DadDSP::cBiQuad

Namespace : DadDSP::cBiQuad
Files : BiquadFilter.h / BiquadFilter.cpp
Directory : DAD_FORGE/DSP
Description : Versatile biquad filter class implementing Cookbook formulas for audio EQ filter coefficients, supporting 10 filter types (LPF, HPF, BPF, Notch, PEQ, Shelf, All-pass) with stereo processing and 24dB option.

📋 Class Description

The cBiQuad class is a biquad digital filter implementation used for real-time audio processing. It implements the coefficients formulas by Robert Bristow-Johnson (Cookbook formulae), allowing precise control over frequency responses. The class supports:

  • 10 filter types : Low Pass Filter (LPF), High Pass Filter (HPF), Band Pass Filter (BPF), Notch Filter, Parametric Equalizer (PEQ), and low/high Shelf filters (LSH/HSH) with 24dB variants
  • Stereo Processing : Native management of left/right channels with separate filter states
  • 24dB Option : Cascade of two biquad stages for steep slope filters
  • Normalized Calculations : Precalculated coefficients for optimized processing

Tip
To help configure and visualize filters, you can use the Python utility:

cd "....../DAD_FORGE/@Python Utilities/BiQuad Visu/"
uv run biquad.py

This tool displays the filter frequency response according to the selected parameters. —

🎯 Associated Enumerations and Structures

FilterType

Element Value Description
LPF 0 Low Pass Filter
LPF24 1 24 dB/octave Low Pass Filter
HPF 2 High Pass Filter
HPF24 3 24 dB/octave High Pass Filter
BPF 4 Band Pass Filter
NOTCH 5 Notch Filter
PEQ 6 Parametric Equalizer (Peaking EQ)
LSH 7 Low Shelf Filter
HSH 8 High Shelf Filter
AFP 9 All-Pass Filter

sFilterState

Element / Variable Type Description
x1 float Previous input sample x[n-1]
x2 float Earlier input sample x[n-2]
y1 float Previous output sample y[n-1]
y2 float Earlier output sample y[n-2]

Method: Reset() - Resets all states to zero.

eChannel

Element Value Description
Left 0 Left audio channel
Right 1 Right audio channel

📚 Public Methods

Initialize

Element Details
Method void Initialize(float sampleRate, float cutoffFreq, float gainDb, float bandwidth, FilterType type)
Description Initializes the filter with configuration parameters: sampling frequency, cutoff frequency, gain in decibels, bandwidth, and filter type. Automatically calculates filter coefficients.
Parameter(s)  
sampleRate Sampling rate in Hz (e.g., 44100.0f for CD audio)
cutoffFreq Cutoff frequency in Hz where the response reaches -3dB
gainDb Gain applied to the filter in decibels (positive = boost, negative = cut)
bandwidth Filter bandwidth (wider = faster transition)
type Type of filter to use (LPF, HPF, BPF, Notch, PEQ, LSH, HSH, AFP, LPF24, HPF24)

CalculateParameters

Element Details
Method void CalculateParameters()
Description Recalculates the filter coefficients based on current parameters (cutoff frequency, gain, bandwidth, and type). Uses Robert Bristow-Johnson’s Cookbook formulas. Coefficients are normalized for optimized processing. Executes a memory barrier (DMB) to ensure data consistency in multi-threaded environments.

GainDb

Element Details
Method float GainDb(float freq)
Description Calculates the filter gain in decibels at a given frequency. Allows for analyzing the frequency response without sample processing.
Parameter(s)  
freq Analysis frequency in Hz (0 to sampleRate/2)
Return Filter gain at the specified frequency, expressed in decibels (dB)

ProcessFlast12dbStereo

Element Details
Method inline void ProcessFlast12dbStereo(AudioBuffer* pIn, AudioBuffer* pOut)
Description Fast stereo processing for 12dB/octave filters. Applies the filter to the left and right channels separately without additional stage cascading. Optimized for real-time processing with minimal CPU overhead.
Parameter(s)  
pIn Pointer to the input audio buffer containing unfiltered samples
pOut Pointer to the output audio buffer where filtered samples will be stored

Process

Element Details
Method inline float Process(float sample, eChannel Channel = eChannel::Left)
Description Processes a single audio sample through the filter. For 24dB filters (LPF24, HPF24), it cascades two biquad stages: the first stage for the steep transition, and the second stage as the main stage. Supports mono or stereo processing via the Channel parameter.
Parameter(s)  
sample Input audio sample (normalized amplitude)
Channel Processing channel: Left for left channel, Right for right channel (default: Left)
Return Filtered output audio sample

setSampleRate

Element Details
Method inline void setSampleRate(float sampleRate)
Description Sets the sampling frequency of the audio system. Updates the inverse sampling rate for frequency calculations.
Parameter(s)  
sampleRate Sampling frequency in Hz

setCutoffFreq

Element Details
Method inline void setCutoffFreq(float cutoffFreq)
Description Sets the filter’s cutoff frequency. The frequency at which the response reaches -3dB relative to the nominal gain.
Parameter(s)  
cutoffFreq Cutoff frequency in Hz

setGainDb

Element Details
Method inline void setGainDb(float gainDb)
Description Sets the filter’s gain in decibels. Positive values increase amplitude (boost), negative values reduce amplitude (cut).
Parameter(s)  
gainDb Gain in decibels (e.g., +6.0f for 6dB boost, -12.0f for 12dB cut)

