Conclusions

In summary, only the Blackman window clearly revealed all of the oboe harmonics. This is because the spectral dynamic range of signal exceeded that of the window transform in the case of rectangular and Hamming windows. In other words, the side lobes corresponding to the loudest low-frequency harmonics were comparable to or louder than the signal harmonics at high frequencies.

Note that preemphasis (flattening the spectral envelope using a preemphasis filter) would have helped here by reducing the spectral dynamic range of the signal (see §10.3 for a number of methods). In voice signal processing, approximately $ +6$ dB/octave preemphasis is common because voice spectra generally roll off at $ -6$ dB per octave [162]. If $ X(\omega)$ denotes the original voice spectrum and $ X_p(\omega)$ the preemphasized spectrum, then one method is to use a ``leaky first-order difference''

$\displaystyle X_p(\omega) = (1-0.95\,e^{-j\omega T})X(\omega).$ (4.30)

For voice signals, the preemphasized spectrum $ \vert X_p(\omega)\vert$ tends to have a relatively ``flat'' magnitude envelope compared to $ \vert X(\omega)\vert$ . This preemphasis can be taken out (inverted) by the simple one-pole filter $ 1/(1-0.95z^{-1})$ .


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Blackman-Windowed Oboe Recording