### Abstract

Language | English |
---|---|

Title of host publication | 15th International Conference on Systems, Signals and Image Processing, 2008 |

Publisher | IEEE |

Pages | 229-232 |

Number of pages | 3 |

ISBN (Print) | 978-80-227-2856-0 |

DOIs | |

Publication status | Published - Jun 2008 |

### Fingerprint

### Keywords

- Hilbert transforms
- acoustic signal processing
- audio signal processing
- musical acoustics
- signal representation
- spectral analysis
- Hilbert spectrum calculation
- data dependant AM-FM basis function
- empirical mode decomposition
- instantaneous amplitude
- instantaneous frequency
- intrinsic mode function
- model parameter manipulation
- musical audio synthesis
- musical sound analysis

### Cite this

*15th International Conference on Systems, Signals and Image Processing, 2008*(pp. 229-232). IEEE. https://doi.org/10.1109/IWSSIP.2008.4604409

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*15th International Conference on Systems, Signals and Image Processing, 2008.*IEEE, pp. 229-232. https://doi.org/10.1109/IWSSIP.2008.4604409

**Modelling I.M.F's produced by E.M.D for musical audio for synthesis and manipulation.** / Fulton, Michael; Soraghan, J.J.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Modelling I.M.F's produced by E.M.D for musical audio for synthesis and manipulation

AU - Fulton, Michael

AU - Soraghan, J.J.

PY - 2008/6

Y1 - 2008/6

N2 - This paper describes a process with which to analyse musical sounds by first applying empirical mode decomposition to find a set of data dependant AM-FM basis functions. These basis functions are such that they facilitate Hilbert Spectrum calculation, which describes the signal in terms of its instantaneous amplitude and phase, and hence instantaneous frequency. The IF and IA are then modelled, which allows for representation of the IMFs analytically. This provides a greater insight into the content the basis functions, as EMD is only defined by its algorithm and has no mathematical proof, as yet. Secondly, this modelling allows for the interpretation of the Hilbert Spectrum for musical audio as well as providing a novel representation of the signal as a sum of AM-FM basis functions. This technique is validated by applying the modelling of the IMFs produced for a piano note. Manipulation of the model parameters of the IA and IF of IMFs can be exploited to change the signal content and project the modelled data beyond the given input samples. Details of this procedure are contained in this paper as is an example of this process being applied to synthesise multiple notes of differing pitch and duration from a very small segment of an instrument sound.

AB - This paper describes a process with which to analyse musical sounds by first applying empirical mode decomposition to find a set of data dependant AM-FM basis functions. These basis functions are such that they facilitate Hilbert Spectrum calculation, which describes the signal in terms of its instantaneous amplitude and phase, and hence instantaneous frequency. The IF and IA are then modelled, which allows for representation of the IMFs analytically. This provides a greater insight into the content the basis functions, as EMD is only defined by its algorithm and has no mathematical proof, as yet. Secondly, this modelling allows for the interpretation of the Hilbert Spectrum for musical audio as well as providing a novel representation of the signal as a sum of AM-FM basis functions. This technique is validated by applying the modelling of the IMFs produced for a piano note. Manipulation of the model parameters of the IA and IF of IMFs can be exploited to change the signal content and project the modelled data beyond the given input samples. Details of this procedure are contained in this paper as is an example of this process being applied to synthesise multiple notes of differing pitch and duration from a very small segment of an instrument sound.

KW - Hilbert transforms

KW - acoustic signal processing

KW - audio signal processing

KW - musical acoustics

KW - signal representation

KW - spectral analysis

KW - Hilbert spectrum calculation

KW - data dependant AM-FM basis function

KW - empirical mode decomposition

KW - instantaneous amplitude

KW - instantaneous frequency

KW - intrinsic mode function

KW - model parameter manipulation

KW - musical audio synthesis

KW - musical sound analysis

UR - http://dx.doi.org/10.1109/IWSSIP.2008.4604409

U2 - 10.1109/IWSSIP.2008.4604409

DO - 10.1109/IWSSIP.2008.4604409

M3 - Chapter

SN - 978-80-227-2856-0

SP - 229

EP - 232

BT - 15th International Conference on Systems, Signals and Image Processing, 2008

PB - IEEE

ER -