digitalFilter

Digital filter

The Coefficients property has been replaced by the Numerator and Denominator properties. For more information, see Version History.

Description

Use designfilt to design and edit digitalFilter objects.

Use designfilt in the form d = designfilt(resp,Name,Value) to design a digital filter d with response type resp. Customize the filter using name-value arguments.
Use designfilt in the form designfilt(d) to edit an existing filter, d.
Note
This is the only way to edit an existing digitalFilter object. Its properties are otherwise read-only.
Use filter in the form dataOut = filter(d,dataIn) to filter a signal with a digitalFilter d. The input can be a double- or single-precision vector. It can also be a matrix with as many columns as there are input channels. You can also use the filtfilt and fftfilt functions with digitalFilter objects.
Use Filter Analyzer to visualize a digitalFilter.

Properties

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Coefficients

`Numerator` — Numerator coefficients
row vector | L-by-3 matrix

Numerator coefficients, returned as one of these:

Row vector for FIR filters.
L-by-3 matrix for IIR filters, where L is the number of second-order cascaded sections. See Return Digital Filters in CTF Format for more information.

`Denominator` — Denominator coefficients
`1` | L-by-3 matrix

Denominator coefficients, returned as one of these:

1 for FIR filters.
L-by-3 matrix for IIR filters, where L is the number of second-order cascaded sections. See Return Digital Filters in CTF Format for more information.

Specifications

The Specification properties returned in a digitalFilter object depend on the filter response and design specified when creating the object using designfilt. All properties are read-only.

Filter Response

`FrequencyResponse` — Frequency response type
`'lowpass'` | `'highpass'` | `'bandpass'` | `'bandstop'` | `'differentiator'` | `'hilbert'` | `'arbmag'`

Filter response type, returned as one of these:

'lowpass' for a lowpass filter
'highpass' for a highpass filter
'bandpass' for a bandpass filter
'bandstop' for a bandstop filter
'differentiator' for an FIR differentiator filter
'hilbert' for an FIR Hilbert transformer filter
'arbmag' for an FIR filter of arbitrary magnitude response

`ImpulseResponse` — Impulse response type
`'fir'` | `'iir'`

Impulse response type, returned as 'fir' or 'iir'.

Filter Design

For more information about filter design properties, see Sample Rate, Frequency Constraints, Filter Order, Magnitude Constraints, and Design Method.

Object Functions

Filtering

`fftfilt`	FFT-based FIR filtering using overlap-add method
`filter`	1-D digital filter
`filtfilt`	Zero-phase digital filtering
`bandpass`	Bandpass-filter signals
`bandstop`	Bandstop-filter signals
`highpass`	Highpass-filter signals
`lowpass`	Lowpass-filter signals

Filter Analysis

`double`	Cast coefficients of digital filter to double precision
`filt2block`	Generate Simulink filter block
`filtord`	Filter order
`firtype`	Type of linear phase FIR filter
`freqz`	Frequency response of digital filter
`grpdelay`	Average filter delay (group delay)
`impz`	Impulse response of digital filter
`impzlength`	Impulse response length
`info`	Information about digital filter
`isallpass`	Determine whether filter is allpass
`isdouble`	Determine if digital filter coefficients are double precision
`isfir`	Determine if digital filter has finite impulse response
`islinphase`	Determine whether filter has linear phase
`ismaxphase`	Determine whether filter is maximum phase
`isminphase`	Determine whether filter is minimum phase
`issingle`	Determine if digital filter coefficients are single precision
`isstable`	Determine whether filter is stable
`phasedelay`	Phase delay of digital filter
`phasez`	Phase response of digital filter
`single`	Cast coefficients of digital filter to single precision
`ss`	Convert digital filter to state-space representation
`stepz`	Step response of digital filter
`tf`	Convert digital filter to transfer function
`zerophase`	Zero-phase response of digital filter
`zpk`	Convert digital filter to zero-pole-gain representation
`zplane`	Zero-pole plot for discrete-time systems

Examples

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Lowpass IIR Filter

Open Live Script

Design a lowpass IIR filter with order 8, passband frequency 35 kHz, and passband ripple 0.2 dB. Specify a sample rate of 200 kHz. Visualize the frequency response of the filter.

lpFilt = designfilt("lowpassiir",FilterOrder=8, ...
         PassbandFrequency=35e3,PassbandRipple=0.2, ...
         SampleRate=200e3);
freqz(lpFilt)

$Figure contains 2 axes objects. Axes object 1 with title Phase, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Phase (degrees) contains an object of type line. Axes object 2 with title Magnitude, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Magnitude (dB) contains an object of type line.$

Use the filter you designed to filter a 1000-sample random signal.

dataIn = randn(1000,1);
dataOut = filter(lpFilt,dataIn);

Output the filter coefficients, expressed as cascaded transfer functions.

ctfNum = lpFilt.Numerator

ctfNum = 4×3

    0.2666    0.5333    0.2666
    0.1943    0.3886    0.1943
    0.1012    0.2023    0.1012
    0.0318    0.0636    0.0318

ctfDen = lpFilt.Denominator

ctfDen = 4×3

    1.0000   -0.8346    0.9073
    1.0000   -0.9586    0.7403
    1.0000   -1.1912    0.5983
    1.0000   -1.3810    0.5090

