designParamEQ

Design parametric equalizer

The designParamEQ function has changed. For more information, see Version History.

Syntax

[B,A] = designParamEQ(Name=Value)

Description

[B,A] = designParamEQ(Name=Value) designs a parametric equalizer with options specified using one or more name-value arguments. You can specify design options, including gain, center frequency, and bandwidth.

Examples

Design Two-Band Parametric Equalizer

Specify the filter order, peak gain in dB, normalized center frequencies, and normalized bandwidth of the bands of the parametric equalizer.

N = [2, ...
     4];
 
GdB = [6, ...
      -4]; 
  
wc = [0.25, ...
              0.75]; 
          
bw = [0.12, ...
              0.1];

Generate the filter coefficients using the specified parameters.

[B,A] = designParamEQ(FilterOrder=N,Gain=GdB, ...
    CenterFrequency=wc,Bandwidth=bw);

Visualize the frequency response of the designed filter.

freqz([B,A]);

Filter Audio Using SOS Parametric Equalizer

Design a second-order sections (SOS) parametric equalizer using designParamEQ and filter an audio stream.

Create audio file reader and audio device writer System objects. Use the sample rate of the reader as the sample rate of the writer.

frameSize = 256;
fileReader = dsp.AudioFileReader("RockGuitar-16-44p1-stereo-72secs.wav",SamplesPerFrame=frameSize);
sampleRate = fileReader.SampleRate;
deviceWriter = audioDeviceWriter(SampleRate=sampleRate);

Play the audio signal through your device.

count = 0;
while count < 2500
    audio = fileReader();
    deviceWriter(audio);
    count = count + 1;
end
reset(fileReader)

Design an SOS parametric equalizer suitable for use with dsp.SOSFilter.

N = [4,4];
G = [-25,35];
wc = [0.01,0.5];
bw = [0.35,0.5];
[B,A] = designParamEQ(FilterOrder=N,Gain=G, ...
    CenterFrequency=wc,Bandwidth=bw);

Create an SOS filter.

myFilter = dsp.SOSFilter(B,A);

Create a spectrum analyzer to visualize the original audio signal and the audio signal passed through the parametric equalizer.

scope = spectrumAnalyzer( ...
    SampleRate=sampleRate, ...
    PlotAsTwoSidedSpectrum=false, ...
    FrequencyScale="log", ...
    Title="Original and Equalized Signals", ...
    ShowLegend=true, ...
    ChannelNames=["Original Signal","Equalized Signal"]);

Play the filtered audio signal and visualize the original and filtered spectrums.

count = 0;
while count < 2500
    originalSignal = fileReader();
    equalizedSignal = myFilter(originalSignal);
    scope([originalSignal(:,1),equalizedSignal(:,1)]);
    deviceWriter(equalizedSignal);
    count = count + 1;
end

As a best practice, release the objects once done.

release(deviceWriter)
release(fileReader)
release(scope)

Filter Audio Using FOS Parametric Equalizer

Design a fourth-order sections (FOS) parametric equalizer using designParamEQ and filter an audio stream.

Construct audio file reader and audio device writer System objects. Use the sample rate of the reader as the sample rate of the writer.

frameSize = 256;
fileReader = dsp.AudioFileReader( ...
    "RockGuitar-16-44p1-stereo-72secs.wav",SamplesPerFrame=frameSize);
sampleRate = fileReader.SampleRate;
deviceWriter = audioDeviceWriter(SampleRate=sampleRate);

Play the audio signal through your device.

count = 0;
while count < 2500
    x = fileReader();
    deviceWriter(x);
    count = count + 1;
end
reset(fileReader)

Design FOS parametric equalizer coefficients.

N = [2 4];
G = [5 10];
wc = [0.025 0.65];
Q = [1 1.86];
mode = "fos";

[B,A] = designParamEQ(FilterOrder=N,Gain=G, ...
    CenterFrequency=wc,QualityFactor=Q,CascadeSectionsForm=mode);

Construct FOS IIR filters.

myFilter = dsp.FourthOrderSectionFilter(B,A);

Visualize the frequency response of the parametric equalizer.

freqz(myFilter)

Construct a spectrum analyzer to visualize the original audio signal and the audio signal passed through the parametric equalizer.

scope = spectrumAnalyzer( ...
    SampleRate=sampleRate, ...
    PlotAsTwoSidedSpectrum=false, ...
    FrequencyScale="log", ...
    Title="Original and Equalized Signals", ...
    ShowLegend=true, ...
    ChannelNames=["Original Signal","Equalized Signal"]);

Play the filtered audio signal and visualize the original and filtered spectra.

count = 0;
while count < 2500
    x = fileReader();
    y = myFilter(x);
    
    scope([x(:,1),y(:,1)]);
    
    deviceWriter(y);
    
    count = count + 1;
end

As a best practice, release the objects once done.

release(fileReader)
release(deviceWriter)
release(scope)

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: [B,A] = designParamEQ(CenterFrequency=0.5,QualityFactor=4) designs a parametric equalizer with a center frequency of 0.5π rad/sample and a quality factor of 4.

