designShelvingEQ

Design shelving equalizer

Syntax

[B,A] = designShelvingEQ(gain,slope,Fc)

[B,A] = designShelvingEQ(gain,slope,Fc,type)

[B,A] = designShelvingEQ(___,Orientation=ornt)

Description

[B,A] = designShelvingEQ(gain,slope,Fc) designs a low-shelf equalizer with the specified gain, slope, and cutoff frequency Fc. B and A are the numerator and denominator coefficients, respectively, of a single second-order section (biquad) IIR filter.

[B,A] = designShelvingEQ(gain,slope,Fc,type) specifies the design type as a low-shelving or high-shelving equalizer.

[B,A] = designShelvingEQ(___,Orientation=ornt) specifies the orientation of the returned filter coefficients as "column" or "row".

Examples

Filter Audio Using Low-Shelf Equalizer

Create audio file reader and audio device writer 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);

deviceWriter = audioDeviceWriter(SampleRate=fileReader.SampleRate);

Play the audio signal through your device.

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

Design a second-order sections (SOS) low-shelf equalizer.

gain = 10;
slope = 3;
Fc = 0.025;

[B,A] = designShelvingEQ(gain,slope,Fc);

Visualize your shelving filter design.

SOS = [B',[1,A']];
fvtool(dsp.BiquadFilter(SOSMatrix=SOS), ...
    Fs=fileReader.SampleRate, ...
    FrequencyScale="log")

Create a biquad filter object.

myFilter = dsp.BiquadFilter( ...
    SOSMatrixSource="Input port", ...
    ScaleValuesInputPort=false);

Create a spectrum analyzer object to visualize the original audio signal and the audio signal passed through your low-shelf equalizer.

scope = dsp.SpectrumAnalyzer( ...
    SampleRate=fileReader.SampleRate, ...
    PlotAsTwoSidedSpectrum=false, ...
    FrequencyScale="log", ...
    FrequencyResolutionMethod="WindowLength", ...
    WindowLength=frameSize, ...
    Title="Original and Equalized Signal", ...
    ShowLegend=true, ...
    ChannelNames={'Original Signal','Equalized Signal'});

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

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

As a best practice, release your objects once done.

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

Design High-Shelf Equalizer

Design three second-order IIR high shelf equalizers using designShelvingEQ. The three shelving equalizers use three separate gain specifications.

Specify sample rate, peak gain, slope coefficient, and normalized cutoff frequency for the three shelving equalizers. The sample rate is in Hz. The peak gain is in dB.

Fs = 44.1e3;

gain1 = -6;
gain2 = 6;
gain3 = 12;

slope = 0.8;

Fc = 18000/(Fs/2);

Design the filter coefficients using the specified parameters.

[B1,A1] = designShelvingEQ(gain1,slope,Fc,"hi",Orientation="row");
[B2,A2] = designShelvingEQ(gain2,slope,Fc,"hi",Orientation="row");
[B3,A3] = designShelvingEQ(gain3,slope,Fc,"hi",Orientation="row");

Visualize your filter design.

fvt = fvtool([B1,A1;[1 0 0 1 0 0]], ...
    [B2,A2;[1 0 0 1 0 0]], ...
    [B3,A3;[1 0 0 1 0 0]], ...
    Fs=Fs);

legend(fvt,"gain = "+[gain1 gain2 gain3]+" dB",Location="northwest")

Design Low-Shelf Equalizer

Design three second-order IIR low-shelf equalizers using designShelvingEQ. The three shelving equalizers use three separate slope specifications.

Specify sampling frequency, peak gain, slope coefficient, and normalized cutoff frequency for three shelving equalizers. The sampling frequency is in Hz. The peak gain is in dB.

Fs = 44.1e3;

gain = 5;

slope1 = 0.5;
slope2 = 0.75;
slope3 = 1;

Fc = 1000/(Fs/2);

Design the filter coefficients using the specified parameters.

[B1,A1] = designShelvingEQ(gain,slope1,Fc,Orientation="row");
[B2,A2] = designShelvingEQ(gain,slope2,Fc,Orientation="row");
[B3,A3] = designShelvingEQ(gain,slope3,Fc,Orientation="row");

Visualize your filter design.

fvt = fvtool( ...
    dsp.BiquadFilter([B1,A1]), ...
    dsp.BiquadFilter([B2,A2]), ...
    dsp.BiquadFilter([B3,A3]), ...
    Fs=Fs, ...
    FrequencyScale="log");

legend(fvt,"slope = 0.5","slope = 0.75","slope = 1")

Input Arguments

gain — Peak gain (dB)

real scalar

Peak gain in dB, specified as a real scalar.

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

slope — Slope coefficient

positive scalar

Slope coefficient, specified as a positive scalar.

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

Fc — Normalized cutoff frequency

real scalar in the range [0, 1]

Normalized cutoff frequency, specified as a real scalar in the range [0, 1], where 1 corresponds to the Nyquist frequency (π rad/sample).

Normalized cutoff frequency is implemented as half the shelving filter gain, or gain/2 dB.

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

type — Filter type

"lo" (default) | 'hi'

Filter type, specified as "lo" or "hi".

• "lo"–– Low shelving equalizer

• "hi"–– High shelving equalizer

Data Types: char | string

ornt — Orientation of returned filter coefficients

"column" (default) | "row"

Orientation of returned filter coefficients, specified as "column" or "row".

• Set ornt to "row" for interoperability with FVTool, dsp.DynamicFilterVisualizer, and dsp.FourthOrderSectionFilter.

• Set ornt to "column" for interoperability with dsp.BiquadFilter.

Data Types: char | string

Output Arguments

B — Numerator filter coefficients

three-element column vector | three-element row vector

Numerator filter coefficients, returned as a vector. The size and interpretation of B depend on the orientation, ornt:

• If ornt is set to "column", then B is returned as a three-element column vector.

• If ornt is set to "row", then B is returned as a three-element row vector.

.

A — Denominator filter coefficients

two-element column vector | three-element row vector

Denominator filter coefficients of the designed second-order IIR filter, returned as a vector. The size and interpretation of A depend on the orientation, ornt:

• If ornt is set to "column", then A is returned as a two-element column vector. A does not include the leading unity coefficient.

• If ornt is set to "row", then A is returned as a three-element row vector.

References

[1] Bristow-Johnson, Robert. "Cookbook Formulae for Audio EQ Biquad Filter Coefficients." Accessed September 13, 2021. https://webaudio.github.io/Audio-EQ-Cookbook/Audio-EQ-Cookbook.txt.

Extended Capabilities

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

Version History

Introduced in R2016a