More About

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Cascaded Transfer Functions

Partitioning an IIR digital filter into cascaded sections improves its numerical stability and reduces its susceptibility to coefficient quantization errors. The cascaded form of a transfer function H(z) in terms of the L transfer functions H₁(z), H₂(z), …, H_L(z) is

$H (z) = \prod_{l = 1}^{L} H_{l} (z) = H_{1} (z) \times H_{2} (z) \times \dots \times H_{L} (z) .$

Return Digital Filters in CTF Format

Get the filter coefficients by specifying to return B = d.Numerator and A = d.Denominator from a digitalFilter object d. That way, you can have digital filters in CTF format for analysis, visualization and signal filtering.

Filter Coefficients

When you specify to return the numerator and denominator coefficients in the CTF format, the L-row matrices B and A are returned as

$B = [\begin{matrix} b_{11} & b_{12} & \dots & b_{1, m + 1} \\ b_{21} & b_{22} & \dots & b_{2, m + 1} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ b_{L 1} & b_{L 2} & \dots & b_{L, m + 1} \end{matrix}], A = [\begin{matrix} 1 & a_{12} & \dots & a_{1, n + 1} \\ 1 & a_{22} & \dots & a_{2, n + 1} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ 1 & a_{L 2} & \dots & a_{L, n + 1} \end{matrix}],$

such that the full transfer function of the filter is

$H (z) = \frac{b_{11} + b_{12} z^{- 1} + \dots + b_{1, m + 1} z^{- m}}{1 + a_{12} z^{- 1} + \dots + a_{1, n + 1} z^{- n}} \times \frac{b_{21} + b_{22} z^{- 1} + \dots + b_{2, m + 1} z^{- m}}{1 + a_{22} z^{- 1} + \dots + a_{2, n + 1} z^{- n}} \times \dots \times \frac{b_{L 1} + b_{L 2} z^{- 1} + \dots + b_{L, m + 1} z^{- m}}{1 + a_{L 2} z^{- 1} + \dots + a_{L, n + 1} z^{- n}},$

where m ≥ 0 is the numerator order of the filter and n ≥ 0 is the denominator order.

References

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

Version History

Introduced in R2014a

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R2024b: Use `Numerator` and `Denominator` properties in `digitalFilter` object

Obtain the numerator and denominator coefficients of digital filters designed with Cascaded Transfer Functions. Starting in R2024b, the Numerator and Denominator properties replace the Coefficients property.

For a digitalFilter object filt, you must update your code to get the filter coefficients B (numerator) and A (denominator).

Impulse Response Type	Original Code in R2024a or Earlier	Updated Code in R2024b
IIR	B = filt.Coefficients(:,1:3); A = filt.Coefficients(:,4:6);	B = filt.Numerator; A = filt.Denominator;
FIR	B = filt.Coefficients;	B = filt.Numerator;

digitalFilter

Description

Properties

Coefficients

`Numerator` — Numerator coefficients
row vector | L-by-3 matrix

`Denominator` — Denominator coefficients
`1` | L-by-3 matrix

Specifications

`FrequencyResponse` — Frequency response type
`'lowpass'` | `'highpass'` | `'bandpass'` | `'bandstop'` | `'differentiator'` | `'hilbert'` | `'arbmag'`

`ImpulseResponse` — Impulse response type
`'fir'` | `'iir'`

Object Functions

Examples

Lowpass IIR Filter

More About

Cascaded Transfer Functions

Return Digital Filters in CTF Format

References

Version History

R2024b: Use `Numerator` and `Denominator` properties in `digitalFilter` object

See Also

Live Editor Tasks

Apps

Objects

Functions

digitalFilter

Description

Properties

Coefficients

Numerator — Numerator coefficients row vector | L-by-3 matrix

Denominator — Denominator coefficients 1 | L-by-3 matrix

Specifications

FrequencyResponse — Frequency response type 'lowpass' | 'highpass' | 'bandpass' | 'bandstop' | 'differentiator' | 'hilbert' | 'arbmag'

ImpulseResponse — Impulse response type 'fir' | 'iir'

Object Functions

Examples

Lowpass IIR Filter

More About

Cascaded Transfer Functions

Return Digital Filters in CTF Format

References

Version History

R2024b: Use Numerator and Denominator properties in digitalFilter object

See Also

Live Editor Tasks

Apps

Objects

Functions

`Numerator` — Numerator coefficients
row vector | L-by-3 matrix

`Denominator` — Denominator coefficients
`1` | L-by-3 matrix

`FrequencyResponse` — Frequency response type
`'lowpass'` | `'highpass'` | `'bandpass'` | `'bandstop'` | `'differentiator'` | `'hilbert'` | `'arbmag'`

`ImpulseResponse` — Impulse response type
`'fir'` | `'iir'`

R2024b: Use `Numerator` and `Denominator` properties in `digitalFilter` object