dsp.LowpassFilter

FIR or IIR lowpass filter

Description

The dsp.LowpassFilter object independently filters each channel of the input over time using the given design specifications. You can set the FilterType property to 'FIR' or 'IIR' to implement the object as an FIR or an IIR lowpass filter.

When the FilterType property is set to 'FIR', using this object is an alternative to using the firceqrip and firgr functions with dsp.FIRFilter. The dsp.LowpassFilter object condenses the two-step process into one. You can use measure to verify that the design meets the prescribed specifications.

To filter each channel of your input:

1. Create the dsp.LowpassFilter object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

This object supports C/C++ code generation and SIMD code generation under certain conditions. This object also supports code generation for ARM^® Cortex^®-M and ARM Cortex-A processors. For more information, see Code Generation.

Creation

Syntax

LPF = dsp.LowpassFilter

LPF = dsp.LowpassFilter(Name=Value)

Description

LPF = dsp.LowpassFilter returns a minimum order FIR lowpass filter with the default filter settings. Calling the object with the default property settings filters the input data with a passband frequency of 8 kHz, a stopband frequency of 12 kHz, a passband ripple of 0.1 dB, and a stopband attenuation of 80 dB.

LPF = dsp.LowpassFilter(Name=Value) returns a lowpass filter with additional properties specified by one or more Name-Value pair arguments. Name is the property name and Value is the corresponding value. For example, PassbandFrequency=8000 sets the passband frequency specification of the filter to 8000 Hz.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

FilterType — Type of filter response

'FIR' (default) | 'IIR'

Type of filter response, specified as one of these options:

• 'FIR' — The object designs an FIR lowpass filter.

• 'IIR' — The object designs an IIR lowpass (biquad) filter.

DesignForMinimumOrder — Flag to design minimum order filter

true (default) | false

Flag to design minimum order filter, specified as:

• true –– The object designs the minimum order filter that meets the filter design specifications.

• false –– The object designs the filter with the order that you specify in the FilterOrder property.

FilterOrder — Order of the FIR or IIR filter

50 (default) | positive integer

Order of the FIR or IIR filter, specified as a positive integer.

Dependencies

To enable this property, set DesignForMinimumOrder to false.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

PassbandFrequency — Filter passband edge frequency

8000 (default) | real positive scalar

Filter passband edge frequency, specified as a real positive scalar in Hz or in normalized frequency units (since R2023a).

If you set the NormalizedFrequency property to:

• false –– The value of the passband edge frequency is in Hz and must be less than the stopband frequency and half the SampleRate property value.

• true –– The value of the passband edge frequency is in normalized frequency units. The value must be a positive scalar less than 1.0.

(since R2023a)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

StopbandFrequency — Filter stopband edge frequency

12000 (default) | real positive scalar

Filter stopband edge frequency, specified as a real positive scalar in Hz or in normalized frequency units (since R2023a).

If you set the NormalizedFrequency property to:

• false –– The value of the stopband edge frequency is in Hz. The value must be greater than the passband edge frequency and less than half the SampleRate property value.

• true –– The value of the stopband edge frequency is in normalized frequency units. The value must be a positive scalar greater than the passband edge frequency and less than 1.0.

(since R2023a)

Dependencies

To enable this property, set the DesignForMinimumOrder property to true.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

PassbandRipple — Maximum ripple of filter response in the passband

0.1 (default) | real positive scalar

Maximum ripple of filter response in the passband, specified as a real positive scalar in dB.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

StopbandAttenuation — Minimum attenuation in the stopband

80 (default) | real positive scalar

Minimum attenuation in the stopband, specified as a real positive scalar in dB.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

NormalizedFrequency — Flag to set frequencies in normalized units

false (default) | true

Since R2023a

Flag to set frequencies in normalized units, specified as one of these values:

• true –– The passband edge and stopband edge frequencies must be in the normalized frequency units and less than 1.0.

• false –– The passband edge and stopband edge frequencies are in Hz. You can specify the input sample rate through the SampleRate property.

Data Types: logical

SampleRate — Input sample rate

44100 (default) | real positive scalar

Input sample rate in Hz, specified as a real positive scalar.