setBandwidth

Element Details
Method inline void setBandwidth(float bandwidth)
Description Sets the filter’s bandwidth. Controls the transition slope around the cutoff frequency. Wider = sharper transition.
Parameter(s)  
bandwidth Normalized bandwidth (typically 0.01 to 1.0)

setType

Element Details
Method inline void setType(FilterType type)
Description Sets the filter type to be used. Determines the coefficient formulas applied during parameter calculation.
Parameter(s)  
type Filter type (LPF, HPF, BPF, Notch, PEQ, LSH, HSH, AFP, LPF24, HPF24)

getSampleRate

Element Details
Method inline float getSampleRate()
Description Retrieves the configured sampling frequency of the audio system.
Return Sampling frequency in Hz

getCutoffFreq

Element Details
Method inline float getCutoffFreq()
Description Retrieves the current cutoff frequency of the filter.
Return Cutoff frequency in Hz

getGainDb

Element Details
Method inline float getGainDb()
Description Retrieves the current gain of the filter in decibels.
Return Gain in decibels (dB)

getBandwidth

Element Details
Method inline float getBandwidth()
Description Retrieves the current bandwidth of the filter.
Return Normalized bandwidth

getType

Element Details
Method inline FilterType getType()
Description Retrieves the currently configured filter type.
Return Current filter type (FilterType)

Process

Element Details
Method inline float Process(float sample, sFilterState &FilterState)
Description Direct mono sample processing using the biquad difference equation: y[n] = b0x[n] + b1x[n-1] + b2x[n-2] - a1y[n-1] - a2*y[n-2]. Automatically updates the delay state for the next iteration.
Parameter(s)  
sample Input audio sample (normalized amplitude)
FilterState Reference to the filter state containing lag values x1, x2, y1, y2
Return Filtered output audio sample

🔒 Protected / Private Methods

No protected or private methods.

📦 Data Members (Variables)

Public Variables

No public variables.

Protected / Private Variables

Member Type Description
m_InvSampleRate float Inverse sampling rate (1/sampleRate) in seconds
m_cutoffFreq float Cutoff frequency in Hz
m_gainDb float Filter gain in decibels
m_bandwidth float Normalized bandwidth parameter
m_type FilterType Configured filter type
m_a0 volatile float Normalized numerator coefficient b0
m_a1 volatile float Normalized numerator coefficient b1
m_a2 volatile float Normalized numerator coefficient b2
m_a3 volatile float Normalized denominator coefficient a1
m_a4 volatile float Normalized denominator coefficient a2
m_FilterState[0] sFilterState Filter state: Stage 1 left channel
m_FilterState[1] sFilterState Filter state: Stage 2 left channel (main)
m_FilterState[2] sFilterState Filter state: Stage 1 right channel
m_FilterState[3] sFilterState Filter state: Stage 2 right channel (main)

💡 Usage Example 

// Insert code example here
#include "DadDSP.h"

using namespace DadDSP;

int main() {
    // Configuration audio
    const float SAMPLE_RATE = 44100.0f;
    
    // Creation and initialization of a Parametric EQ bandpass filter
    cBiQuad filter;
    filter.Initialize(SAMPLE_RATE, 1000.0f, 3.0f, 1.0f, FilterType::PEQ);
    
    // Dynamic configuration - real-time adjustment
    filter.setCutoffFreq(500.0f);      // Change cutoff frequency
    filter.setGainDb(-6.0f);           // 6dB cut
    filter.setBandwidth(0.5f);         // Moderate bandwidth
    filter.CalculateParameters();      // Recalculates the filter coefficients based on current parameters
    
    // Frequency response analysis
    float gainAt100Hz = filter.GainDb(100.0f);
    float gainAt1000Hz = filter.GainDb(1000.0f);
    
    // Mono sample processing
    sFilterState state;
    state.Reset();
    for (int i = 0; i < numSamples; i++) {
        float inputSample = audioInput[i];
        float outputSample = filter.Process(inputSample, state);
        audioOutput[i] = outputSample;
    }
    
    // Fast stereo processing (12dB/octave)
    cBiQuad stereoFilter;
    stereoFilter.Initialize(SAMPLE_RATE, 2000.0f, 0.0f, 0.1f, FilterType::LPF);
    
    AudioBuffer* pIn = &inputBuffer;
    AudioBuffer* pOut = &outputBuffer;
    stereoFilter.ProcessFlast12dbStereo(pIn, pOut);
    
    // Full stereo processing (24dB/octave)
    cBiQuad highPassFilter;
    highPassFilter.Initialize(SAMPLE_RATE, 30.0f, 0.0f, 1.0f, FilterType::HPF24);
    
    for (int i = 0; i < numSamples; i++) {
        float leftInput = pIn->Left[i];
        float rightInput = pIn->Right[i];
        
        float leftOutput = highPassFilter.Process(leftInput, eChannel::Left);
        float rightOutput = highPassFilter.Process(rightInput, eChannel::Right);
        
        pOut->Left[i] = leftOutput;
        pOut->Right[i] = rightOutput;
    }
    
    return 0;
}

DAD_FORGE/DSP - Dad Design DSP Library
Copyright (c) 2024-2026 Dad Design.

This site uses Just the Docs, a documentation theme for Jekyll.