0.2 Harmonic detection  (Page 2/2)

To get rid of the first problem, we started using vectors that had a window of three ones around integer multiples of the candidate to allow some wiggle room for the actual location of the higher harmonics. Finally, we tried taking the logarithm of the values in the spectrum with the hope that the borders of the harmonics would stick up much farther than adjacent frequencies. If this held true to a greater extent than any other random locations in the spectrum, we could isolate the harmonics with the right type of high pass filter. In the end, we discovered each of these techniques were pretty good at finding harmonics in a certain kind of spectrum and failed miserably in other conditions. We needed something that worked all the time.

Hitting the jackpot

The algorithm that works far and away better than any others we tested relies on the principle that the DFT of a chunk, like the time domain version of the chunk itself, has non-periodic and periodic aspects. In the first half of the DFT, the only repetition comes from the evenly spaced peaks of the harmonics. Everything else, whether noise or spectrum elements resulting from a consonant, is not periodic. Therefore, we take the first half of the magnitude of our DFT as a new signal to look at. Naturally, to analyze it we take the DFT of this vector, and look at the magnitude of the result. So now we have the tongue twisting magnitude of the DFT of the magnitude of the first half of the DFT of the original signal chunk. The DFT of the DFT!

The new spectrum invariably contains a very large DC value and a lot of power on the low end of the spectrum resulting from the necessarily positive average value of a magnitude plot (remember we used the magnitude of the original DFT) along with non-periodic elements from noise or consonants. But for n greater than two or three, this new DFT goes straight to zero and stays there until it hits the only periodic element of the original DFT –the harmonics. By ignoring the first couple of values on our new spectrum, we very accurately find the first harmonic by taking the first frequency with a magnitude that is on par with the large DC value. If no such frequencies exist, we can safely assume that the chunk does not contain a vowel and does not need manipulation. This new sneaky trick (taking the DFT of the DFT) is very precise and extremely consistent, especially in the presence of noise. In fact, had we discovered this earlier, there is probably another whole project in developing this particular tool in much greater depth. It could be used to automatically detect different types of human sounds, such as separate voiced and unvoiced fricative sounds as well as the tried and true vowels. Another use would be to compute the signal to noise ratio without having access to the original signal and figuring out whether the signal chunk should even be considered worthy of processing because of the prevalence of noise.