[Swift] Equalizing Audio Signal with vDSP.Biquad

README.md

[Swift] Equalizing Audio Signal with vDSP.Biquad

This script reads /tmp/input.wav, applies the low-pass filter, and writes the modified signal as /tmp/output.wav.

To run, open Terminal.app and hit the following command:

$ swift main.swift

Including the low-pass filter, I defined 8 filters. Enjoy DSP with Swift :D

See Also

1. Equalizing Audio with vDSP - Apple Developer
2. Cookbook formulae for audio EQ biquad filter coefficients

LICENSE

MIT

main.swift

import Accelerate
import AVFoundation

class FilterParameter {
    let b0: Double
    let b1: Double
    let b2: Double
    let a1: Double
    let a2: Double

    init(_ b0: Double, _ b1: Double, _ b2: Double, _ a1: Double, _ a2: Double) {
        self.b0 = b0
        self.b1 = b1
        self.b2 = b2
        self.a1 = a1
        self.a2 = a2
    }
}

class LowPassFilterParameter: FilterParameter {
    init(sampleRate: Double, frequency: Double, q: Double) {
        let w0: Double = 2.0 * Double.pi * frequency / sampleRate
        let alpha: Double = sin(w0) / (2.0 * q)

        let a0: Double = 1.0 + alpha
        let a1: Double = -2.0 * cos(w0)
        let a2: Double = 1.0 - alpha
        let b0: Double = (1.0 - cos(w0)) / 2.0
        let b1: Double = 1.0 - cos(w0)
        let b2: Double = (1.0 - cos(w0)) / 2.0

        super.init(b0 / a0, b1 / a0, b2 / a0, a1 / a0, a2 / a0)
    }
}

class HighPassFilterParameter: FilterParameter {
    init(sampleRate: Double, frequency: Double, q: Double) {
        let w0: Double = 2.0 * Double.pi * frequency / sampleRate
        let alpha: Double = sin(w0) / (2.0 * q)

        let a0: Double = 1.0 + alpha
        let a1: Double = -2.0 * cos(w0)
        let a2: Double = 1.0 - alpha
        let b0: Double = (1.0 + cos(w0)) / 2.0
        let b1: Double = -1.0 * (1.0 + cos(w0))
        let b2: Double = (1.0 + cos(w0)) / 2.0

        super.init(b0 / a0, b1 / a0, b2 / a0, a1 / a0, a2 / a0)
    }
}

class AllPassFilterParameter: FilterParameter {
    init(sampleRate: Double, frequency: Double, q: Double) {
        let w0: Double = 2.0 * Double.pi * frequency / sampleRate
        let alpha: Double = sin(w0) / (2.0 * q)

        let a0: Double = 1.0 + alpha
        let a1: Double = -2.0 * cos(w0)
        let a2: Double = 1.0 - alpha
        let b0: Double = 1.0 - alpha
        let b1: Double = -2.0 * cos(w0)
        let b2: Double = 1.0 + alpha

        super.init(b0 / a0, b1 / a0, b2 / a0, a1 / a0, a2 / a0)
    }
}

class BandPassFilterParameter: FilterParameter {
    init(sampleRate: Double, frequency: Double, width: Double) {
        let w0: Double = 2.0 * Double.pi * frequency / sampleRate
        let alpha: Double = sin(w0) * sinh(log(2.0) / 2.0 * width * w0 / sin(w0))

        let a0: Double = 1.0 + alpha
        let a1: Double = -2.0 * cos(w0)
        let a2: Double = 1.0 - alpha
        let b0: Double = alpha
        let b1: Double = 0.0
        let b2: Double = -1.0 * alpha

        super.init(b0 / a0, b1 / a0, b2 / a0, a1 / a0, a2 / a0)
    }
}

class BandRejectFilterParameter: FilterParameter {
    init(sampleRate: Double, frequency: Double, width: Double) {
        let w0: Double = 2.0 * Double.pi * frequency / sampleRate
        let alpha: Double = sin(w0) * sinh(log(2.0)/2.0 * width * w0 / sin(w0))

        let a0: Double = 1.0 + alpha
        let a1: Double = -2.0 * cos(w0)
        let a2: Double = 1.0 - alpha
        let b0: Double = 1.0
        let b1: Double = -2.0 * cos(w0)
        let b2: Double = 1.0

        super.init(b0 / a0, b1 / a0, b2 / a0, a1 / a0, a2 / a0)
    }
}

class LowShelfFilterParameter: FilterParameter {
    init(sampleRate: Double, frequency: Double, q: Double, gain: Double) {
        let w0: Double = 2.0 * Double.pi * frequency / sampleRate
        let a: Double = pow(10.0, (gain / 40.0))
        let beta: Double = a.squareRoot() / q

        let a0: Double = (a + 1.0) + (a - 1.0)*cos(w0) + beta * sin(w0)
        let a1: Double = -2.0 * ((a - 1.0) + (a + 1.0)*cos(w0))
        let a2: Double = (a + 1.0) + (a - 1.0)*cos(w0) - beta * sin(w0)
        let b0: Double = a * ((a + 1.0) - (a - 1.0)*cos(w0) + beta * sin(w0))
        let b1: Double = 2.0 * a * ((a - 1.0) - (a + 1.0)*cos(w0))
        let b2:Double =  a * ((a + 1.0) - (a - 1.0)*cos(w0) - beta * sin(w0))

        super.init(b0 / a0, b1 / a0, b2 / a0, a1 / a0, a2 / a0)
    }
}

class HighShelfFilterParameter: FilterParameter {
    init(sampleRate: Double, frequency: Double, q: Double, gain: Double) {
        let w0: Double = 2.0 * Double.pi * frequency / sampleRate
        let a: Double = pow(10.0, (gain / 40.0))
        let beta: Double = a.squareRoot() / q

