Spectral Envelope

Figure 1: Comparison of the spectral envelopes of the oboe and the clarinet. We can see from these spectral envelopes (blue curves) that the oboe’s spectrum has more energy in the higher harmonics than the clarinet. This correlates with a higher spectral centroid for the oboe.

Figure 2: Comparison of spectral spreads for a crash cymbal (left) and clarinet (right). The frequency spectrum extracted from the sound of two crash cymbals (on the left) is characterized by a higher spectral spread value than that of a clarinet sound (on the right) as shown by the width of its spectral envelope. This means that the sound components are generally more distant from the spectral centroid value (red line) in the case of crash cymbals.

Figure 3: Comparison of spectral skewness curves for pink noise (left side) and blue noise (right side). The spectral skewness of pink noise (on the left of figure 3) is positive due to the presence of higher energy below the spectral centroid (red vertical line). Notice how its energy has been condensed to the left, creating a longer “tail” to the right of the spectral centroid. The spectral skewness of blue noise, on the other hand, shows a slight negative tendency due to the presence of energy above the spectral centroid (on the right) .

Figure 4: Comparative representation of different spectral kurtosis values of filtered crash cymbals. Both plots present the amplitude spectra and spectral envelopes of filtered crash cymbals, which were processed in a way that the spectral spread remains constant with different spectral kurtosis values. See how the left spectrum is “flatter” (lower kurtosis) while the right picture shows a more “pointed” distribution, with thicker tails on the sides (higher kurtosis). In both cases, the energy is distributed following essentially the same average frequency distance from the spectral centroid, which is why the spectral spread values are identical.

Figure 5: Amplitude spectrum with a regression line (in black). The spectral slope corresponds to the gradient of the line (from [1], p.14).

Figure 6: Frequency spectrum with a red vertical line indicating the spectral rolloff point (from [1], p.15). The red line marks the point under which  95% of the energy is stored.