Parametric Equalizer Design

Design tunable parametric equalizer coefficients

Since R2024a

• 

Libraries:
Audio Toolbox / Filters

Description

The Parametric Equalizer Design block designs a parametric equalizer with the specified filter order, gain, and either of these parameter combinations:

• Center frequency and bandwidth

• Center frequency and quality factor

• Center frequency and octave bandwidth

• Band edge frequencies

The block outputs filter coefficients of cascaded second-order section (SOS) or fourth-order section (FOS) filters, which you can use with the Second-Order Section Filter or Fourth-Order Section Filter blocks to filter audio signals. You can tune the filter parameters during simulation.

Examples

Design Parametric Equalizer in Simulink

Use the Parametric Equalizer Design block to design a parametric equalizer and pass the coefficients to a Second-Order Section Filter block to filter a signal of random noise. Tune the filter parameters using the dashboard controls and see how the spectrum of the filtered signal changes.

Ports

Input

N — Filter order

positive even integer

Use this port to specify the value of the Filter order parameter.

Dependencies

To enable this port, select the Specify filter order from input port parameter.

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

G — Gain (dB)

real scalar

Use this port to specify the value of the Gain (dB) parameter.

Dependencies

To enable this port, select the Specify gain from input port parameter.

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

Fc — Normalized center frequency

scalar in range [0,1]

Use this port to specify the value of the Normalized center frequency parameter.

Dependencies

To enable this port, select the Specify normalized center frequency from input port parameter. This port does not apply (since R2026a) when you set the Specification parameter to Band edge frequencies.

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

BW — Normalized bandwidth

scalar in range [0,1]

Use this port to specify the value of the Normalized bandwidth parameter.

Dependencies

To enable this port, set the Specification parameter to Center frequency and bandwidth and select the Specify normalized bandwidth from input port parameter.

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

Q — Quality factor

scalar

Since R2026a

Use this port to specify the value of the Quality factor parameter.

Dependencies

To enable this port, set the Specification parameter to Center frequency and quality factor and select the Specify quality factor from input port parameter.

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

O — Octave bandwidth

scalar

Since R2026a

Use this port to specify the value of the Octave bandwidth parameter.

Dependencies

To enable this port, set the Specification parameter to Center frequency and octave bandwidth and select the Specify octave bandwidth from input port parameter.

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

Fedge — Band edge frequencies

two-element row vector

Since R2026a

Use this port to specify the value of the Band edge frequencies parameter.

Dependencies

To enable this port, set the Specification parameter to Band edge frequencies and select the Specify band edge frequencies from input port parameter.

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

Output

Num — Numerator filter coefficients

matrix

Numerator filter coefficients, returned as a matrix.

• For SOS filters, the block returns the coefficients as an N-by-3 matrix.

• For FOS filters, the block returns the coefficients as an N-by-5 matrix.

N is the number of filter sections and depends on the Maximum filter order parameter. If Filter order is less than the Maximum filter order, then the block sets the unused sections to pass-through sections.

Dependencies

• The data type of the output depends on the Output data type parameter.

• The output dimensions depend on the Maximum filter order and Filter cascade sections form parameters.

Data Types: single | double

Den — Denominator filter coefficients

matrix

Denominator filter coefficients, returned as a matrix.

• For SOS filters, the block returns the coefficients as an N-by-3 matrix.

• For FOS filters, the block returns the coefficients as an N-by-5 matrix.

N is the number of filter sections and depends on the Maximum filter order parameter. If Filter order is less than Maximum filter order, then the block sets the unused sections to pass-through sections.

Dependencies

• The data type of the output depends on the Output data type parameter.

• The output dimensions depend on Maximum filter order and Filter cascade sections form parameters.

Data Types: single | double

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Smooth tuned filter parameters — Smooth filter parameters when tuning

off (default) | on

Select this parameter to gradually change a filter parameter to the new value when tuning it. If you clear this parameter, the tuned parameter immediately switches to the new value. Specify the level of smoothing with the Smoothing factor parameter.

Smoothing factor — Smoothing factor for tuned parameters

0.6 (default) | scalar in range [0,1)

Smoothing factor for tuned parameters, specified as a scalar in the range [0,1). As the smoothing factor approaches 1, a tuned parameter changes more gradually to the new value. A smoothing factor of 0 is equivalent to no smoothing.

For more information about smoothing, see Smoothing.

Tunable: Yes

Dependencies

To enable this parameter, select the Smooth tuned filter parameters parameter.

Maximum filter order — Maximum filter order

2 (default) | positive even integer

Maximum filter order of the designed coefficients, specified as a positive even integer. The Filter order parameter cannot exceed this value.

Specify filter order from input port — Use additional input port to specify filter order

off (default) | on

When you select this parameter, an additional input port, N, is added to the block.

Filter order — Filter order

2 (default) | positive even integer

Filter order of designed coefficients, specified as a positive even integer.

Tunable: Yes

Dependencies

• To enable this parameter, clear the Specify filter order from input port parameter.

• The value of this parameter cannot exceed Maximum filter order.

Specify gain from input port — Use additional input port to specify gain

off (default) | on

When you select this parameter, an additional input port, G, is added to the block. Use this port to specify the gain of the filter.

Gain (dB) — Gain (dB)

0 (default) | real scalar

Gain of the filter in dB, specified as a real scalar.

Tunable: Yes

Dependencies

To enable this parameter, clear the Specify gain from input port parameter.

Specification — Parameters to use to design filter

Center frequency and bandwidth (default) | Center frequency and quality factor | Center frequency and octave bandwidth | Band edge frequencies

Since R2026a

• Center frequency and bandwidth — Design the filter using Normalized center frequency and Normalized bandwidth.

• Center frequency and quality factor — Design the filter using Normalized center frequency and Quality factor.

