Dsp Cookbook

DSP Cookbook

Practical DSP algorithm implementations for audio plugins. Production-ready code examples with JUCE framework integration, covering filters, dynamics, modulation, delays, and common audio effects.

Table of Contents

1. Filters
2. Dynamics Processors
3. Modulation Effects
4. Delay-Based Effects
5. Saturation & Distortion
6. Parameter Smoothing
7. Utility Functions

Filters

Biquad Filter (2nd Order IIR)

Use for: EQ, lowpass, highpass, bandpass, notch filters

class BiquadFilter {
public:
    enum class Type {
        Lowpass,
        Highpass,
        Bandpass,
        Notch,
        Allpass,
        PeakingEQ,
        LowShelf,
        HighShelf
    };

    void setCoefficients(Type type, float frequency, float sampleRate,
                        float Q = 0.707f, float gainDB = 0.0f) {
        const float w0 = juce::MathConstants<float>::twoPi * frequency / sampleRate;
        const float cosw0 = std::cos(w0);
        const float sinw0 = std::sin(w0);
        const float alpha = sinw0 / (2.0f * Q);
        const float A = std::pow(10.0f, gainDB / 40.0f);  // For shelf/peak

        float b0, b1, b2, a0, a1, a2;

        switch (type) {
            case Type::Lowpass:
                b0 = (1.0f - cosw0) / 2.0f;
                b1 = 1.0f - cosw0;
                b2 = (1.0f - cosw0) / 2.0f;
                a0 = 1.0f + alpha;
                a1 = -2.0f * cosw0;
                a2 = 1.0f - alpha;
                break;

            case Type::Highpass:
                b0 = (1.0f + cosw0) / 2.0f;
                b1 = -(1.0f + cosw0);
                b2 = (1.0f + cosw0) / 2.0f;
                a0 = 1.0f + alpha;
                a1 = -2.0f * cosw0;
                a2 = 1.0f - alpha;
                break;

            case Type::Bandpass:
                b0 = alpha;
                b1 = 0.0f;
                b2 = -alpha;
                a0 = 1.0f + alpha;
                a1 = -2.0f * cosw0;
                a2 = 1.0f - alpha;
                break;

            case Type::PeakingEQ:
                b0 = 1.0f + alpha * A;
                b1 = -2.0f * cosw0;
                b2 = 1.0f - alpha * A;
                a0 = 1.0f + alpha / A;
                a1 = -2.0f * cosw0;
                a2 = 1.0f - alpha / A;
                break;

            // Add other types as needed...
        }

        // Normalize coefficients
        coeffs.b0 = b0 / a0;
        coeffs.b1 = b1 / a0;
        coeffs.b2 = b2 / a0;
        coeffs.a1 = a1 / a0;
        coeffs.a2 = a2 / a0;
    }

    float processSample(float input) {
        const float output = coeffs.b0 * input
                           + coeffs.b1 * z1
                           + coeffs.b2 * z2
                           - coeffs.a1 * y1
                           - coeffs.a2 * y2;

        // Update state
        z2 = z1;
        z1 = input;
        y2 = y1;
        y1 = output;

        return output;
    }

    void reset() {
        z1 = z2 = y1 = y2 = 0.0f;
    }

private:
    struct Coefficients {
        float b0 = 1.0f, b1 = 0.0f, b2 = 0.0f;
        float a1 = 0.0f, a2 = 0.0f;
    } coeffs;

    float z1 = 0.0f, z2 = 0.0f;  // Input delays
    float y1 = 0.0f, y2 = 0.0f;  // Output delays
};

Usage:

BiquadFilter filter;
filter.setCoefficients(BiquadFilter::Type::Lowpass, 1000.0f, 48000.0f, 0.707f);

for (int i = 0; i < buffer.getNumSamples(); ++i) {
    float input = buffer.getSample(0, i);
    float output = filter.processSample(input);
    buffer.setSample(0, i, output);
}

State Variable Filter (SVF)

Use for: Smooth parameter changes, multimode filters

class StateVariableFilter {
public:
    enum class Mode { Lowpass, Highpass, Bandpass };

    void prepare(double sampleRate) {
        this->sampleRate = sampleRate;
    }

    void setParameters(float cutoff, float resonance, Mode mode) {
        this->mode = mode;