CenterFrequency — Normalized center frequency of equalizer bands

0.1 (default) | scalar | row vector

Normalized center frequency of the equalizer bands, specified as a scalar or row vector.

• CenterFrequency must be real valued and in the range (0,1), where 1 corresponds to the Nyquist frequency (π rad/sample).

• If you specify CenterFrequency as a row vector, then designParamEQ designs one equalizer for each element of the specified row vector.

• If you specify CenterFrequency as a row vector, then you can specify one of these bandwidth specifications: Bandwidth, QualityFactor, or OctaveBandwidth. You cannot specify BandEdgeFrequencies in this case. For more information, see Bandwidth Specifications.

• If you specify CenterFrequency and a bandwidth specification (Bandwidth, QualityFactor, or OctaveBandwidth) as row vectors, then both vectors must have the same size.

Data Types: single | double

Bandwidth — Normalized bandwidth of equalizer bands

0.1 (default) | scalar | row vector

Normalized bandwidth of the equalizer bands, specified as a scalar or row vector.

• Bandwidth must be real valued and in the range (0,1), where 1 corresponds to the Nyquist frequency (π rad/sample).

• If you specify Bandwidth, do not specify QualityFactor, OctaveBandwidth, or BandEdgeFrequencies. For more information, see Bandwidth Specifications.

• If you specify Bandwidth and CenterFrequency as row vectors, then both vectors must be of the same size.

The function measures the normalized bandwidth at G/2 dB, where G is the gain specified in Gain. If the gain is -Inf dB (notch filter), then designParamEQ measures the normalized bandwidth at the 3 dB attenuation point, 10⋅log₁₀(0.5).

Data Types: single | double

QualityFactor — Quality factor of equalizer bands

positive scalar | row vector

Since R2026a

Quality factor (or Q factor) of the equalizer bands, specified as a positive scalar or row vector of positive scalars.

• If you specify QualityFactor, do not specify Bandwidth, OctaveBandwidth, or BandEdgeFrequencies. For more information, see Bandwidth Specifications.

• If you specify QualityFactor and CenterFrequency as row vectors, then both vectors must be of the same size.

The Q factor is defined as the center frequency ω_c divided by the bandwidth BW, or Q = ω_c/BW.

Data Types: single | double

OctaveBandwidth — Octave bandwidth of equalizer bands

positive scalar | row vector

Since R2026a

Octave bandwidth of the equalizer bands, specified as a positive scalar or row vector of positive scalars.

• If you specify OctaveBandwidth, do not specify Bandwidth, QualityFactor, or BandEdgeFrequencies. For more information, see Bandwidth Specifications.

• If you specify OctaveBandwidth and CenterFrequency as row vectors, then both vectors must be of the same size.

The octave bandwidth is defined as the base-2 logarithmic ratio between the upper band edge frequency and the lower band edge frequency.

Data Types: single | double

BandEdgeFrequencies — Normalized upper and lower band edge frequencies of equalizer bands

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

Since R2026a

Normalized upper and lower band edge frequencies of the equalizer bands, specified as a two-element vector or two-row matrix.

• BandEdgeFrequencies must be real valued and in the range (0,1), where 1 corresponds to the Nyquist frequency (π rad/sample).

• The first and second element or row in the specified vector or matrix represent the lower and upper band edge frequencies, respectively.

• If you specify BandEdgeFrequencies as a matrix, the function interprets each column as a separate equalizer band.

• If you specify BandEdgeFrequencies, do not specify CenterFrequency, Bandwidth, QualityFactor, or OctaveBandwidth. For more information, see Bandwidth Specifications.

Data Types: single | double

FilterOrder — Filter order

2 (default) | scalar | row vector

Filter order, specified as a scalar or row vector the same length as CenterFrequencies.

If you specify FilterOrder as a vector, each element must be an even number.

