Simcenter Testing Solutions Tone-to-Noise Ratio and Prominence Ratio

Direct YouTube link: https://youtu.be/JpEwoOeJkzA
 

Screaming turbo chargers, whining gears, buzzing mosquitoes! Tones are everywhere!

Even low amplitude tones can be very irritating. A tone is typically a single frequency that is audible to the human ear. Think of mosquito’s whine – very low amplitude, but very irritating indeed.

Using a traditional measure of sound like a decibel is not enough to characterize tones. Instead, the twin metrics of Prominence Ratio (PR) and Tone-to-Noise Ratio (TTNR) can be used quantify the presence of distinctly audible tones in a sound signal.

Article contents:
1. Background
2. Tone-to-Noise Ratio (TTNR)
  2.1 Tone on Random Example
3. Prominence Ratio (PR)
  3.1 Runup Example
4. Background Sound Considerations
5. Low Frequency
6. Calculating TTNR and PR in Simcenter Testlab
   6.1 2D Display Method
   6.2 3D Colormap Method
7.  Standards
8. Conclusions

1.  Background

Rather than using the absolute level of the tone, these metrics look at the level of the tone relative to the background sound level to determine how prominent, or noticeable, the tone is to a listener.

Even if a single frequency is visible in a sound spectrum, it does not mean it can be heard as distinct tone. If the tone is not high enough relative to the background, it will not be perceived by a listener. This is shown in Figure 1.

Figure 1: Left – Tone is not high enough relative to background sound level to be heard as distinct tone. Right – Tone is high enough relative to background to be heard as distinct audible tone.

So how high above the background noise must a tone be to be considered prominent? This rest of this article describes how the Tone-to-Noise Ratio and Prominence Ratio metrics are calculated, and the required threshold levels for tones. Some illustrative examples are also provided.

2. Tone-to-Noise Ratio

In the Tone-to-Noise Ratio (TTNR) approach, the level of a tone must be at least 8 dB above the level of the masking noise level to be distinctly audible to a listener.
 

Direct YouTube link: https://youtu.be/Uh6rz387ur0
 

What is a masking noise level? It is the background sound that if high enough in amplitude, makes it impossible for the human ear to pick out the tone. This masking level is calculated in a frequency range, or critical band, that contains the tone as shown in Figure 2. The human ear has 24 different critical bands as defined by the Bark Scale.

Figure 2: Tone-to-Noise Ratio - A distinctly audible tone must be 8 dB or higher above masking level

To calculate the Tone-to-Noise Ratio, the following operations are performed on a spectrum of the sound:

• The level of the tone (T) is calculated, which is shown in green in Figure 2.
• The level of the critical band (C) is calculated, which corresponds to pink frequency range in Figure 2. This includes the tone.
• The level of the tone (T) is subtracted from the critical band level (C), which yields the masking noise level (M). This subtraction also includes adjustments for the frequency width of the tone and critical band.
• The difference between the tone level (T) and the masking noise level (M) is calculated. The difference is expressed in decibels. This is the Tone-to-Noise Ratio as shown in Equation 1.

Note that the levels are usually expressed in Pa² and no A-weighting is applied to the spectrum.

Equation 1: Tone-to-Noise Ratio (TTNR) is dB difference between Tone level (T) and the Masking level (M)

For a tone to be distinctly audible, the difference between the tone and the masking level must be at least eight decibels. For frequencies lower than 1000 Hz, the difference must be slightly more than eight decibels.

2.1 Tone on Random Example

To demonstrate how Tone-to-Noise Ratio works, a single 2000 Hertz tone was combined with a constant, random background noise. The level of the 2000 Hertz tone was then increased by 3 dB over five iterations.

The spectrum for six different tone and background combinations was computed as shown in Figure 3. Notice that in all cases the peak clearly shows in the spectrum. However, the tone-to-noise ratio metric will indicate if the tone can be heard distinctly above the background noise, or if it melts in with the background noise and cannot be heard.