        // Calculate coefficients (Chamberlin SVF)
        const float g = std::tan(juce::MathConstants<float>::pi * cutoff / sampleRate);
        const float k = 2.0f - 2.0f * resonance;  // resonance 0-1

        a1 = 1.0f / (1.0f + g * (g + k));
        a2 = g * a1;
        a3 = g * a2;
    }

    float processSample(float input) {
        const float v3 = input - ic2eq;
        const float v1 = a1 * ic1eq + a2 * v3;
        const float v2 = ic2eq + a2 * ic1eq + a3 * v3;

        ic1eq = 2.0f * v1 - ic1eq;
        ic2eq = 2.0f * v2 - ic2eq;

        switch (mode) {
            case Mode::Lowpass:  return v2;
            case Mode::Highpass: return input - k * v1 - v2;
            case Mode::Bandpass: return v1;
            default: return v2;
        }
    }

    void reset() {
        ic1eq = ic2eq = 0.0f;
    }

private:
    Mode mode = Mode::Lowpass;
    double sampleRate = 44100.0;
    float a1 = 0.0f, a2 = 0.0f, a3 = 0.0f;
    float ic1eq = 0.0f, ic2eq = 0.0f;  // Integrator state
};

Dynamics Processors

Compressor

Use for: Dynamics control, leveling, punchy mixes

class Compressor {
public:
    void prepare(double sampleRate) {
        this->sampleRate = sampleRate;
        envelope = 0.0f;
    }

    void setParameters(float thresholdDB, float ratio, float attackMs, float releaseMs) {
        threshold = juce::Decibels::decibelsToGain(thresholdDB);
        this->ratio = ratio;

        // Calculate time constants
        attackCoeff = std::exp(-1.0f / (attackMs * 0.001f * sampleRate));
        releaseCoeff = std::exp(-1.0f / (releaseMs * 0.001f * sampleRate));
    }

    float processSample(float input) {
        const float inputLevel = std::abs(input);

        // Envelope follower
        if (inputLevel > envelope)
            envelope = attackCoeff * envelope + (1.0f - attackCoeff) * inputLevel;
        else
            envelope = releaseCoeff * envelope + (1.0f - releaseCoeff) * inputLevel;

        // Compute gain reduction
        float gainReduction = 1.0f;
        if (envelope > threshold) {
            const float excess = envelope / threshold;
            gainReduction = std::pow(excess, 1.0f / ratio - 1.0f);
        }

        return input * gainReduction;
    }

    float getGainReductionDB() const {
        return juce::Decibels::gainToDecibels(envelope > threshold
            ? std::pow(envelope / threshold, 1.0f / ratio - 1.0f)
            : 1.0f);
    }

    void reset() {
        envelope = 0.0f;
    }

private:
    double sampleRate = 44100.0;
    float threshold = 1.0f;
    float ratio = 4.0f;
    float attackCoeff = 0.0f;
    float releaseCoeff = 0.0f;
    float envelope = 0.0f;
};

Limiter (Look-Ahead)

class Limiter {
public:
    void prepare(double sampleRate, int maxBlockSize) {
        this->sampleRate = sampleRate;

        // Look-ahead buffer (5ms typical)
        const int lookAheadSamples = static_cast<int>(0.005 * sampleRate);
        delayBuffer.setSize(2, lookAheadSamples);
        delayBuffer.clear();
        writePos = 0;
    }

    void setThreshold(float thresholdDB) {
        threshold = juce::Decibels::decibelsToGain(thresholdDB);
    }

    float processSample(float input, int channel) {
        // Write to delay buffer
        delayBuffer.setSample(channel, writePos, input);

        // Read delayed sample
        const float delayed = delayBuffer.getSample(channel, writePos);

        // Analyze future peak
        float peak = 0.0f;
        for (int i = 0; i < delayBuffer.getNumSamples(); ++i) {
            peak = std::max(peak, std::abs(delayBuffer.getSample(channel, i)));
        }

        // Calculate gain
        float gain = 1.0f;
        if (peak > threshold) {
            gain = threshold / peak;
        }

        writePos = (writePos + 1) % delayBuffer.getNumSamples();

        return delayed * gain;
    }

    void reset() {
        delayBuffer.clear();
        writePos = 0;
    }

private:
    double sampleRate = 44100.0;
    float threshold = 1.0f;
    juce::AudioBuffer<float> delayBuffer;
    int writePos = 0;
};

Modulation Effects

Chorus

class Chorus {
public:
    void prepare(double sampleRate, int maxBlockSize) {
        this->sampleRate = sampleRate;

        // Delay line (50ms max)
        const int bufferSize = static_cast<int>(0.05 * sampleRate);
        delayBuffer.setSize(2, bufferSize);
        delayBuffer.clear();
        writePos = 0;

        lfo.setSampleRate(sampleRate);
    }

    void setParameters(float rate, float depth, float mix) {
        lfo.setFrequency(rate);
        this->depth = depth;
        this->mix = mix;
    }

    float processSample(float input, int channel) {
        // Write to delay buffer
        delayBuffer.setSample(channel, writePos, input);

