Frequency-Slope Estimation and Its Application to Parameter Estimation for Non-Stationary Sinusoids
| Autor: | Axel Röbel |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
020301 aerospace & aeronautics
Noise (signal processing) Estimation theory Speech recognition Fast Fourier transform Mathematical analysis Estimator 020206 networking & telecommunications Sinusoidal model 02 engineering and technology Discrete Fourier transform Computer Science Applications Amplitude 0203 mechanical engineering 0202 electrical engineering electronic engineering information engineering Media Technology Music Energy (signal processing) Mathematics |
| Zdroj: | Computer Music Journal. 32:68-79 |
| ISSN: | 1531-5169 0148-9267 |
| DOI: | 10.1162/comj.2008.32.2.68 |
| Popis: | Sinusoidal models are often used for the representa- tion, analysis, or transformation of music or speech signals (Quatieri and McAulay 1986; Amatriain et al. 2002.). An important step that is necessary for obtaining the sinusoidal model lies in estimating the amplitudes, frequencies, and phases of the sinusoids from the peaks of the Discrete Fourier Transform (DFT). The estimation is rather simple provided the signal is stationary. A standard method for this estimation is the quadratically interpolated Fast Fourier Transform (QIFFT) estimator (Abe and Smith 2005). The QIFFT estimator uses the bin at the maximum of each spectral peak together with its two neighbors to establish a second- order poly- nomial model of the log amplitude and unwrapped phase of the peak. The amplitude and frequency estimates of the sinusoid that is related to the spectral peak are then derived from the height and frequency position of the maximum of the polyno- mial. The evaluation of the phase polynomial at the frequency position provides the estimate of the phase of the sinusoid. For non- stationary sinusoids, the parameter esti- mation becomes more diffi cult, because the QIFFT algorithm is severely biased whenever the fre- quency is not constant. The term bias refers to the systematic estimation error, that is, the error of the estimator that exists even if no measurement noise is present. For the partials in natural vibrato signals, the estimation bias of the QIFFT estimator accounts for a signifi cant amount of residual energy (i.e., the energy remaining after subtracting the sinusoidal model from the original signal). This is the major reason for the perceived voiced energy in the resid- ual of vibrato signals. A number of algorithms with low estimation bias for non- stationary sinusoids have been proposed. Algorithms that try to implement a maximum |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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