# Pitch extraction using Euclid's algorithm implemented through sinewave crossings or iterative demodulation

#### Abstract

Pitch is a key element in organizing the surrounding sound environment. Understanding how the human brain detects pitch will increase general understanding of the human auditory and neurological systems. In this research, new methods of pitch detection thought to be similar to the one used by humans are presented. Pitch is the perception of fundamental frequency (F0) of a sound and is based on the periodicity of sound waves. The new methods of pitch detection presented are computationally simple and do not require the storage of past data in correspondence with the human ability to calculate pitch nearly instantaneously. Voiced speech sounds have multiple frequency components consisting of F0 plus several harmonics occurring at integer multiples of the F0. The fundamental frequency, and thus the pitch, can therefore be calculated by finding the greatest common divisor (GCD) of harmonic frequencies. Euclid's iterative subtraction algorithm is a simple method of calculating the GCD by iteratively subtracting and comparing two integers until two equal integers that are also equal to the GCD are reached. This technique can be implemented to determine F0 from two harmonics by iteratively achieving frequency differences and comparing frequency components present. The new pitch detection algorithms begin by separating harmonics with a cochlea-like Gammatone filterbank, and then obtaining a frequency difference via demodulation and low-pass filtering, demodulation with complex signals, or the use of time intervals between points at which equal-amplitude sinewaves coincide. Demodulation of two real signals produces the superposition of frequency difference and frequency sum components. A lowpass filter is utilized to remove the frequency sum component. When demodulating with complex signals, a frequency difference can be achieved without a lowpass filter by simply multiplying one harmonic with the complex conjugate of a second harmonic. The sinewave coincidence method makes use of the fact that the time intervals between equal-amplitude harmonically-related sinusoid intersections are equal to the reciprocal of their frequency difference. These processes are repeated until F0, and thus the pitch, is reached. Matlab simulations of all three methods demonstrate their performance on synthetically-generated sounds and on recorded speech sentences. The demodulation/LPF and sinewave coincidence methods prove to be successful pitch detection methods while demodulation with complex signals are able to produce a general estimate of F0, but are unable to detect rapid frequency changes.

#### Subject Area

Electrical engineering

#### Recommended Citation

Adrienne Mundorf,
"Pitch extraction using Euclid's algorithm implemented through sinewave crossings or iterative demodulation"
(2011).
*Dissertations and Master's Theses (Campus Access).*
Paper AAI1497506.

https://digitalcommons.uri.edu/dissertations/AAI1497506