# impz

Impulse response of digital filter

## Syntax

## Description

`[`

returns the impulse response of the digital filter represented as Cascaded Transfer Functions (CTF) with numerator coefficients `h`

,`t`

] = impz(`B,A`

,"ctf")`B`

and denominator coefficients
`A`

.* (since R2024b)*

`[`

returns the impulse response of the digital filter `h`

,`t`

] = impz(`d`

)`d`

. Use `designfilt`

to generate `d`

based on frequency-response
specifications.

`impz(___)`

with no output arguments plots the impulse
response of the filter.

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

## Algorithms

`impz`

filters a length-`n`

impulse sequence
using

filter(b,a,[1 zeros(1,n-1)])

and plots the result using `stem`

.

**Note**

If the input to `impz`

is single precision, the function computes the
impulse response using single-precision arithmetic and returns single-precision
output.

When `impz`

calculates `n`

automatically, the
algorithm depends on the properties of the filter:

FIR filters —

`n`

is the length of`b`

.IIR filters —

`impz`

first finds the poles of the transfer function using`roots`

.If the filter is unstable,

`n`

is chosen to be the point at which the term from the largest pole reaches 10^{6}times its original value.If the filter is stable,

`n`

is chosen as the point at which the term from the largest-amplitude pole is 5 × 10^{–5}times its original amplitude.If the filter is oscillatory with poles on the unit circle only,

`impz`

computes five periods of the slowest oscillation.If the filter has both oscillatory and damped terms,

`n`

is the greater of five periods of the slowest oscillation, or the point at which the term due to the largest pole is 5 × 10^{–5}times its original amplitude.

`impz`

also allows for delays in the numerator polynomial. The number
of delays is incorporated into the computation of the number of samples.

## References

[1] Lyons, Richard G. *Understanding Digital Signal Processing*. Upper
Saddle River, NJ: Prentice Hall, 2004.

## Extended Capabilities

## Version History

**Introduced before R2006a**

## See Also

### Apps

### Functions

`ctffilt`

|`designfilt`

|`digitalFilter`

|`impulse`

(Control System Toolbox) |`impzlength`

|`stem`