3 research outputs found
Evolution of classifiers for pitch estimation of piano music using cartesian genetic programming
Pitch Estimation, also known as Fundamental Frequency (F0) estimation, has been a
popular research topic for many years, and is still investigated nowadays. The goal of
Pitch Estimation is to find the pitch or fundamental frequency of a digital recording of
a speech or musical notes. It plays an important role, because it is the key to identify
which notes are being played and at what time.
Pitch Estimation of real instruments is a very hard task to address. Each instrument
has its own physical characteristics, which reflects in different spectral characteristics.
Furthermore, the recording conditions can vary from studio to studio and background
noises must be considered.
This dissertation presents a novel approach to the problem of Pitch Estimation, using
Cartesian Genetic Programming (CGP).We take advantage of evolutionary algorithms,
in particular CGP, to explore and evolve complex mathematical functions that act as
classifiers. These classifiers are used to identify piano notes pitches in an audio signal.
To help us with the codification of the problem, we built a highly flexible CGP Toolbox,
generic enough to encode different kind of programs. The encoded evolutionary
algorithm is the one known as 1 + , and we can choose the value for . The toolbox
is very simple to use. Settings such as the mutation probability, number of runs and
generations are configurable. The cartesian representation of CGP can take multiple
forms and it is able to encode function parameters. It is prepared to handle with different
type of fitness functions: minimization of f(x) and maximization of f(x) and
has a useful system of callbacks.
We trained 61 classifiers corresponding to 61 piano notes. A training set of audio signals
was used for each of the classifiers: half were signals with the same pitch as the
classifier (true positive signals) and the other half were signals with different pitches
(true negative signals). F-measure was used for the fitness function. Signals with the
same pitch of the classifier that were correctly identified by the classifier, count as a
true positives. Signals with the same pitch of the classifier that were not correctly
identified by the classifier, count as a false negatives. Signals with different pitch of the classifier that were not identified by the classifier, count as a true negatives. Signals
with different pitch of the classifier that were identified by the classifier, count as a
false positives.
Our first approach was to evolve classifiers for identifying artifical signals, created by
mathematical functions: sine, sawtooth and square waves. Our function set is basically
composed by filtering operations on vectors and by arithmetic operations with
constants and vectors. All the classifiers correctly identified true positive signals and
did not identify true negative signals. We then moved to real audio recordings.
For testing the classifiers, we picked different audio signals from the ones used during
the training phase. For a first approach, the obtained results were very promising, but
could be improved. We have made slight changes to our approach and the number of
false positives reduced 33%, compared to the first approach.
We then applied the evolved classifiers to polyphonic audio signals, and the results
indicate that our approach is a good starting point for addressing the problem of Pitch
Estimation
Extended Average Magnitude Difference Function (EAMDF) Based Pitch Detection
This paper presents a new extended average magnitude difference function for noise robust pitch detection.
Average magnitude difference function based algorithms are suitable for real time operations, but suffer from incorrect pitch
detection in noisy conditions. The proposed new extended average magnitude difference function involves in sufficient number
of averaging for all lag values compared to the original average magnitude difference function, and thereby eliminates the
falling tendency of the average magnitude difference function without emphasizing pitch harmonics at higher lags, which is a
severe limitation of other existing improvements of the average magnitude difference function. A noise robust post processing
that explores the contribution of each frequency channel is also presented. Experimental results on Keele pitch database in
different noise level, both with white and color noise, shows the superiority of the proposed extended average magnitude
difference function based pitch detection method over other methods based on average magnitude difference function