Dependency

To enable this property, set NormalizedFrequency to false. (since R2023a)

Data Types: single | double

Fixed-Point Properties

RoundingMethod — Rounding method for output fixed-point operations

'Floor' (default) | 'Ceiling' | 'Convergent' | 'Nearest' | 'Round' | 'Simplest' | 'Zero'

Rounding method for output fixed-point operations, specified as a character vector. For more information on the rounding modes, see Precision and Range.

CoefficientsDataType — Word and fraction lengths of coefficients

numerictype(1,16) (default) | numerictype object

Word and fraction lengths of coefficients, specified as a numerictype object. The default, numerictype(1,16) corresponds to a signed numeric type object with 16-bit coefficients and a fraction length determined based on the coefficient values, to give the best possible precision.

This property is not tunable.

Word length of the output is same as the word length of the input. Fraction length of the output is computed such that the entire dynamic range of the output can be represented without overflow. For details on how the fraction length of the output is computed, see Fixed-Point Precision Rules for Avoiding Overflow in FIR Filters.

Usage

Syntax

y = LPF(x)

Description

y = LPF(x) lowpass filters the input signal, x. y is a lowpass-filtered version of x.

Input Arguments

x — Noisy data input

vector | matrix

Noisy data input, specified as a vector or a matrix. If the input signal is a matrix, each column of the matrix is treated as an independent channel. The number of rows in the input signal denote the channel length. This object accepts variable-size inputs. After the object is locked, you can change the size of each input channel, but you cannot change the number of channels.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi
Complex Number Support: Yes

Output Arguments

y — Filtered output

vector | matrix

Filtered output, returned as a vector or a matrix. The output has the same size, data type, and complexity characteristics as the input.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi
Complex Number Support: Yes

Object Functions

To use an object function, specify the System object™ as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Specific to dsp.LowpassFilter

freqz	Frequency response of discrete-time filter System object
fvtool	Visualize frequency response of DSP filters
impz	Impulse response of discrete-time filter System object
info	Information about filter System object
coeffs	Returns the filter System object coefficients in a structure
cost	Estimate cost of implementing filter System object
grpdelay	Group delay response of discrete-time filter System object
generatehdl	Generate HDL code for quantized DSP filter (requires Filter Design HDL Coder)
measure	Measure frequency response characteristics of filter System object
outputDelay	Determine output delay of single-rate or multirate filter

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Impulse and Frequency Response of FIR and IIR Lowpass Filters

Create a minimum-order FIR lowpass filter for data sampled at 44.1 kHz. Specify a passband frequency of 8 kHz, a stopband frequency of 12 kHz, a passband ripple of 0.1 dB, and a stopband attenuation of 80 dB.

Fs = 44.1e3; 
filtertype = 'FIR';
Fpass = 8e3;
Fstop = 12e3; 
Rp = 0.1;
Astop = 80;
FIRLPF = dsp.LowpassFilter(SampleRate=Fs,...
                             FilterType=filtertype,...
                             PassbandFrequency=Fpass,...
                             StopbandFrequency=Fstop,...
                             PassbandRipple=Rp,...
                             StopbandAttenuation=Astop);

Design a minimum-order IIR lowpass filter with the same properties as the FIR lowpass filter. Change the FilterType property of the cloned filter to IIR.

IIRLPF = clone(FIRLPF);
IIRLPF.FilterType = 'IIR';

Plot the impulse response of the FIR lowpass filter. The zeroth-order coefficient is delayed by 19 samples, which is equal to the group delay of the filter. The FIR lowpass filter is a causal FIR filter.

fvtool(FIRLPF,Analysis='impulse')

Plot the impulse response of the IIR lowpass filter.

fvtool(IIRLPF,Analysis='impulse')

Plot the magnitude and phase response of the FIR lowpass filter.

fvtool(FIRLPF,Analysis='freq')

Plot the magnitude and phase response of the IIR lowpass filter.

fvtool(IIRLPF,Analysis='freq')

Calculate the cost of implementing the FIR lowpass filter.

cost(FIRLPF)

ans = struct with fields:
                  NumCoefficients: 39
                        NumStates: 38
    MultiplicationsPerInputSample: 39
          AdditionsPerInputSample: 38

