# filtord

## Syntax

``n = filtord(b,a)``
``n = filtord(sos)``
``n = filtord(d)``

## Description

example

````n = filtord(b,a)` returns the filter order, `n`, for the causal rational system function specified by the numerator coefficients, `b`, and denominator coefficients, `a`.```

example

````n = filtord(sos)` returns the filter order for the filter specified by the second-order sections matrix, `sos`. `sos` is a K-by-6 matrix. The number of sections, K, must be greater than or equal to 2. Each row of `sos` corresponds to the coefficients of a second-order filter. The ith row of the second-order section matrix corresponds to ```[bi(1) bi(2) bi(3) ai(1) ai(2) ai(3)]```.```

example

````n = filtord(d)` returns the filter order, `n`, for the digital filter, `d`. Use the function `designfilt` to generate `d`.```

## Examples

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Design a 20th-order FIR filter with normalized cutoff frequency $0.5\pi$ rad/sample using the window method. Verify the filter order.

```b = fir1(20,0.5); n = filtord(b)```
```n = 20 ```

Design the same filter using `designfilt` and verify its order.

```di = designfilt('lowpassfir','FilterOrder',20,'CutoffFrequency',0.5); ni = filtord(di)```
```ni = 20 ```

Design FIR equiripple and IIR Butterworth filters from the same set of specifications. Determine the difference in filter order between the two designs.

```fir = designfilt('lowpassfir','DesignMethod','equiripple','SampleRate',1e3, ... 'PassbandFrequency',100,'StopbandFrequency',120, ... 'PassbandRipple',0.5,'StopbandAttenuation',60); iir = designfilt('lowpassiir','DesignMethod','butter','SampleRate',1e3, ... 'PassbandFrequency',100,'StopbandFrequency',120, ... 'PassbandRipple',0.5,'StopbandAttenuation',60); FIR = filtord(fir)```
```FIR = 114 ```
`IIR = filtord(iir)`
```IIR = 41 ```

## Input Arguments

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Numerator coefficients, specified as a scalar or a vector. If the filter is an allpole filter, `b` is a scalar. Otherwise, `b` is a row or column vector.

Example: `b = fir1(20,0.25)`

Data Types: `single` | `double`
Complex Number Support: Yes

Denominator coefficients, specified as a scalar or a vector. If the filter is an FIR filter, `a` is a scalar. Otherwise, `a` is a row or column vector.

Example: `[b,a] = butter(20,0.25)`

Data Types: `single` | `double`
Complex Number Support: Yes

Matrix of second order-sections, specified as a K-by-6 matrix. The system function of the Kth biquad filter has the rational Z-transform

`${H}_{k}\left(z\right)=\frac{{B}_{k}\left(1\right)+{B}_{k}\left(2\right){z}^{-1}+{B}_{k}\left(3\right){z}^{-2}}{{A}_{k}\left(1\right)+{A}_{k}\left(2\right){z}^{-1}+{A}_{k}\left(3\right){z}^{-2}}.$`

The coefficients in the Kth row of the matrix, `sos`, are ordered as follows.

`$\left[\begin{array}{cccccc}{B}_{k}\left(1\right)& {B}_{k}\left(2\right)& {B}_{k}\left(3\right)\text{ }& {A}_{k}\left(1\right)& {A}_{k}\left(2\right)& {A}_{k}\left(3\right)\end{array}\right].$`

The frequency response of the filter is the system function evaluated on the unit circle with

`$z={e}^{j2\pi f}.$`

Data Types: `single` | `double`
Complex Number Support: Yes

Digital filter, specified as a `digitalFilter` object. Use `designfilt` to generate a digital filter based on frequency-response specifications.

Example: ```d = designfilt('lowpassiir','FilterOrder',3,'HalfPowerFrequency',0.5)``` specifies a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.

## Output Arguments

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Filter order, specified as an integer.

## Version History

Introduced in R2013a