designParamEQ

Design parametric equalizer

Syntax

[B,A] = designParamEQ(N,gain,centerFreq,bandwidth)

[B,A] = designParamEQ(N,gain,centerFreq,bandwidth,mode)

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

Description

[B,A] = designParamEQ(N,gain,centerFreq,bandwidth) designs an Nth-order parametric equalizer with specified gain, center frequency, and bandwidth. B and A are matrices of numerator and denominator coefficients, with columns corresponding to cascaded second-order section (SOS) filters.

[B,A] = designParamEQ(N,gain,centerFreq,bandwidth,mode) specifies whether the parametric equalizer is implemented with second-order sections or fourth-order sections (FOS).

[B,A] = designParamEQ(___,Name,Value) specifies options using one or more Name,Value pair arguments.

Examples

Design Two-Band Parametric Equalizer

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

N = [2, ...
     4];
 
gain = [6, ...
      -4]; 
  
centerFreq = [0.25, ...
              0.75]; 
          
bandwidth = [0.12, ...
              0.1];

Generate the filter coefficients using the specified parameters.

[B,A] = designParamEQ(N,gain,centerFreq,bandwidth,"Orientation","row");

Visualize your filter design.

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];
gain = [-25,35];
centerFreq = [0.01,0.5];
bandwidth = [0.35,0.5];
[B,A] = designParamEQ(N,gain,centerFreq,bandwidth,Orientation="row");

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 your 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 your 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];
gain = [5,10];
centerFreq = [0.025,0.65];
bandwidth = [0.025,0.35];
mode = "fos";

[B,A] = designParamEQ(N,gain,centerFreq,bandwidth,mode,Orientation="row");

Construct FOS IIR filters.

myFilter = dsp.FourthOrderSectionFilter(B,A);

Visualize the frequency response of your parametric equalizer.

freqz(myFilter)

Construct a spectrum analyzer to visualize the original audio signal and the audio signal passed through your 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 your objects once done.

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

Input Arguments

N — Filter order

scalar | row vector

Filter order, specified as a scalar or row vector the same length as centerFreq. Elements of the vector must be even integers.

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

gain — Peak gain (dB)

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

centerFreq — Normalized center frequency of equalizer bands

scalar | row vector

Normalized center frequency of equalizer bands, specified as a scalar or row vector of real values in the range 0 to 1, where 1 corresponds to the Nyquist frequency (π rad/sample). If centerFreq is specified as a row vector, separate equalizers are designed for each element of centerFreq.

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

bandwidth — Normalized bandwidth

scalar | row vector

Normalized bandwidth, specified as a scalar or row vector the same length as centerFreq. Elements of the vector are specified as real values in the range 0 to 1, where 1 corresponds to the Nyquist frequency (π rad/sample).

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: $$10\times {\log }_{10}\left(0.5\right)$$.

To convert octave bandwidth to normalized bandwidth, calculate the associated Q-factor as

$$Q=\frac{\sqrt{2^{\left(octavebandwidth\right)}}}{2^{\left(octavebandwidth\right)}-1}.$$

Then convert to bandwidth

$$bandwidth=\frac{centerFreq}{Q}.$$

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

mode — Design mode

'sos' (default) | 'fos'

Design mode, specified as 'sos' or 'fos'.

• 'sos' –– Implements your equalizer as cascaded second-order filters.

• 'fos' –– Implements your equalizer as cascaded fourth-order filters. Because fourth-order sections do not require the computation of roots, they are generally more computationally efficient.

Data Types: char | string

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.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'Orientation',"row"

Orientation — Orientation of returned filter coefficients

"column" (default) | "row"

Orientation of returned filter coefficients, specified as the comma-separated pair consisting of 'Orientation' and "column" or "row".

Data Types: char | string

Output Arguments

B — Numerator filter coefficients

matrix

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

• If 'Orientation' is set to "column" and mode is set to "sos", then B is returned as an L-by-3 matrix. Each column corresponds to the numerator coefficients of your cascaded second-order sections.

• If 'Orientation' is set to "column" and mode is set to "fos", then B is returned as an L-by-5 matrix. Each column corresponds to the numerator coefficients of your cascaded fourth-order sections.

• If 'Orientation' is set to "row" and mode is set to "sos", then B is returned as a 3-by-L matrix. Each row corresponds to the numerator coefficients of your cascaded second-order sections.

• If 'Orientation' is set to "row" and mode is set to "fos", then B is returned as a 5-by-L matrix. Each row corresponds to the numerator coefficients of your cascaded fourth-order sections.

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 'Orientation' is set to "column" and mode is set to "sos", then A is returned as an L-by-2 matrix. Each column corresponds to the denominator coefficients of your cascaded second-order sections. A does not include the leading unity coefficients.

• If 'Orientation' is set to "column" and mode is set to "fos", then A is returned as an L-by-4 matrix. Each column corresponds to the denominator coefficients of your cascaded fourth-order sections. A does not include the leading unity coefficients.

• If 'Orientation' is set to "row" and mode is set to "sos", then A is returned as a 3-by-L matrix. Each row corresponds to the denominator coefficients of your cascaded second-order sections.

• If 'Orientation' is set to "row" and mode is set to "fos", then A is returned as a 5-by-L matrix. Each row corresponds to the denominator coefficients of your cascaded fourth-order sections.

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

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.