# impzlength

Length of impulse response of discrete-time filter System object

## Syntax

``len = impzlength(sysobj)``
``len = impzlength(sysobj,tol)``
``len = impzlength(___,Arithmetic=arithType)``

## Description

example

````len = impzlength(sysobj)` returns the length of the impulse response of the filter System object™.```
````len = impzlength(sysobj,tol)` specifies the tolerance to increase or decrease the length accuracy.```
````len = impzlength(___,Arithmetic=arithType)` analyzes the filter System object based on the arithmetic specified in `arithType`, using either of the previous syntaxes.For more input options, see `impzlength` in Signal Processing Toolbox™.```

## Examples

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This example requires DSP System Toolbox™ software.

Design a 4th-order lowpass elliptic filter with a cutoff frequency of 0.4$\pi$ rad/sample. Specify 1 dB of passband ripple and 60 dB of stopband attenuation. Design the filter in pole-zero-gain form and obtain the second order section matrix using the `zp2sos `function. Create an SOS filter object and input the object to `impzlength`.

```[z,p,k] = ellip(4,1,60,.4); [sos,g] = zp2sos(z,p,k); [num,den] = sos2ctf(sos); hSosFilt = dsp.SOSFilter(Structure='Direct form I',... Numerator=num,Denominator=den,... ScaleValues=g); len = impzlength(hSosFilt)```
```len = 80 ```

Design an IIR Butterworth and an FIR equiripple filter for data sampled at 1 kHz. Set the passband frequency to 100 Hz and the stopband frequency to 150 Hz. Set the passband ripple to 0.5 dB and the stopband attenuation to 60 dB. Create System objects for the filters and compare the filter impulse response sequence lengths.

```d = fdesign.lowpass('Fp,Fst,Ap,Ast',100,150,0.5,60,1000); Hd1 = design(d,'butter',SystemObject=true)```
```Hd1 = dsp.SOSFilter with properties: Structure: 'Direct form II' CoefficientSource: 'Property' Numerator: [9x3 double] Denominator: [9x3 double] HasScaleValues: true ScaleValues: [0.1020 0.0927 0.0852 0.0793 0.0748 0.0713 0.0689 0.0673 0.0665 1] Use get to show all properties ```
`Hd2 = design(d,'equiripple',SystemObject=true)`
```Hd2 = dsp.FIRFilter with properties: Structure: 'Direct form' NumeratorSource: 'Property' Numerator: [-7.9808e-04 -2.8559e-04 0.0011 0.0036 0.0064 0.0079 0.0063 0.0012 -0.0059 -0.0115 -0.0116 -0.0044 0.0081 0.0197 0.0229 0.0126 -0.0098 -0.0346 -0.0473 -0.0340 0.0109 0.0808 0.1572 0.2164 0.2387 0.2164 0.1572 ... ] (1x49 double) InitialConditions: 0 Use get to show all properties ```
`len = [impzlength(Hd1) impzlength(Hd2)]`
```len = 1×2 183 49 ```

## Input Arguments

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Tolerance for IIR filter effective impulse response length, specified as a positive number. The tolerance determines the term in the absolutely summable sequence after which subsequent terms are considered to be 0. Increasing the tolerance returns a shorter effective impulse response sequence length. Decreasing the tolerance returns a longer effective impulse response sequence length.

Arithmetic used in the filter analysis, specified as `'double'`, `'single'`, or `'Fixed'`. When the arithmetic input is not specified and the filter System object is unlocked, the analysis tool assumes a double-precision filter. When the arithmetic input is not specified and the System object is locked, the function performs the analysis based on the data type of the locked input.

The `'Fixed'` value applies to filter System objects with fixed-point properties only.

When the `'Arithmetic'` input argument is specified as `'Fixed'` and the filter object has the data type of the coefficients set to `'Same word length as input'`, the arithmetic analysis depends on whether the System object is unlocked or locked.

• unlocked –– The analysis object function cannot determine the coefficients data type. The function assumes that the coefficients data type is signed, has a 16-bit word length, and is auto scaled. The function performs fixed-point analysis based on this assumption.

• locked –– When the input data type is `'double'` or `'single'`, the analysis object function cannot determine the coefficients data type. The function assumes that the data type of the coefficients is signed, has a 16-bit word length, and is auto scaled. The function performs fixed-point analysis based on this assumption.

To check if the System object is locked or unlocked, use the `isLocked` function.

When the arithmetic input is specified as `'Fixed'` and the filter object has the data type of the coefficients set to a custom numeric type, the object function performs fixed-point analysis based on the custom numeric data type.

## Output Arguments

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Length of the impulse response, specified as a positive integer. For stable IIR filters with absolutely summable impulse responses, `impzlength` returns an effective length for the impulse response beyond which the coefficients are essentially zero. You can control this cutoff point by specifying the optional `tol` input argument.

## Version History

Introduced in R2013a

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