Figure 3: Identical random background noise with six different 2000 Hertz tones that are 3 dB apart

As shown in Figure 4, the tone-to-noise values range from about zero to 13 decibels above background. When the tones exceed 8 dB above the background masking level, the tone is considered to be distinctly perceivable to a human listener. Notice the legend in Figure 4 also has a column for TTNR Prominent. This is a companion metric that reduces the result to a simple Yes/No to indicate whether the tone is audible.

The difference of the tone level (T) and the masking level (M) can be negative. The masking level is the ‘sum’ of all the data in the critical band, which may not appear to be higher than the tone in the normal spectrum view.

Figure 4: The Tone-to-Noise Ratio legend contains the dB levels of the tone versus the background level. The TTNR Prominent shows Yes/No indicating if a tone can be heard distinctly.

Prominence Ratio is similar to Tone-to-Noise ratio, but uses only critical bands in its calculations.

Prominence Ratio is similar to Tone-to-Noise ratio, but uses only critical bands in its calculations.

3. Prominence Ratio

In the Prominence Ratio (PR) method, a discrete tone is said to be prominent if it has a value of 9 dB or higher. In the calculation of Prominence Ratio, the critical band containing the tone or tones is compared to the adjacent two critical bands as shown in Figure 5.

Figure 5: Prominence Ratio - A distinctly audible tone band (green) must be 9 dB or higher than the combined masking level of the two adjacent critical bands (red).

To calculate PR the following is performed:

• Level of the critical band (B) containing the tone, or tones, is calculated. Critical band B is shown in green in Figure 5.
• Level of the two adjacent (A and C) critical bands is calculated. Critical band A and C are shown in red in Figure 5.
• The prominence ratio is calculated by taking the log of the tone critical band (B) divided by the average of A and C as shown in Equation 2.

The level is usually expressed in Pa² and has no A-weighting applied.

Equation 2: Prominence Ratio is decibel difference of the tone critical band level (B) and the averaged adjacent critical bands (A and C).

In order for a tone to be considered prominent for frequencies lower than 1000 Hertz, a difference greater than 9 dB is needed.

The main difference between Tone-to-Noise Ratio (TTNR) and Prominence Ratio (PR) is that in TTNR a tone is evaluated, while in PR a critical band is evaluated. Some products make several tones, clustered together. For example, a gear mesh produces a main tone and sideband frequencies. Using Prominence Ratio, this grouping of tones can be evaluated.

3.1 Runup Example

Prominence Ratio and Tone-to-Noise-Ratio can be used for both stationary sound spectrums from products, and on sound maps of product runups. In a runup, the product is swept from its minimum operating speed to the maximum speed. The tones may come and go as the product sweeps thru its operating speed range.

Direct YouTube link: https://youtu.be/3LvToeNik8c
 

In this example, the tones produced by two different products, Brand A and Brand B, will be evaluated with both traditional spectral maps and prominence ratio maps. The advantages of a prominence ratio maps versus traditional spectral maps will be illustrated.

Figure 6 shows the runup speed sweep signatures of the two different products: Brand A and Brand B that produces tones via orders:

• Brand A contains two orders (28 and 60) that produce tones.
• Brand B contains an order (159.5) that produces a tone.

The decibel level tones versus rpm of Brand A (28th and 60th order) and Brand B (159.5 order) are overlaid in Figure 6.

Figure 6: Spectral colormap and order results do not match perception.

The orders of Brand A are a much higher decibel level than Brand B. This might lead to the conclusion that Brand A has more noticeable and distinctly audible tones than Brand B.

However, listening to the two runups, this is not true throughout the entire runup. Brand A has some noticeable tones at the beginning of the runup, while Brand B contains tones throughout the runup.

Instead of relying on a spectral map analysis, a prominence ratio map computed from the same recordings of Brand A and B can be used to analyze the tones.

