Abstract

This thesis presents a novel short-time frequency analysis algorithm, namely Instantaneous Harmonic Analysis (IHA), using a decomposition scheme based on sinusoidals. An estimate for instantaneous amplitude and phase elements of the constituent components of real-valued signals with respect to a set of reference frequencies is provided. In the context of musical audio analysis, the instantaneous amplitude is interpreted as presence of the pitch in time. The thesis examines the potential of improving the automated music analysis process by utilizing the proposed algorithm. For that reason, it targets the following two areas: Multiple Fundamental Frequency Estimation (MFFE), and note on-set/off-set detection.

The IHA algorithm uses constant-Q filtering by employing Windowed Sinc Filters (WSFs) and a novel phasor construct. An implementation of WSFs in the continuous model is used. A new relation between the Constant-Q Transform (CQT) and WSFs is presented. It is demonstrated that CQT can alternatively be implemented by applying a series of logarithmically scaled WSFs while its window function is adjusted, accordingly. The relation between the window functions is provided as well. A comparison of the proposed IHA algorithm with WSFs and CQT demonstrates that the IHA phasor construct delivers better estimates for instantaneous amplitude and phase lags of the signal components.

The thesis also extends the IHA algorithm by employing a generalized kernel function, which in nature, yields a non-orthonormal basis. The kernel function represents the timbral information and is used in the MFFE process. An effective algorithm is proposed to overcome the non-orthonormality issue of the decomposition scheme. To examine the performance improvement of the note on-set/off-set detection process, the proposed algorithm is used in the context of Automatic Music Transcription (AMT). A prototype of an audioto-MIDI system is developed and applied on synthetic and real music signals. The results of the experiments on real and synthetic music signals are reported. Additionally, a multi-dimensional generalization of the IHA algorithm is presented. The IHA phasor construct is extended into the hyper-complex space, in order to deliver the instantaneous amplitude and multiple phase elements for each dimension.