# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English version of the page.

To view all translated materials including this page, select Japan from the country navigator on the bottom of this page.

# normalize

Normalize filter numerator or feed-forward coefficients

## Syntax

```normalize(hq) g = normalize(hd) ```

## Description

`normalize(hq)` normalizes the filter numerator coefficients for a quantized filter to have values between -1 and 1. The coefficients of `hq` change — `normalize` does not copy `hq` and return the copy. To restore the coefficients of `hq` to the original values, use `denormalize`.

Note that for lattice filters, the feed-forward coefficients stored in the property `lattice` are normalized.

`g = normalize(hd)` normalizes the numerator coefficients for the filter `hq` to between -1 and 1 and returns the gain `g` due to the normalization operation. Calling `normalize` again does not change the coefficients. `g` always returns the gain returned by the first call to normalize the filter.

## Examples

collapse all

Create a direct form II quantized filter that uses second-order sections. Then use normalize to maximize the use of the range of representable coefficients.

```d = fdesign.lowpass('n,fp,ap,ast',8,.5,2,40); hd = design(d,'ellip'); hd.arithmetic ='fixed';```

Check the filter coefficients. Note that InitialSOSMatrix(3,2)>1

`InitialSOSMatrix = hd.sosMatrix;`

Use normalize to modify the coefficients into the range between -1 and 1. The output g contains the gains applied to each section of the SOS filter.

`g = normalize(hd);`

None of the numerator coefficients exceed -1 or 1.