Abstract
Fractional linear prediction (FLP), as a generalization of conventional linear prediction (LP), was recently successfully applied in different fields of research and engineering, such as biomedical signal processing, speech modeling and image processing. The FLP model has a similar design as the conventional LP model, i.e., it uses a linear combination of “fractional terms” with different orders of fractional derivative. Assuming only one “fractional term” and using limited number of previous samples for prediction, FLP model with “restricted memory” is presented in this paper and the closed-form expressions for calculation of FLP coefficients are derived. This FLP model is fully comparable with the widely used low-order LP, as it uses the same number of previous samples, but less predictor coefficients, making it more efficient. Two different datasets, MIDI Aligned Piano Sounds (MAPS) and Orchset, were used for the experiments. Triads representing the chords composed of three randomly chosen notes and usual Western musical chords (both of them from MAPS dataset) served as the test signals, while the piano recordings from MAPS dataset and orchestra recordings from the Orchset dataset served as the musical signal. The results show enhancement of FLP over LP in terms of model complexity, whereas the performance is comparable.
Highlights
The sinusoidal model is widely used for representation of pseudo-stationary signals, especially in audio coding [1] and musical signal processing [2]
We present Fractional linear prediction (FLP) with memory restricted to maximum of four previous samples and apply it to prediction of randomly generated test chords, usual chords in Western music and piano parts extracted from the MIDI Aligned Piano Sounds dataset; and musical parts extracted from symphonies, ballets and other classical musical forms, and interpreted by symphonic orchestras, from the Orchset dataset
Experiments were performed using two test signals: the three-note chords composed of randomly chosen notes (MAPS–RAND subset), usual three-notes Western musical chords (MAPS–usual chords in Western music (UCHO) subset), and two musical signals: piano recordings (MAPS–music pieces (MUS) subset) and orchestra recordings (Orchset)
Summary
The sinusoidal model is widely used for representation of pseudo-stationary signals, especially in audio coding [1] and musical signal processing [2]. Parameters of the sinusoidal model are determined frame-wise from the input audio/musical signal, and a sound is synthesized using the extracted parameters [3]. A pure tone can be represented as a single sine wave, whereas the musical chords are produced by combining three or more sine waves with different frequencies. Any musical tone can be described as a combination of sine waves or its partials, each with its own amplitude, phase and frequency of vibration [4]. A sine wave can be fully described using three parameters: amplitude, phase and frequency Such signal is redundant; there is no need to encode and transmit each signal sample
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