• Center frequency and octave bandwidth — Design the filter using Normalized center frequency and Octave bandwidth.

• Band edge frequencies — Design the filter using Band edge frequencies.

Specify normalized center frequency from input port — Use additional input port to specify normalized center frequency

off (default) | on

When you select this parameter, an additional input port, Fc, is added to the block.

Dependencies

This parameter does not apply when you set the Specification parameter to Band edge frequencies. (since R2026a)

Normalized center frequency — Normalized center frequency

0.2 (default) | scalar in range [0,1]

Normalized center frequency of the filter, specified as a scalar in the range [0,1] where 1 corresponds to the Nyquist frequency.

Tunable: Yes

Dependencies

To enable this parameter, clear the Specify normalized center frequency from input port parameter. This parameter does not apply (since R2026a) when you set the Specification parameter to Band edge frequencies.

Specify normalized bandwidth from input port — Use additional input port to specify normalized bandwidth

off (default) | on

When you select this parameter, an additional input port, BW, is added to the block.

Dependencies

To enable this parameter, set the Specification parameter to Center frequency and bandwidth.

Normalized bandwidth — Normalized bandwidth

0.1 (default) | scalar in range [0,1]

Normalized bandwidth of the filter, specified as a scalar in the range [0,1], where 1 corresponds to the Nyquist frequency.

Normalized bandwidth is measured at gain/2 dB. If gain is set to -Inf (notch filter), normalized bandwidth is measured at the 3 dB attenuation point: 10 × log₁₀0.5.

Tunable: Yes

Dependencies

To enable this parameter, set the Specification parameter to Center frequency and bandwidth and clear the Specify normalized bandwidth from input port parameter.

Specify quality factor from input port — Option to use additional input port to specify quality factor

off (default) | on

Since R2026a

Select this parameter to specify the quality factor through the input port Q.

Dependencies

To enable this parameter, set the Specification parameter to Center frequency and quality factor.

Quality factor — Quality factor

1 (default) | scalar

Since R2026a

Quality factor of the filter, specified as a scalar.

Tunable: Yes

Dependencies

To enable this parameter, set the Specification parameter to Center frequency and quality factor and clear the Specify quality factor from input port parameter.

Specify octave bandwidth from input port — Use additional input port to specify octave bandwidth

off (default) | on

Since R2026a

Select this parameter to specify the octave bandwidth through the input port O.

Dependencies

To enable this parameter, set the Specification parameter to Center frequency and octave bandwidth.

Octave bandwidth — Octave bandwidth

1 (default) | scalar

Since R2026a

Octave bandwidth of the filter, specified as a scalar.

Tunable: Yes

Dependencies

To enable this parameter, set the Specification parameter to Center frequency and octave bandwidth and clear the Specify octave bandwidth from input port parameter.

Specify band edge frequencies from input port — Use additional input port to specify band edge frequencies

off (default) | on

Since R2026a

Select this parameter to specify the band edge frequencies through the input port Fedge.

Dependencies

To enable this parameter, set the Specification parameter to Band edge frequencies.

Band edge frequencies — Band edge frequencies

[0.1,0.3] (default) | two-element row vector

Since R2026a

Band edge frequencies of the filter, specified as a two-element vector.

Tunable: Yes

Dependencies

To enable this parameter, set the Specification parameter to Band edge frequencies and clear the Specify band edge frequencies from input port parameter.

Filter cascade sections form — Form of cascaded filter sections

Second-order sections (default) | Fourth-order sections

Form of cascaded filter sections, specified as Second-order sections for SOS filters or Fourth-order sections for FOS filters.

Output data type — Data type of output coefficients

double (default) | single

Data type of output coefficients, specified as double or single.

Sample time — Sample time of block

-1 (default) | positive scalar

Sample time of the block, in seconds, specified as -1 or a positive scalar. Setting this parameter to -1 means Simulink determines the sample time automatically for you. You can set this parameter to enable the design block to run at a slower rate than the filtering block.

Simulate using — Specify type of simulation to run

Interpreted execution (default) | Code generation

• Interpreted execution –– Simulate model using the MATLAB^® interpreter. This option shortens startup time but has a slower simulation speed than Code generation. In this mode, you can debug the source code of the block.

• Code generation –– Simulate model using generated C code. The first time you run a simulation, Simulink generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time, but the speed of the subsequent simulations is comparable to Interpreted execution.

Block Characteristics

Data Types	double | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

Algorithms

Smoothing

When you select Smooth tuned filter parameters, the Parametric Equalizer Design block uses the following formula to gradually adjust the parameter to the target value when tuning. The block redesigns the filter at each time step with the intermediate parameter values, until the target value is reached.

$$g[n]=\alpha g[n-1]+(1-\alpha )t[n],$$

where:

• n is the time step in the simulation.

• g is the instantaneous smoothed parameter.

• t is the target value for the tuned parameter.

• α is the smoothing factor, specified by the Smoothing factor parameter.

Filter Order Smoothing

When smoothing the Filter order parameter, the block rounds the smoothed parameter to the nearest even integer at each iteration. The block does not redesign the filter on time steps where the filter order stays the same and no other parameters are changing.

References

[1] Orfanidis, Sophocles J. "High-Order Digital Parametric Equalizer Design." Journal of the Audio Engineering Society. Vol. 53, November 2005, pp. 1026–1046.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2024a

R2026a: Specify quality factor, octave bandwidth, or band edge frequencies

You can specify the parametric equalizer using center frequency and quality factor, center frequency and octave bandwidth, or band edge frequencies.

If you design a parametric equalizer using the new parameters and then open the model in an older version of Simulink, the software replaces the equalizer block with an empty subsystem block. If you try to run the model, the block throws an error.