Is That Tone Significant? – The Prominence Ratio

The Prominence Ratio is a technique designed to see if there are any aurally prominent tones in a signal. Primarily, the prominence ratio is applicable where we have a noise source with a few tones and we need an objective measure to assess if the tones are “prominent”. That is, to assess whether the tones are likely to be heard.

It is formally defined in ANSI S1.13-2005 “Measurement of Sound Pressure Levels in Air” for general use and in ECMA 74 9th Edition December 2005, “Measurement of Airborne Noise Emitted by Information Technology and Telecommunications Equipment” specifically for noise from computers and associated peripherals.

The considered view is that our hearing appears to assess sounds in frequency bandwidths. That is, the ear behaves like a bank of filters where, in general, the bandwidth of each filter increases with frequency. What this means is that two or more tones, spaced such that they are all in the same band, sound as if they are just one tone within that band; conversely two tones separated by more than a critical bandwidth are perceived as being separate. In a simplified form then the ear appears to “analyse” the sound into the “energy” in each band. This then forms the basis of the prominence ratio. We use the term “energy” as the measure is based on the square of the sound pressures, X_p, in three adjacent bands. If we denote these by X_L, X_M and X_U for the Lower, Middle and Upper bands respectively then the Prominence Ratio for the middle band, PR_M, is given by

PR_M=\frac{X_M}{(X_L + X_U)/2}dB

In the world of psychoacoustics there is debate over the width of each critical band. There is one measure of critical bandwidth in ERBs, associated with Moore, and another in Bark, associated with Zwicker. Figure 1 below shows these bandwidths plotted versus frequency together with some 1/Nth octave bandwidths.

Bandwidths v frequencies

Figure 1: Bandwidths v frequencies

Above 1kHz the ERB bandwidth is very similar to 1/9th octave and the Bark bandwidth is approximately like 1/6th octave.

ANSI S1.13 and ECMA 74 use the Bark based Critical Bandwidths. However, when investigating the possibility of several close narrow bands it is useful to be able to select one of the 1/Nth octave bandwidths.

A tone is classed as prominent if the Prominence Ratio exceeds the following limits

PR(f) \ge 9.0 + log(1000/f)~~~\textrm{for f < 1000Hz} PR(f) \ge 9.0~~~\textrm{for f }\ge \textrm{1000Hz}

The shape of the Prominence Ratio curve is not initially what one might expect. Consider first a standard white noise signal. In Figure 2 below, the first graph shows a section of the signal and the second graph is the corresponding Prominence Ratio.

White noise and corresponding prominence ratio

Figure 2: White noise and corresponding prominence ratio

As expected the prominence ratio is essentially zero. However, if a small sinewave at 2kHz is added to the time history then we see results like those in Figure 3 below.

White noise plus 2kHz sinewave with corresponding prominence ratio

Figure 3: White noise plus 2kHz sinewave with corresponding prominence ratio

There is no discernible difference in the time signals and as expected the prominence ratio shows a peak at 2kHz.

But it also shows significant dips before and after the peak. These ‘dips’ are a direct result of the way the Prominence Ratio is defined. Recall our equation for PR_M above. When the Prominence Ratio is being computed over the region from about 1600 to 1850Hz then the peak at 2kHz will be in the upper band, thus causing the Prominence Ratio to be lowered. A similar situation occurs over the 2150 to 2550Hz region except that now the 2KHz tone is in the lower band.

The width of the region of high prominence ratio is approximately 300Hz as expected as that is the width of a Bark based critical band at that frequency.

A more realistic signal is shown in Figure 4 below.

A "real" signal

Figure 4: A “real” signal

This looks like yet another random signal. This time, however, we have what appears to be three regions of prominence as you can see in Figure 5.

Prominence ratio of signal from Figure 4

Figure 5: Prominence ratio of signal from Figure 4

The multiplicity of the negative dips can be annoying! As an option a low limit threshold is useful as illustrated below. It is also clearly useful if the software determines the number of tones that exceed the ANSI/ ECMA criteria and, of course, makes available these values together with an estimate of the frequency at which they occur. The DATS analysis software stores these with the resulting signals. They can be seen as annotations on the graph in Figure 6.

Prominence ratio with dips removed and prominent tones annotated

Figure 6: Prominence ratio with dips removed and prominent tones annotated

The prominence ratio of the middle “peak” has a distinct “lump” on the leading edge at around the 7 dB level. If we analyse using a narrower bandwidth, in this case 1/9th  octave Prominence Ratio, then the figure below actually shows four peaks. Because we are using a narrower bandwidth then the levels are a little lower. Also shown below is the frequency spectrum of the signal, which again shows four distinct spikes.

Prominence ration using 1/9th octave & corresponding frequency spectrum

Figure 7: Prominence ration using 1/9th octave & corresponding frequency spectrum

Although the Prominence Ratio was defined for steady state signals it is often useful to see it as a frequency time analysis.

Prominence ratio plotted against time

Figure 8: Prominence ratio plotted against time

This shows that the tone at around 3kHz is actually a tone burst occurring approximately in the centre of the signal.

 

 

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Dr Colin Mercer

Chief Signal Processing Analyst at Prosig
Dr Colin Mercer was formerly at the Institute of Sound and Vibration Research (ISVR), University of Southampton where he founded the Data Analysis Centre. He then went on to found Prosig in 1977. Colin retired as Chief Signal Processing Analyst at Prosig in December 2016. He is a Chartered Engineer and a Fellow of the British Computer Society.

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2 thoughts on “Is That Tone Significant? – The Prominence Ratio

  1. stuart Mugford, P.Eng, Calgary, AB, Canada

    Dear Dr. Mercer.
    A provocative article, thank you very much. About 12 years ago I participated in a test to determine if imminent A/F bearing failure could be detected in Bearing #4 (I think it was) of a GE LM1600 gas generator. The bearing is located in the hot end of the gas turbine, surrounded by extremely hot, turbulent air flow. There is no direct physical contact with the outside world, as both inner and outer races rotate, resulting in a low energy repetitive impact type fault located within high energy random noise sources, with very poor transmissibility to the outside world, situation. When this bearing fails, consequences are catastrophic. The test consisted of mounting an intentionally flawed bearing, and running the turbine, and using various technologies to determine if any evidence of the flaw could be detected. The answer was, “maybe” the flaw could be detected, but not with sufficient certainty or clarity to justify shutting down a large pipeline compressor station, and taking the GG apart to inspect the bearing. What do you think? Does this technique hold promise? The technologies used 12 years ago were quite sophisticated.
    Stu Mugford, P.Eng. (Calgary)

    1. colindirect

      Stu
      Thanks for comments. The Prominence Ratio certainly could be used in monitoring for vibrations as well as acoustics, but one would need to note that the frequency bands get wider at higher frequencies.

      In the specific case you mentioned with roller bearings the frequencies are known if it is possible to determine the speeds of the inner and outer races. In that situation narrow band filtering would improve the signal to noise ratio. It would also probably be better to sample, or resample, synchronised to the main shaft speed. We actually do a lot of work on turbines of various types with our PROTOR systems.

      So in your case I suspect an approach using selected non standard frequency bands and then a revised prominence ratio assessment could prove advantageous. As always with these situations assessing the level of ‘badness’ is challenging as we usually have a lot of good data but very little ‘bad condition’ data. We have on some occasions found that relying on measures related to just the frequency amplitudes is not enough. Phase changes can be quite interesting, after all phase is 50% of the info.
      Colin

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