# freqz

Frequency response of digital filter

## Syntax

## Description

`[`

returns the `h`

,`w`

] = freqz(`B,A`

,"ctf",`n`

)`n`

-point frequency response of the digital
filter represented as Cascaded Transfer Functions (CTF) with numerator coefficients `B`

and denominator
coefficients `A`

.* (since R2024b)*

`freqz(___)`

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

## Examples

## Input Arguments

## Output Arguments

## More About

## Tips

You can obtain filters in CTF format, including the scaling gain. Use the outputs of digital IIR filter design functions, such as

`butter`

,`cheby1`

,`cheby2`

, and`ellip`

. Specify the`"ctf"`

filter-type argument in these functions and specify to return`B`

,`A`

, and`g`

to get the scale values.*(since R2024b)*If you have an irreducible multirate filter, use the

`freqzmr`

(DSP System Toolbox) function to analyze the filter in the frequency domain. For more information on irreducible multirate filters, see Overview of Multirate Filters (DSP System Toolbox).*(since R2024a)*The

`freqzmr`

(DSP System Toolbox) function requires DSP System Toolbox™.*(since R2024a)*

## Algorithms

The frequency response of a digital filter can be interpreted as the transfer function
evaluated at
*z* = *e*^{jω}
[1].

`freqz`

determines the transfer function from
the (real or complex) numerator and denominator polynomials you specify
and returns the complex frequency response, *H*(*e*^{jω}),
of a digital filter. The frequency response is evaluated at sample
points determined by the syntax that you use.

`freqz`

generally uses an FFT algorithm to compute the frequency response
whenever you do not supply a vector of frequencies as an input argument. It computes the
frequency response as the ratio of the transformed numerator and denominator
coefficients, padded with zeros to the desired length.

When you do supply a vector of frequencies as input, `freqz`

evaluates the
polynomials at each frequency point and divides the numerator response by the
denominator response. To evaluate the polynomials, the function uses Horner's
method.

## References

[1] Oppenheim, Alan V., and Ronald W. Schafer, with John R. Buck.
*Discrete-Time Signal Processing*. 2nd Ed. Upper Saddle River,
NJ: Prentice Hall, 1999.

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

## Extended Capabilities

## Version History

**Introduced before R2006a**