（Swift）vDSPでイコライザを実装する

はじめに

vDSPは数値計算やデジタル信号処理を高速に行うためのライブラリです。Xcodeに同梱されているため、すぐに利用できます。

vDSPには双二次フィルタ（vDSP.Biquad）が含まれています。iOS 14から利用できるようになったので試してみましょう。

実装例

以下に実装例を示します。/tmp/input.wavを読み込み、ローパスフィルタ（カットオフ周波数 220 Hz / Q値 1.23）を適用した結果を/tmp/output.wavとして書き込む処理です。

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 = 440 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")

上記の内容をmain.swiftとして保存し、以下のように実行します。

$ swift main.swift

実装例にはローパスフィルタを含め、合計8種類のフィルタを定義しました。パラメータをいじって遊んでみてください。

実装の注意点

注意というほどではありませんが、vDSP.Biquadに渡す係数は6個ではなく5個です。a0が1に正規化されています。

参考文献

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