        // Calculate modulated delay time
        const float lfoValue = lfo.processSample();
        const float baseDelay = 0.010f * sampleRate;  // 10ms base
        const float modDelay = baseDelay + depth * 0.005f * sampleRate * lfoValue;

        // Read from delay buffer with linear interpolation
        const float readPos = writePos - modDelay;
        const float delayed = readDelayBuffer(channel, readPos);

        writePos = (writePos + 1) % delayBuffer.getNumSamples();

        // Mix dry and wet
        return input * (1.0f - mix) + delayed * mix;
    }

    void reset() {
        delayBuffer.clear();
        writePos = 0;
        lfo.reset();
    }

private:
    float readDelayBuffer(int channel, float position) {
        // Wrap position
        while (position < 0)
            position += delayBuffer.getNumSamples();

        const int pos1 = static_cast<int>(position) % delayBuffer.getNumSamples();
        const int pos2 = (pos1 + 1) % delayBuffer.getNumSamples();
        const float frac = position - std::floor(position);

        const float samp1 = delayBuffer.getSample(channel, pos1);
        const float samp2 = delayBuffer.getSample(channel, pos2);

        // Linear interpolation
        return samp1 + frac * (samp2 - samp1);
    }

    double sampleRate = 44100.0;
    float depth = 0.5f;
    float mix = 0.5f;
    juce::AudioBuffer<float> delayBuffer;
    int writePos = 0;

    // Simple LFO
    struct LFO {
        void setSampleRate(double sr) { sampleRate = sr; }
        void setFrequency(float freq) { frequency = freq; }
        float processSample() {
            const float output = std::sin(phase);
            phase += juce::MathConstants<float>::twoPi * frequency / sampleRate;
            if (phase >= juce::MathConstants<float>::twoPi)
                phase -= juce::MathConstants<float>::twoPi;
            return output;
        }
        void reset() { phase = 0.0f; }

        double sampleRate = 44100.0;
        float frequency = 1.0f;
        float phase = 0.0f;
    } lfo;
};

Delay-Based Effects

Simple Delay

class SimpleDelay {
public:
    void prepare(double sampleRate) {
        this->sampleRate = sampleRate;

        // Max delay: 2 seconds
        const int bufferSize = static_cast<int>(2.0 * sampleRate);
        delayBuffer.setSize(2, bufferSize);
        delayBuffer.clear();
        writePos = 0;
    }

    void setParameters(float delayTimeMs, float feedback, float mix) {
        delaySamples = static_cast<int>(delayTimeMs * 0.001f * sampleRate);
        this->feedback = juce::jlimit(0.0f, 0.95f, feedback);  // Prevent runaway
        this->mix = mix;
    }

    float processSample(float input, int channel) {
        // Read delayed sample
        const int readPos = (writePos - delaySamples + delayBuffer.getNumSamples())
                          % delayBuffer.getNumSamples();
        const float delayed = delayBuffer.getSample(channel, readPos);

        // Write input + feedback
        const float toWrite = input + delayed * feedback;
        delayBuffer.setSample(channel, writePos, toWrite);

        writePos = (writePos + 1) % delayBuffer.getNumSamples();

        // Mix
        return input * (1.0f - mix) + delayed * mix;
    }

    void reset() {
        delayBuffer.clear();
        writePos = 0;
    }

private:
    double sampleRate = 44100.0;
    int delaySamples = 0;
    float feedback = 0.0f;
    float mix = 0.5f;
    juce::AudioBuffer<float> delayBuffer;
    int writePos = 0;
};

Saturation & Distortion

Soft Clipper

inline float softClip(float input, float threshold = 0.7f) {
    if (std::abs(input) < threshold)
        return input;

    const float sign = input > 0.0f ? 1.0f : -1.0f;
    const float abs = std::abs(input);

    // Soft knee above threshold
    return sign * (threshold + (1.0f - threshold) * std::tanh((abs - threshold) / (1.0f - threshold)));
}

Waveshaper (Polynomial)

inline float waveshape(float input, float drive) {
    const float x = input * drive;

    // Cubic waveshaping: y = x - (x^3)/3
    return x - (x * x * x) / 3.0f;
}

Tube-Style Saturation

inline float tubeSaturation(float input, float drive) {
    const float x = input * drive;

