数组 – 如何知道数组是否代表正弦波？

正如评论员@NeilForrester所指出的那样,FFTs就是这样做的.编写自己的高效FFT并不容易,但是如果使用Objective-C,Accelerate框架的 vDSP routines提供了一种直接的方法 – 由于使用了UnsafePointer和UnsafeMutablePointer参数,因此在Swift中并不那么简单.这是一个使用FFT的简单Swift示例.

import Foundation
import Accelerate

public struct GFFT {
    let size: Int
    let halfSize: Int
    let log2n: vDSP_Length
    let twoOverSize: [Float]
    var weights: FFTSetup

    init?(size: Int) {
        self.size = size
        self.log2n = vDSP_Length(log2(Float(size)))
        guard let weights = vDSP_create_fftsetup(log2n,FFTRadix(kFFTRadix2)) else {
            print("Aargh in GFFT.fft - weights failed")
            return nil
        }
        self.halfSize = size / 2
        self.twoOverSize = [2 / Float(size)]
        self.weights = weights
    }

    public func forward(realArray: [Float]) -> (magnitude: [Float],phase: [Float]) {
        assert(realArray.count == self.size,"Aargh in GFFT.forward - size mismatch")
        var real = realArray // copy into var
        var imag = GFFT.zeros(size)
        var magnitudesSquared = GFFT.zeros(self.halfSize)
        var magnitudes = GFFT.zeros(self.halfSize)
        var normalizedMagnitudes = GFFT.zeros(self.halfSize)
        var phases = GFFT.zeros(self.halfSize)

        var splitComplex = DSPSplitComplex(realp: &real,imagp: &imag)

        vDSP_fft_zip(self.weights,&splitComplex,1,self.log2n,FFTDirection(FFT_FORWARD))

        vDSP_zvmags(&splitComplex,&magnitudesSquared,vDSP_Length(self.halfSize))
        vvsqrtf(&magnitudes,[Int32(self.halfSize)])

        vDSP_zvphas(&splitComplex,&phases,vDSP_Length(self.halfSize))

        vDSP_vsmul(&magnitudes,self.twoOverSize,&normalizedMagnitudes,vDSP_Length(self.halfSize))

        // you may choose to return magnitudesSquared,for the power
        // magnitudes for the scaled amplitudes or 
        // normalizedMagnitudes for,well,normalised magnitude.
        return (normalizedMagnitudes,phases)
    }
    private static func zeros(_ n: Int) -> [Float] { return [Float](repeating: 0,count: n) }
}

let testInput = (0 ..< 512).map {
    return sin(Float($0))
}
if let fft = GFFT(size: testInput.count) {
    let (freq,phase) = fft.forward(realArray: testInput)
    freq.map({$0})
}

游乐场输出：

至于你测试什么,它将取决于你得到的实际输出,所以我会试验实际数据给你的东西,但你的测试应该是这样的：

>找到振幅的平均值>找到最大振幅>检查两者的比率(最大值/平均值)是否高>检查最大值的索引是否接近零(或者它可能是直流信号)>检查任何其他局部最大值(并且会有一些)远小于全局最大值.