Estimating Frequency and Amplitude of Sinusoids in Harmonic Signals

Diploma Thesis (Acrobat Reader 2.652KB)

Additive synthesis is a meaningful sound model for analysis and processing of sound that represents a signal as a sum of individually controllable sinusoids. The accuracy of twelve frame-based parameter estimators which determine frequency and amplitude of the partials in harmonic sounds are tested with sinusoidal, static, time-varying and natural-like test sounds. The estimation errors are determined by the known frequency content of the test signals and the output of the estimators. The errors are smallest for the method proposed here which directly fits the analytical shape of the window main lobe into the frequency spectrum. Among the commonly known estimators, derivative algorithm, phase vocoder and spectrum reassignment give the best numerical results. The Matlab implementation provides a platform to evaluate new approaches for frame-based parameter estimators and readily shows the effectiveness compared to the standard algorithms.

Parameter estimation directly from MDCT coefficients has limitations and further research is necessary in this area. The ODFT, a frequency-shifted discrete Fourier transform, is shown as the natural link between the DFT and the MDCT. A parameter estimator based on ODFT is presented. It provides accurate results and becomes useful in MDCT based audio coding. Furthermore it is exemplarily demonstrated that a combined analysis with DFT and ODFT can reduce the estimation error at low frequencies.