How do I know if an array represents sine wave?

Question

I'm working with accelerometer and collecting data for past few seconds. The motion I want to detect can be represented as sine wave in terms of values I'm getting from motion sensor. So to make it sure, I want a way to check if the data returned from sensor do represents a sine wave.

What I want to avoid is to manually compare each value in array and draw a decision.

I'm wondering if there's an efficient way which could tell if my array represents a sine wave or not.

Answer 1

As commentator @NeilForrester points out, FFTs are the way to do this. Writing your own efficient FFT is not easy, but the Accelerate framework's vDSP routines provide a straight-forward way to do it if you are using Objective-C - not so straightforward in Swift, due to the use of UnsafePointer and UnsafeMutablePointer parameters. Here's a simple Swift example of using the FFT.

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, 1, &magnitudesSquared, 1, vDSP_Length(self.halfSize))
        vvsqrtf(&magnitudes, &magnitudesSquared, [Int32(self.halfSize)])

        vDSP_zvphas(&splitComplex, 1, &phases, 1, vDSP_Length(self.halfSize))

        vDSP_vsmul(&magnitudes, 1, self.twoOverSize, &normalizedMagnitudes, 1, 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})
}

Playground output:

As to what you test, it will depend on the actual outputs you get, so I would experiment with what the actual data gives you, but your test should be something like :

• find the mean of the amplitudes
• find the maximum amplitude
• check that the ratio of the two (max / mean) is high
• check that the index of the maximum isn't near zero (or it's likely a DC signal)
• check that any other local maxima (and there will be some) are much smaller than the global maximum.