Autospectrum computation with vDSP_zaspec doesn't work

Question

I try to compute the autospectrum of a recorded signal, I use the function vDSP_zaspec. Normally the output array is real.

class  func autoSpectrum (input: [Float])->[Float] {
        
        var real = [Float](input)
        var imaginary = [Float](repeating: 0.0, count : input.count)
        var Output:[Float] = [Float](repeating:0 , count: input.count)
        let length = vDSP_Length(real.count/2)
   
        real.withUnsafeMutableBufferPointer {realBP in
                   imaginary.withUnsafeMutableBufferPointer {imaginaryBP in
                      
                       var splitComplex = DSPSplitComplex(realp: realBP.baseAddress!, imagp: imaginaryBP.baseAddress!)
                       vDSP_zaspec(&splitComplex, &Output, vDSP_Length(input.count))
                    
                   }
               }
    let value = vDSP.rootMeanSquare(Output)
   Output = vDSP.divide(Output, value)

        return Output
    }

I did a test with a 500 Hz sin wave and this is what the Output array looks like :

The chart is far from the expected result...The result looks like the absolute value of the recorded audio file...

If someone could help me, it will be great !

Answer 1

vDSP_zaspec returns the sum of each real part squared and the corresponding imaginary part squared. The Apple documentation describes it as "Compute the element-wise sum of the squares of the real and imaginary parts of a complex vector".

The following pieces of code calculate the same results:

var real: [Float] = [-2, 7, -3]
var imaginary: [Float] = [4, -1, -4]

var vDSPresult: [Float] = [0, 0, 0]
var scalarResult: [Float] = [0, 0, 0]

real.withUnsafeMutableBufferPointer {realBP in
    imaginary.withUnsafeMutableBufferPointer {imaginaryBP in
        var splitComplex = DSPSplitComplex(realp: realBP.baseAddress!,
                                           imagp: imaginaryBP.baseAddress!)
        vDSP_zaspec(&splitComplex,
                    &vDSPresult,
                    vDSP_Length(vDSPresult.count))
        
    }
}

print(vDSPresult)

for i in 0 ..< scalarResult.count {
    scalarResult[i] = pow(real[i], 2) + pow(imaginary[i], 2)
}

print(scalarResult)