Direct YouTube link: https://youtu.be/h-rS2l4P_Dg
 

It is helpful to set the Y-axis scale on prominence ratio map from 0 to 9 db. Anything above 9 dB, is colored red. This means it is above the threshold to be heard as a distinctly audible tone. Doing so leads to the following conclusions from Figure 7:

• The prominence ratio map of Brand A shows two tones from 28^th and 60^th order that come and go at the beginning of the runup.
• The prominence ratio map of Brand B shows that 159.5 order is a distinct and audible tone throughout the runup.

Figure 7: Opposite conclusion with Prominence Ratio Map versus Spectral Colormap

This example illustrates the importance of not evaluating the absolute decibel level of a tone. Rather it is important to understand the level of the tone relative to the masking noise level surrounding the tone. In particular, the 159.5 order is a very low level in terms of absolute decibels as shown in Figure 8. When listening, this tone is very distinct and noticeable.

Figure 8: Top – Brand A had tones at beginning of runup in both Spectral and Prominence Ratio map. Bottom – Brand B has 159.5 order tone, most clearly indicated in Prominence Ratio map.

Because the 159.5 order tone is surrounded by almost no background noise, it is very noticeable and can be distinctly heard throughout the runup. Without using a Prominence Ratio map, it would not be obviously that this is the most noticeable tone in the runup.

Note that the tone gets wider as it increases in frequency in the prominence ratio map. This is because critical bands in human hearing become wider at higher frequencies.

4. Background Sound Considerations

What exactly is meant by the background sound?

The background sound is an important concept. For example, the background level should not be confused with the overall level. The overall level is a single number that represents the sound level of the entire sound spectrum, from 0 to 20,000 Hertz typically.


Direct YouTube link: https://youtu.be/vdSTAhYOhHY
 

In Figure 9, the overall sound level is 87.6 dB, while the level of an individual tone is 81.5 dB. Being that the tone level is less than the overall, it might lead one to conclude that the tone is not audible. However, this is not the case. The tone is distinctly audible.

Figure 9: Top – Tone is less than overall, Bottom – Tone is prominent and audible

It is the background level in the critical band immediately around the tone that matters. In the bottom picture of Figure 9, the tone is 11 decibels higher than the critical band masking level immediately surrounding the tone. The overall level of the entire spectrum does not influence whether the tone can be distinctly heard.

The importance of background sound must also be accounted for when testing for whether tones are audible or not. In Figure 10, pictured on the left is a component test for an airplane propeller. Measuring the tonal content of the component by itself would not be a reliable indicator of whether the tones would be audible in the final application shown on the right.

Figure 10: Component test in lab is not reliable for determining if tones will be audible while using the product. Component must be tested in application use case to understand complete tonal behavior.

Without the appropriate background, the tonal estimate does not yield useful results.

If the background sound of the end application is not present, the component tested in isolation will exhibit dominant and distinctly audible tones!

5. Low Frequency

The thresholds described in the article (9 dB for Prominence Ratio, 8 dB for Tone-to-Noise Ratio) for a tone to be audible only apply for frequencies 1000 Hz and higher.

Below 1000 Hz, a higher separation between the tone and background must be achieved as shown in Figure 11.

Figure 11: Threshold for audible tone is higher for frequencies below 1000 Hz for Tone-to-Noise Ratio and Prominence Ratio.

These levels are described in the standards referenced at the end of this article.

6.  Calculating TTNR and PR in Simcenter Testlab

Tone-to-Noise Ratio (TTNR) and Prominence Ratio (PR) can be calculated in two different ways in Simcenter Testlab:

• 2D Display Method - In a FrontBack display with a spectrum, cursor calculations can be used to determine the TTNR and PR.
• 3D Colormap Method - For runups or time varying colormaps, TTNR and PR colormaps can be calculated in throughput processing

6.1 2D Display Method

In Simcenter Testlab, to determine the Tone-to-Noise Ratio or Prominence Ratio of a tone in a spectrum, right click in a display and add a Single X Cursor. Position the cursor on the peak of the tone.

