designShelvingEQ

Design shelving equalizer

Syntax

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

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

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

Description

[B,A] = designShelvingEQ(gain,slope,Fc) designs a low-shelf equalizer with the specified gain, slope, and cutoff frequency, Fc. The equalizer is returned as cascaded second-order section (SOS) IIR filters.

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

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

Examples

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.

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

legend("slope = 0.5", ...
    "slope = 0.75", ...
    "slope = 1");

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. Call setup to reduce the computational load of initialization in an audio stream loop.

frameSize = 256;

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

sampleRate = fileReader.SampleRate;

deviceWriter = audioDeviceWriter( ...
    "SampleRate",sampleRate);

setup(fileReader)
setup(deviceWriter,ones(frameSize,2))

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",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.

setup(scope,ones(frameSize,2))
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 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;

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.

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("gain = -6 dB", ...
       "gain =  6 dB", ...
       "gain = 12 dB", ...
       "Location","NorthWest")

Input Arguments

gain — Peak gain (dB)

real scalar in the range –12 to 12

Peak gain in dB, specified as a real scalar in the range –12 to 12.

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

slope — Slope coefficient

real scalar in the range 0 to 5

Slope coefficient, specified as a real scalar in the range 0 to 5.

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

Fc — Normalized cutoff frequency

real scalar in the range 0 to 1

Normalized cutoff frequency, specified as a real scalar in the range 0 to 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

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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":

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

• Set 'Orientation' 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 depends on the Orientation:

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

• If 'Orientation' 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 depends on the Orientation:

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

• If 'Orientation' 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 March 02, 2016. http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt.

Extended Capabilities

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