Calculate the cost of implementing the IIR lowpass filter. The IIR filter is more efficient to implement than the FIR filter.

cost(IIRLPF)

ans = struct with fields:
                  NumCoefficients: 18
                        NumStates: 14
    MultiplicationsPerInputSample: 18
          AdditionsPerInputSample: 14

Calculate the group delay of the FIR lowpass filter.

grpdelay(FIRLPF)

Calculate the group delay of the IIR lowpass filter. The FIR filter has a constant group delay (linear phase), while its IIR counterpart does not.

grpdelay(IIRLPF)

Filter White Gaussian Noise Signal with FIR Lowpass Filter

Create a lowpass filter using the dsp.LowpassFilter System object™. Setting the NormalizedFrequency property to true designs the filter with frequency specifications in normalized frequency units.

LPF = dsp.LowpassFilter(NormalizedFrequency=true)

LPF = 
  dsp.LowpassFilter with properties:

               FilterType: 'FIR'
    DesignForMinimumOrder: true
        PassbandFrequency: 0.3628
        StopbandFrequency: 0.5442
           PassbandRipple: 0.1000
      StopbandAttenuation: 80
      NormalizedFrequency: true

  Use get to show all properties

Create a spectrumAnalyzer object to visualize the input and output signal spectra. With a sample rate of 44.1e3 Hz, the passband frequency and the stopband frequency of the filter translate to 8000 Hz and 12000 Hz, respectively.

SA = spectrumAnalyzer(SampleRate=44.1e3,...
                      PlotAsTwoSidedSpectrum=false,ShowLegend=true,...
                      YLimits=[-150 30],...
                      Title='Input Signal and Output Signal of Lowpass Filter');
SA.ChannelNames = {'Input','Output'};

Run the lowpass filter algorithm to filter the white Gaussian noisy input signal. View the input and output signals using the spectrum analyzer.

for k = 1:100
    Input = randn(1024,1);
    
    Output = LPF(Input);
    
    SA([Input,Output]);
end

Filter White Gaussian Noise with IIR Lowpass Filter

Set up the IIR lowpass filter. The sampling rate of the white Gaussian noise is 44,100 Hz. The passband frequency of the filter is 8 kHz, the stopband frequency is 12 kHz, the passband ripple is 0.1 dB, and the stopband attenuation is 80 dB.

Fs = 44.1e3;
filtertype = 'IIR';
Fpass = 8e3;
Fstop = 12e3;
Rp = 0.1;
Astop = 80;
LPF = dsp.LowpassFilter(SampleRate=Fs,...
                             FilterType=filtertype,...
                             PassbandFrequency=Fpass,...
                             StopbandFrequency=Fstop,...
                             PassbandRipple=Rp,...
                             StopbandAttenuation=Astop);

View the magnitude response of the lowpass filter.

fvtool(LPF)

Create a spectrum analyzer object.

SA = spectrumAnalyzer(SampleRate=Fs,...
    PlotAsTwoSidedSpectrum=false,...
    ShowLegend=true,YLimits=[-150 30],...
    Title='Input Signal and Output Signal of IIR Lowpass Filter');
SA.ChannelNames = {'Input','Output'};

Filter the white Gaussian noisy input signal. View the input and output signals using the spectrum analyzer.

for k = 1:100
    Input = randn(1024,1);

    Output = LPF(Input);

    SA([Input,Output]);
end

Measure Frequency Response Characteristics of Lowpass Filter

Measure the frequency response characteristics of a lowpass filter. Create a dsp.LowpassFilter System object with default properties. Measure the frequency response characteristics of the filter.