Gain — Peak gain (dB)

3 dB (default) | scalar | row vector

Peak gain in dB, specified as a scalar or row vector the same length as centerFreq. Elements of the vector must be real valued.

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

CascadeSectionsForm — Design mode

"sos" (default) | "fos"

Design mode, specified as one of these values:

• "sos" –– designParamEQ implements the equalizer as a cascade of second-order filters.

• "fos" –– designParamEQ implements the equalizer as a cascade of fourth-order filters. Typically, this implementation is computationally more efficient because fourth-order sections do not require computing the polynomial roots.

Output Arguments

B — Numerator filter coefficients

matrix

Numerator filter coefficients, returned as a matrix. The size and interpretation of B depends on how you specify CascadeSectionsForm:

• If you specify CascadeSectionsForm as "sos", then designParamEQ returns B as an L-by-3 matrix. Each row lists the numerator coefficients of a cascaded second-order section.

• If you specify CascadeSectionsForm as "fos", then designParamEQ returns B as an L-by-5 matrix. Each row lists the numerator coefficients of a cascaded fourth-order section.

A — Denominator filter coefficients

matrix

Denominator filter coefficients, returned as a matrix. The size and interpretation of A depends on the Orientation and mode:

• If you specify CascadeSectionsForm as "sos", then designParamEQ returns A as an L-by-3 matrix. Each row lists the denominator coefficients of a cascaded second-order section.

• If you specify CascadeSectionsForm as "fos", then designParamEQ returns A as an L-by-5 matrix. Each row lists the denominator coefficients of a cascaded fourth-order section.

More About

Bandwidth Specifications

When you design a parametric equalizer, you must specify the equalizer bands either through bandwidth specifications or by listing the band edge frequencies. You can specify in either of these two ways, but not both.

This table lists the possible combinations that you can use to specify the equalizer bands.

Design Method	Arguments to Specify	Values to Specify
Bandwidth specifications	CenterFrequency and Bandwidth	Specify the size as one of these: Scalars A scalar and a row vector Row vectors of the same size For the vectors, specify one column per band.
	CenterFrequency and QualityFactor
	CenterFrequency and OctaveBandwidth
Band edge frequencies	BandEdgeFrequencies	Two-row matrix, one column per band

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 MATLAB® Coder™.

Version History

Introduced in R2016a

R2026a: The designParamEQ function has changed

The designParamEQ function has changed:

• Use name-value arguments instead of positional arguments. This change enables you to design the parametric equalizer calling design specifications directly when you write code.

• Use the QualityFactor, OctaveBandwidth, and BandEdgeFrequencies name-value arguments to design the parametric equalizer with alternative specifications.

• The Orientation name-value argument has been removed. The function returns filter coefficients in row orientation only, which enables you to generate filter coefficients in the cascaded transfer function (CTF) format. Each row contains filter coefficients for a CTF section.

Consider these design specifications.

N = [2 4];               % Filter order
G = [6 4];               % Gain
wc = [0.25 0.75];        % Center frequencies
bw = [0.12 0.11];        % Normalized bandwidth
mode = "fos";            % Design mode

You must make the following updates to your code.

Original Code in R2025b or Earlier	Updated Code in R2026a
[B,A] = designParamEQ(N,G, ... wc,bw, ... Orientation="row")	[B,A] = designParamEQ(FilterOrder=N,Gain=G, ... CenterFrequency=wc,Bandwidth=bw)
[B,A] = designParamEQ(N,G, ... wc,bw,mode, ... Orientation="row")	[B,A] = designParamEQ(FilterOrder=N,Gain=G, ... CenterFrequency=wc,Bandwidth=bw,CascadeSectionsForm=mode)
[B,A] = designParamEQ(N,G, ... wc,bw, ... Orientation="column")	N/A
[B,A] = designParamEQ(N,G, ... wc,bw,mode, ... Orientation="column")	N/A

R2024b: Warning that filter design functions will return coefficients in row orientation by default

The designVarSlopeFilter, designParamEQ, and designShelvingEQ functions will return filter coefficients in row orientation by default in a future release. With row orientation, the functions return the coefficients as matrices where each row contains the coefficients of the corresponding second-order section of the filter.

The default value of the Orientation name-value argument, "column", will be removed in a future release and throws a warning in R2024b. Set Orientation to "row" to return coefficients in row orientation in the current release.

R2024a: Filter design functions will return coefficients in row orientation by default

The designVarSlopeFilter, designParamEQ, and designShelvingEQ functions will return filter coefficients in row orientation by default in a future release.