# What's wrong with this Average Magnitude Difference algorithm?

I implemented this Average Magnitude Difference algorithm in Javascript

var abs = Math.abs
var floor = Math.floor
var POSITIVE_INFINITY = Number.POSITIVE_INFINITY
function autocorrelation (data) {
var length = data.length
var halfLength = floor(length * 0.5)
var summation = null
var smallest = POSITIVE_INFINITY
var smallestOffset = null
for (var o = 1; o < halfLength; o++) {
summation = 0
for (var i = 0; i < halfLength; i++) {
summation += abs(data[i] - data[i + o])
}
average = summation / halfLength
if (average < smallest) {
smallest = average
smallestOffset = o
}
}
return smallestOffset
}


and I use it this way

analyser.getFloatTimeDomainData(data)
var rms = rootMeanSquare(data)
var offset, frequency
if (rms > RMS_MIN) {
offset = autocorrelation(data)
frequency = SAMPLE_RATE / offset
}


to find the frequency of the signal input to the analyser.

Signal input is the output from an oscillator. The oscillator's frequency varies from C0 to B8 and I can't always detect the correct frequency. Can you tell me why, please?

Please, find below two images showing oscillator's frequencies and related detected frequencies

• i didn't vote to close. i wish Adriano might use $\LaTeX$ to express the autocorrelation algorithm in terms of nice, clean generic math. i know C but not Java anything. Jan 12 '17 at 5:22
• This is definitely not the auto-correlation, you might want to check the limits over which you are carrying out the operation and sign at $i+o$.
– A_A
Jan 12 '17 at 12:50

you appear to be implementing the AMDF correctly but you are suffering from the so-called "octave error" problem. you see, a note that is, say, A-440, has a fundamental frequency of 440 Hz. that means the waveform repeats every $\tfrac{1}{440}$-th second. but that same waveform also repeats every $\tfrac{1}{220}$-th second and every $\tfrac{1}{110}$-th second or every $\tfrac{1}{55}$-th second. so, mathematically, it can be construed to be a 220 Hz or 110 Hz or 55 Hz (or even a $\tfrac{3}{440}$-th second period or $\tfrac{440}{3}$ Hz waveform).