        let a0: Double = (a + 1.0) - (a - 1.0)*cos(w0) + beta * sin(w0)
        let a1: Double = 2.0 * ((a - 1.0) - (a + 1.0)*cos(w0))
        let a2: Double = (a + 1.0) - (a - 1.0)*cos(w0) - beta * sin(w0)
        let b0: Double = a * ((a + 1.0) + (a - 1.0)*cos(w0) + beta * sin(w0))
        let b1: Double = -2.0 * a * ((a - 1.0) + (a + 1.0)*cos(w0))
        let b2: Double = a * ((a + 1.0) + (a - 1.0)*cos(w0) - beta * sin(w0))

        super.init(b0 / a0, b1 / a0, b2 / a0, a1 / a0, a2 / a0)
    }
}

class PeakingFilterParameter: FilterParameter {
    init(sampleRate: Double, frequency: Double, width: Double, gain: Double) {
        let w0: Double = 2.0 * Double.pi * frequency / sampleRate
        let alpha: Double = sin(w0) * sinh(log(2.0)/2.0 * width * w0 / sin(w0))
        let a: Double = pow(10.0, (gain / 40.0))

        let a0: Double = 1.0 + alpha / a
        let a1: Double = -2.0 * cos(w0)
        let a2: Double = 1.0 - alpha / a
        let b0: Double = 1.0 + alpha * a
        let b1: Double =  -2.0 * cos(w0)
        let b2: Double = 1.0 - alpha * a

        super.init(b0 / a0, b1 / a0, b2 / a0, a1 / a0, a2 / a0)
    }
}

func readPCMBuffer(url: URL) -> AVAudioPCMBuffer? {
    guard let input = try? AVAudioFile(forReading: url, commonFormat: .pcmFormatInt16, interleaved: false) else {
        return nil
    }
    guard let buffer = AVAudioPCMBuffer(pcmFormat: input.processingFormat, frameCapacity: AVAudioFrameCount(input.length)) else {
        return nil
    }
    do {
        try input.read(into: buffer)
    } catch {
        return nil
    }

    return buffer
}

func writePCMBuffer(url: URL, buffer: AVAudioPCMBuffer) throws {
    let settings: [String: Any] = [
        AVFormatIDKey: buffer.format.settings[AVFormatIDKey] ?? kAudioFormatLinearPCM,
        AVNumberOfChannelsKey: buffer.format.settings[AVNumberOfChannelsKey] ?? 2,
        AVSampleRateKey: buffer.format.settings[AVSampleRateKey] ?? 44100,
        AVLinearPCMBitDepthKey: buffer.format.settings[AVLinearPCMBitDepthKey] ?? 16
    ]

    do {
        let output = try AVAudioFile(forWriting: url, settings: settings, commonFormat: .pcmFormatInt16, interleaved: false)
        try output.write(from: buffer)
    } catch {
        throw error
    }
}

func applyLowPassFilter(from inputPath: String, to outputPath: String) {
    guard let inputBuffer = readPCMBuffer(url: URL(string: inputPath)!) else {
        fatalError("failed to read \(inputPath)")
    }
    guard let outputBuffer = AVAudioPCMBuffer(pcmFormat: inputBuffer.format, frameCapacity: inputBuffer.frameLength) else {
        fatalError("failed to create a buffer for writing")
    }
    guard let inputInt16ChannelData = inputBuffer.int16ChannelData else {
        fatalError("failed to obtain underlying input buffer")
    }
    guard let outputInt16ChannelData = outputBuffer.int16ChannelData else {
        fatalError("failed to obtain underlying output buffer")
    }

    // Calculate a filter coefficients.
    // 
    // Type ... Low-pass
    // Cut off frequency ... 220.0 Hz
    // Q-value ... 1.23
    let parameter = LowPassFilterParameter(sampleRate: inputBuffer.format.sampleRate, frequency: 220.0, q: 1.23)

    // Because the input might be stereo, create filters for each channels.
    var filters = [vDSP.Biquad](repeating: vDSP.Biquad(coefficients: [parameter.b0, parameter.b1, parameter.b2, parameter.a1, parameter.a2], channelCount: 1, sectionCount: 1, ofType: Float.self)!, count: Int(inputBuffer.format.channelCount))

    for channel in 0 ..< Int(inputBuffer.format.channelCount) {
        let p1: UnsafeMutablePointer<Int16> = inputInt16ChannelData[channel]
        let p2: UnsafeMutablePointer<Int16> = outputInt16ChannelData[channel]

        var signal = [Float](repeating: 0.0, count: Int(inputBuffer.frameLength))

        for i in 0 ..< Int(inputBuffer.frameLength) {
            signal[i] = Float(p1[i]) / 32767.0
        }

        signal = filters[channel].apply(input: signal)

        for i in 0 ..< Int(inputBuffer.frameLength) {
            if signal[i] < -1.0 {
                p2[i] = -32767
            } else if signal[i] > 1.0 {
                p2[i] = 32767
            } else {
                p2[i] = Int16(Int(signal[i] * 32767))
            }
        }
    }

    outputBuffer.frameLength = inputBuffer.frameLength

    do {
        try writePCMBuffer(url: URL(string: outputPath)!, buffer: outputBuffer)
    } catch {
        fatalError("failed to write \(outputPath)")
    }
}

applyLowPassFilter(from: "file:///tmp/input.wav", to: "file:///tmp/output.wav")    

Thanks so much