalecheck`

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