# stepz

Step response of digital filter

## Syntax

## Description

`[`

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

,`t`

] = stepz(`B,A`

,"ctf")`B`

and denominator coefficients
`A`

.* (since R2024b)*

`stepz(___)`

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

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

## Algorithms

`stepz`

filters a length `n`

step sequence using

filter(b,a,ones(1,n))

and plots the results using `stem`

.

To compute `n`

in the auto-length case, `stepz`

either
uses `n = length(b)`

for the FIR case, or first finds the poles using
`p = roots(a)`

if `length(a)`

is greater than 1.

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 to be the point at which the term
due to the largest amplitude pole is 5 × 10^{–5} of its original amplitude.

If the filter is oscillatory (poles on the unit circle only), `stepz`

computes five periods of the slowest oscillation.

If the filter has both oscillatory and damped terms, `n`

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

`stepz`

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

|`freqz`

|`grpdelay`

|`impz`

|`phasez`

|`zplane`