Prominence Ratio

The Prominence Ratio (PR) computation is detailed in both ECMA-418-1 (former ECMA 74 Annex D) and ISO7779:1999 standards. It is applicable for tones whose frequencies stand between 89.1 and 11 220 Hz.

Sound: Analysis and Specification provides an automatic tone detection procedure from the signal’s spectrum (with a resolution around one Hz), which is not part of the standards that only define the calculation of PR at a given frequency. The procedure is therefore used prior to the computation of the Prominence Ratio per se.

In Sound: Analysis and Specification, the Prominence Ratio (PR) is included in Tonality computation profile. You may also calculate the PR of an order and display it as a curve of PR versus RPM or time.

For a given frequency f_t, the Prominence Ratio is computed as the ratio between:

• the energy of the critical band centered at f_t (energy X_M between f_1,M and f_2,M on the figure below), and

• the mean of the energies of the two adjacent bands (energy X_U between f_1,U and f_2,U for the upper band, and energy X_L between f_1,L and f_2,L for the lower band).

If the tone frequency is higher than 171.4 Hz, the PR is computed according to the following formula:

10lg [X_M /(X_L + X_U) * 0.5]

If the peak frequency is lower than 171.4 Hz, the lower critical band is narrower and its energy is therefore weighted. The PR is then computed according to the following formula:

10lg [X_M /{[X_L * (100/ Dƒ_L )] + X_U } * 0.5]

A tone is considered as prominent if:

• PR > 9 dB for f_t > 1000 Hz

• PR > 9 + 10 log (1000/f_t) dB for f_t ≤ 1000 Hz.

Two outputs/results are available for the Prominence Ratio computation:

1. The Prominence ratio (dB) curve over the frequency scale. The Prominence ratio value is displayed for each detected tone. The threshold for considering that a given tone is prominent (as defined above) is also displayed as a blue curve.

2. The Detailed Prominent Ratio results, which is an information window displaying the following data:

   • Signal name

   • Sampling frequency

   • Time limits of the analysis

   • Maximal Prominence Ratio on the signal

   • Calculation details for each detected tone (tone frequency, Prominence ratio, tone level, tone bandwidth around the tone, and ratio between the tone bandwidth and critical bandwidth).