LPF = dsp.LowpassFilter

LPF = 
  dsp.LowpassFilter with properties:

               FilterType: 'FIR'
    DesignForMinimumOrder: true
        PassbandFrequency: 8000
        StopbandFrequency: 12000
           PassbandRipple: 0.1000
      StopbandAttenuation: 80
      NormalizedFrequency: false
               SampleRate: 44100

  Use get to show all properties

LPFMeas = measure(LPF)

LPFMeas = 
Sample Rate      : 44.1 kHz  
Passband Edge    : 8 kHz     
3-dB Point       : 9.1311 kHz
6-dB Point       : 9.5723 kHz
Stopband Edge    : 12 kHz    
Passband Ripple  : 0.08289 dB
Stopband Atten.  : 81.6141 dB
Transition Width : 4 kHz     
 

Algorithms

FIR Lowpass Filter

For the minimum order design, the algorithm uses generalized Remez FIR filter design algorithm. For the specified order design, the algorithm uses the constrained equiripple FIR filter design algorithm. The designed filter is then implemented as a linear phase Type-1 filter with a Direct form structure.

IIR Lowpass Filter

In the IIR configuration, the algorithm uses the elliptic design method to compute the SOS and scale values required to meet the filter design specifications. The algorithm uses the SOS and scale values to setup a Direct form I biquadratic IIR filter, which forms the basis of the IIR version of the lowpass filter.

References

[1] Shpak, D.J., and A. Antoniou. "A generalized Remez method for the design of FIR digital filters." IEEE^® Transactions on Circuits and Systems. Vol. 37, Issue 2, Feb. 1990, pp. 161–174.

[2] Selesnick, I.W., and C. S. Burrus. "Exchange algorithms that complement the Parks-McClellan algorithm for linear-phase FIR filter design." IEEE Transactions on Circuits and Systems. Vol. 44, Issue 2, Feb. 1997, pp. 137–143.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

This object supports code generation for ARM Cortex-M and ARM Cortex-A processors. To learn more about ARM Cortex code generation, see Code Generation for ARM Cortex-M and ARM Cortex-A Processors.

This object also supports SIMD code generation using Intel^® AVX2 code replacement library under these conditions:

• FilterType is set to 'FIR'.

• Input signal has a data type of single or double.

The SIMD technology significantly improves the performance of the generated code. For more information, see SIMD Code Generation. To generate SIMD code from this object, see Use Intel AVX2 Code Replacement Library to Generate SIMD Code from MATLAB Algorithms.

HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

This object supports HDL code generation with the Filter Design HDL Coder™ product. For workflows and limitations, see Generate HDL Code for Filter System Objects (Filter Design HDL Coder).

Version History

Introduced in R2015a

R2023a: Support for normalized frequencies

When you set the NormalizedFrequency property to true, you must specify the passband and stopband frequencies in normalized frequency units (0 to 1).

When you set the NormalizedFrequency property to true while creating the object, the passband and stopband frequency values are automatically set to normalized frequency units using the default sample rate of 44100 Hz.

lpFilter = dsp.LowpassFilter(NormalizedFrequency=true)

lpFilter = 
  dsp.LowpassFilter with properties:

               FilterType: 'FIR'
    DesignForMinimumOrder: true
        PassbandFrequency: 0.3628
        StopbandFrequency: 0.5442
           PassbandRipple: 0.1000
      StopbandAttenuation: 80
      NormalizedFrequency: true

When you set the NormalizedFrequency property to true after you create the object, the passband and stopband frequencies must be manually set to the normalized frequency values before you run the object algorithm.

lpFilter = dsp.LowpassFilter

lpFilter = 
  dsp.LowpassFilter with properties:

               FilterType: 'FIR'
    DesignForMinimumOrder: true
        PassbandFrequency: 8000
        StopbandFrequency: 12000
           PassbandRipple: 0.1000
      StopbandAttenuation: 80
      NormalizedFrequency: false
               SampleRate: 44100

To specify the normalized frequency values, set NormalizedFrequency to true and manually convert the frequency values in Hz to normalized values using the input sample rate in Hz. For example, if the input sample rate is 44100 Hz, the corresponding values in normalized units are computed using these equations.

lpFilter.NormalizedFrequency = true;
lpFilter.PassbandFrequency = 8000/(44100/2);
lpFilter.StopbandFrequency = 12000/(44100/2)

lpFilter = 
  dsp.LowpassFilter with properties:

               FilterType: 'FIR'
    DesignForMinimumOrder: true
        PassbandFrequency: 0.3628
        StopbandFrequency: 0.5442
           PassbandRipple: 0.1000
      StopbandAttenuation: 80
      NormalizedFrequency: true