    // Hyperbolic tangent - smooth saturation
    return std::tanh(x) / drive;
}

Parameter Smoothing

Linear Smoother

class ParameterSmoother {
public:
    void reset(double sampleRate, double rampTimeSeconds) {
        this->sampleRate = sampleRate;
        rampSamples = static_cast<int>(rampTimeSeconds * sampleRate);
        currentSample = rampSamples;
    }

    void setTargetValue(float target) {
        if (target != targetValue) {
            startValue = currentValue;
            targetValue = target;
            currentSample = 0;
        }
    }

    float getNextValue() {
        if (currentSample >= rampSamples)
            return targetValue;

        const float alpha = static_cast<float>(currentSample) / rampSamples;
        currentValue = startValue + alpha * (targetValue - startValue);
        ++currentSample;

        return currentValue;
    }

private:
    double sampleRate = 44100.0;
    int rampSamples = 0;
    int currentSample = 0;
    float startValue = 0.0f;
    float targetValue = 0.0f;
    float currentValue = 0.0f;
};

Exponential Smoother (One-Pole)

class ExponentialSmoother {
public:
    void reset(double sampleRate, double timeConstantSeconds) {
        coeff = std::exp(-1.0 / (timeConstantSeconds * sampleRate));
        currentValue = 0.0f;
    }

    void setTargetValue(float target) {
        targetValue = target;
    }

    float getNextValue() {
        currentValue = coeff * currentValue + (1.0f - coeff) * targetValue;
        return currentValue;
    }

private:
    float coeff = 0.0f;
    float targetValue = 0.0f;
    float currentValue = 0.0f;
};

Utility Functions

Decibel Conversion

inline float dBToGain(float dB) {
    return std::pow(10.0f, dB / 20.0f);
}

inline float gainToDB(float gain) {
    return 20.0f * std::log10(gain);
}

Frequency to MIDI Note

inline float frequencyToMIDI(float frequency) {
    return 69.0f + 12.0f * std::log2(frequency / 440.0f);
}

inline float midiToFrequency(float midiNote) {
    return 440.0f * std::pow(2.0f, (midiNote - 69.0f) / 12.0f);
}

Denormal Prevention

inline float preventDenormal(float value) {
    static constexpr float denormalFix = 1.0e-20f;
    return value + denormalFix;
}

// Or use JUCE's built-in
juce::FloatVectorOperations::disableDenormalisedNumberSupport();

Peak Meter (with ballistics)

class PeakMeter {
public:
    void prepare(double sampleRate) {
        // Attack: instantaneous
        // Release: 300ms typical
        releaseCoeff = std::exp(-1.0 / (0.3 * sampleRate));
        peak = 0.0f;
    }

    float processSample(float input) {
        const float absInput = std::abs(input);

        if (absInput > peak) {
            peak = absInput;  // Attack
        } else {
            peak = releaseCoeff * peak + (1.0f - releaseCoeff) * absInput;  // Release
        }

        return peak;
    }

    float getPeakDB() const {
        return juce::Decibels::gainToDecibels(peak);
    }

    void reset() {
        peak = 0.0f;
    }

private:
    float releaseCoeff = 0.0f;
    float peak = 0.0f;
};

Integration with JUCE

Using in AudioProcessor

class MyPluginProcessor : public juce::AudioProcessor {
public:
    void prepareToPlay(double sampleRate, int samplesPerBlock) override {
        filter.prepare(sampleRate);
        filter.setParameters(1000.0f, 0.707f, StateVariableFilter::Mode::Lowpass);

        compressor.prepare(sampleRate);
        compressor.setParameters(-20.0f, 4.0f, 10.0f, 100.0f);
    }

    void processBlock(juce::AudioBuffer<float>& buffer, juce::MidiBuffer&) override {
        for (int channel = 0; channel < buffer.getNumChannels(); ++channel) {
            auto* data = buffer.getWritePointer(channel);

            for (int sample = 0; sample < buffer.getNumSamples(); ++sample) {
                // Apply filter
                data[sample] = filter.processSample(data[sample]);

                // Apply compression
                data[sample] = compressor.processSample(data[sample]);
            }
        }
    }

private:
    StateVariableFilter filter;
    Compressor compressor;
};

References

• Audio EQ Cookbook: /docs/dsp-resources/audio-eq-cookbook.html
• Julius O. Smith DSP Books: /docs/dsp-resources/julius-smith-dsp-books.md
• DAFX Book: /docs/dsp-resources/dafx-reference.md
• Cytomic Filters: /docs/dsp-resources/cytomic-filter-designs.md

Note: All code examples are production-ready and follow realtime-safety rules. Pre-allocate buffers in prepare(), avoid allocations in processSample(), and use proper numerical stability techniques.