1. Optimized threshold selection
for GLRT algorithm
Presented By: Tal Tsror and Koby Berkovich Supervisors: Dr. Ofer Hadar and Mr. Dima Bykhovsky Ben-Gurion University of The Negev, Department of Communication System Engineering
Motivation
The story begins with joining of the writer to SHF consortium, research about separating music problem related to other researches that already performed at BGU.
The research continues to add solutions to tracking and separating the harmonic voice from the harmonic noise environment.
The reasons that led to analysis and testing of the music is: 90 percent harmonic musical singing while speaking is just 60 percent. Intensive researches about music application like voice processing, voice recognition and auto alignment of text and last reason is the amount of changes in statistics of noise.
Ella Fitzgerald – 93% harmonic
Background
Music theory is a field of study that investigates the nature or mechanics of music. It often involves identifying patterns that govern composers' techniques. In a more general sense, music theory also often distills and analyzes the elements of music – rhythm, harmony, melody, structure, and texture. People who study these properties are known as music theorists. There are arguments that mathematics can be used to analyze and understand music, and at its core, to compose the music itself.
Project Goal
Design and simulate algorithm that seek for harmonic information wave in harmonic noise environment. The algorithm identify the singer's voice and to neglect the tones of the musical instruments.
As part of the abilities proof, an activation of the simulation performed on few singing parts with instrumental companion and discovers the singer’s voice. The test is based on the hypothesis that there are a finite number of harmonic waves at the same time
The Simulated Algorithms
Our algorithm begins with preparing song by manual search for voiced parts to compare to automation algorithm. After writing the voiced parts we begin with automation by the following steps: the simulation begin with dividing the songs to segments with overlapping, contains one frequency per segment and then using them at GLRT algorithm and gets the F distribution of the song as a result, information that gives us the percentage of harmonics in the song and by that we can decide which threshold will be optimized for this song. Important note is that we measure the quality of the algorithm by voice tracking means finding best threshold and its not for sure that we will hear it better than other thresholds. We take few measures that helps us check the quality of the results, such as: PFA (Probability of false alarm), PD (Probability of detection) and PE (Error probability, a function of PFA and PD).
ROC
Error Probability
Pitch Tracking
freq
time
This is ROC graph. It presents the Pd (probability of detection) as a function of Pfa(probability of false alarm).
This graph presents the false alarm probability, detection probability and a error probability as a function of the threshold that was chosen, the blue line presents the best threshold
This graph presents the voice and its frequency that was recognized by us – the red lines, and by the simulation – the blue lines.