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The Coefficients property has been replaced by the Numerator and Denominator properties.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

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
stepz	Step response of digital filter
zerophase	Zero-phase response of digital filter
zplane	Zero-pole plot for discrete-time systems

Filter Conversion

ss	Convert digital filter to state-space representation
tf	Convert digital filter to transfer function
zpk	Convert digital filter to zero-pole-gain representation
toMultirate (DSP System Toolbox)	Create multirate filter System object from digital FIR filter object

Examples

Lowpass IIR Filter

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)

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

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

$$H(z)={\displaystyle \prod _{l=1}^L{H}_l(z)}=H_1(z)\times H_2(z)\times \cdots \times H_L(z).$$

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

$$B=\left[\begin{array}{cccc}{b}_{11}& b_{12}& \cdots & b_{1,m+1}\\ b_{21}& b_{22}& \cdots & b_{2,m+1}\\ ⋮& ⋮& \ddots & ⋮\\ b_{L1}& b_{L2}& \cdots & b_{L,m+1}\end{array}\right],A=\left[\begin{array}{cccc}1& a_{12}& \cdots & a_{1,n+1}\\ 1& a_{22}& \cdots & a_{2,n+1}\\ ⋮& ⋮& \ddots & ⋮\\ 1& a_{L2}& \cdots & a_{L,n+1}\end{array}\right],$$

such that the full transfer function of the filter is

$$H\left(z\right)=\frac{b_{11}+b_{12}{z}^{-1}+\cdots +b_{1,m+1}{z}^{-m}}{1+a_{12}{z}^{-1}+\cdots +a_{1,n+1}{z}^{-n}}\times \frac{b_{21}+b_{22}{z}^{-1}+\cdots +b_{2,m+1}{z}^{-m}}{1+a_{22}{z}^{-1}+\cdots +a_{2,n+1}{z}^{-n}}\times \cdots \times \frac{b_{L1}+b_{L2}{z}^{-1}+\cdots +b_{L,m+1}{z}^{-m}}{1+a_{L2}{z}^{-1}+\cdots +a_{L,n+1}{z}^{-n}},$$

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

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;