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A pitch detection algorithm (PDA) is an algorithm designed to estimate the pitch or fundamental frequency of a quasiperiodic or virtually periodic signal, usually a digital recording of speech or a musical note or tone. This can be done in the time domain or the frequency domain. In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, will terminate in a defined end-state. ...
Pitch is the perceived fundamental frequency of a sound. ...
The fundamental tone, often referred to simply as the fundamental, is the lowest frequency in a harmonic series. ...
In mathematics, a function f is said to be quasiperiodic with quasiperiod (sometimes simply called the period) ω if for certain constants a and b, f satisfies the functional equation An example of this is the Jacobi theta function, where shows that for fixed τ it has quasiperiod τ; it also is periodic...
In mathematics, a periodic function is a function that repeats its values after some definite period has been added to its independent variable. ...
In digital recording, the analog signal of a motion-picture/sound is converted into a stream of discrete numbers, representing the changes in air pressure (chroma and luminace values in case of video) through time; thus making an abstract template for the original sound. ...
Speech processing is the study of speech signals and the processing methods of these signals. ...
Time-domain is a term used to describe the analysis of mathematical functions, or real-life signals, with respect to time. ...
Frequency domain is a term used to describe the analysis of mathematical functions with respect to frequency. ...
PDAs are used in various contexts (e.g. phonetics, music information retrieval, musical performance systems) and so there may be different demands placed upon the algorithm. There is as yet no single perfect PDA, so a variety of algorithms exist, most falling broadly into the classes given below Phonetics (from the Greek word φωνή, phone meaning sound, voice) is the study of the sounds of human speech. ...
Music information retrieval or MIR is the interdisciplinary science of retrieving information from music. ...
Time-domain approaches
In the time domain, a PDA typically estimates the period of the quasiperiodic signal, then inverts that value to give the frequency.
One simple approach would be to measure the distance between zero crossing points of the signal (i.e. the Zero Crossing Rate). However, this does not work well with complex waveforms which are composed of multiple sine waves with differing periods. Nevertheless, there are cases in which zero-crossing can be a useful measure, for example in some speech applications where a single source is assumed. The algorithm's simplicity makes it "cheap" to implement. In alternating current, the zero crossing is the instantaneous point at which there is no voltage present. ...
The zero-crossing rate is the rate of sign-changes along a signal. ...
Waveform quite literally means the shape and form of a signal, such as a wave moving across the surface of water, or the vibration of a plucked string. ...
More sophisticated approaches compare segments of the signal with other segments offset by a trial period to find a match. AMDF (average magnitude difference function), ASDF (Average Squared Difference Function), or the similar autocorrelation work this way. These algorithms can give quite accurate results for highly periodic signals. However, they have false detection problems (often "octave errors"), can sometimes cope badly with noisy signals (depending on the implementation) and - in their basic implementations - do not deal with polyphonic sounds (which involve multiple musical notes of different pitches). A plot showing 100 random numbers with a hidden sine function, and an autocorrelation of the series on the bottom. ...
Polyphony is a musical texture consisting of two or more independent melodic voices, as opposed to music with just one voice (monophony) or music with one dominant melodic voice accompanied by chords (homophony). ...
Current time-domain pitch detector algorithms tend to build upon the basic methods referred to above, with additional refinements to bring the performance more in line with a human assessment of pitch. For example, the YIN algorithm[1] and the MPM algorithm[2] are both based upon autocorrelation.
Frequency-domain approaches In the frequency domain, polyphonic detection is possible, usually utilizing the Fast Fourier Transform (FFT) to convert the signal to a frequency spectrum. This requires more processing power as the desired accuracy increases, although the well-known efficiency of the FFT algorithm makes it suitably efficient for many purposes. The Fast Fourier Transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse. ...
Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. ...
FFT may be: Fast Fourier transform Finite Fourier transform, another name for the discrete Fourier transform US Navy hull classification symbol for Reserve Training Frigates Final Fantasy Tactics, a video game. ...
Popular frequency domain algorithms include: the harmonic product spectrum; cepstral analysis and maximum likelihood which attempts to match the frequency domain characteristics to pre-defined frequency maps (useful for detecting pitch of fixed tuning instruments); and the detection of peaks due to harmonic series[3]. A cepstrum (pronounced ) is the result of taking the Fourier transform (FT) of the decibel spectrum as if it were a signal. ...
Maximum likelihood estimation (MLE) is a popular statistical method used to make inferences about parameters of the underlying probability distribution from a given data set. ...
To improve on the pitch estimate derived from the discrete Fourier spectrum, techniques such as spectral reassignment (phase based) or Grandke interpolation (magnitude based) can be used to go beyond the resolution provided by the FFT analysis.
References - ^ A. de Cheveigné and H. Kawahara. YIN, a fundamental frequency estimator for speech and music. The Journal of the Acoustical Society of America, 111:1917, 2002. DOI:10.1121/1.1458024
- ^ P. McLeod and G. Wyvill. A smarter way to find pitch. In Proceedings of the International Computer Music Conference (ICMC’05), 2005.
- ^ Mitre, Adriano; Queiroz, Marcelo; Faria, Régis. Accurate and Efficient Fundamental Frequency Determination from Precise Partial Estimates. Proceedings of the 4th AES Brazil Conference. 113-118, 2006.
A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ...
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