Once the cursor is in place, right click on the cursor and select “Calculations -> Tone-to-Noise Ratio” or "Calculations -> Prominence Ratio" as shown in Figure 12. 

Figure 12: After adding a single cursor, right click on the cursor, select “Calculations -> Tone-to-Noise” or "Calculations -> Prominence Ratio".
 

This will display the dB above the noise background for the selected tone. The other selections, "PR Prominent" and "TTNR Prominent", simply produce a "Yes" or "No' if the tone is audible based on the standard.

When calculating prominence ratio, aligning the cursor on the tone may not yield the highest value. This is because the prominence ratio calculation works with critical bands, not single frequencies.

Figure 13 illustrates this point.  

Figure 13: When calculating Prominence Ratio, the highest value may be occur when the cursor is positioned off of the tone.

The calculation is the ratio of the masking background sound in the adjacent two bands to the middle band. It is possible that the background levels are much higher when the cursor is not placed on the tone.

6.2 3D Colormap Method

To calculate a colormap of Prominence Ratio or Tone-to-Noise Ratio, choose “Tools -> Add-ins” from the main Simcenter Testlab menu. Turn on “Signature Throughput Processing” (36 tokens) and “Sound Quality Metrics” (33 tokens) as shown in Figure 14.

Figure 14: “Tools -> Add-ins -> Sound Quality Metrics”.

In Simcenter Testlab Time Data Processing worksheet (Figure 15):

• In “Acquisition Parameters” set the mode to “Tracking” and choose rpm or time
• In “Section Settings”, turn on “Prominence Ratio Map” and/or “Tone-to-Noise Ratio Map” as desired.

Figure 15: In “Throughput processing -> Section Settings -> Psychoacoustic Metrics"

Press the "Calculate" button. See the knowledge article "Throughput processing tips" for more information on settings and usage.

To create prominence ratio or tone-to-noise ratio order cuts from their prospective waterfall data, use 'Signature Data Post-Processing' from 'Tools -> Add-ins'.

7. Standards

The standards ECMA-74 and ISO 7779 contain information on calculating Tone-to-Noise-Ratio and Prominence Ratio. Both ECMA-74 and ISO 7779 cover tones emitted by IT equipment like computers and printers.

8. Conclusions

When evaluating the tones emitted from a product, it is not always useful to measure the absolute decibel levels of the tones. Instead, the metrics Tone-to-Noise Ratio and Prominence Ratio are more effective for the evaluation of the perception of tones. The metrics account for the tone level relative to the background sound level, which traditional analysis methods do not.

Tones are only one aspect of sound a product can make. The presence, or lack of presence, of tones does not always indicate the end user satisfaction with a product’s sound. Other aspects of sound like loudness, fluctuation, sharpness, etc are also important to consider. The end user expectations are also an important consideration.

Be sure to check out the Tonal Sound Metric Seminar for more information and examples!

Questions?  Email Scott Macdonald (macdonald@siemens.com).

Related Links

• Index of Testing Knowledge Articles
• History of Acoustics
• Sound Pressure
• What is a decibel?
• What is A-weighting?
• Octaves and Human Hearing
• Describing Sounds with Words
• Loudness and Sones
• Articulation Index
• Calculating a Specific Loudness Spectrum in Simcenter Testlab
• How to Calculate N10 Time Varying Loudness in Simcenter Testlab?
• Auditory Masking
• Tonality
• Sharpness
• Fluctuation Strength and Roughness
• Simcenter Testlab Neo: Modulation Metrics
• Critical Bands in Human Hearing
• Kurtosis
• Sound Quality Jury Testing
• Alter Speed of Rotating Sound for Listening
• Simcenter Testlab Sound Diagnosis
• Words to Describe Sounds
• Sound Metrics Unleashed Seminar
• Tonal Sound Metric Seminar
• Sound Quality YouTube Playlist