Tone-to-Noise Ratio and Prominence Ratio
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.
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.
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.
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.
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.
To calculate the Tone-to-Noise Ratio, the following operations are performed on a spectrum of the sound:
Note that the levels are usually expressed in Pa2 and no A-weighting is applied to the spectrum.
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.
Tone-to-Noise Ratio 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.
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.
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.
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.
To calculate PR the following is performed:
The level is usually expressed in Pa2 and has no A-weighting applied.
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.
Runup Application 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.
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:
The decibel level tones versus rpm of Brand A (28th and 60th order) and Brand B (159.5 order) are overlaid in Figure 6.
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.
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:
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.
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.
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.
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.
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.
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!
Calculating Tone-to-Noise Ratio and Prominence Ratio in Simcenter Testlab
Tone-to-Noise Ratio and Prominence Ratio can be calculated in two different ways in Simcenter Testlab:
2D Display Method
In Simcenter Testlab, to determine the Tone-to-Noise 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” as shown in Figure 11. Also add “Calculations -> TTNR Prominent”.
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” and “Sound Quality Metrics” as shown in Figure 12.
In Simcenter Testlab Time Data Processing worksheet (Figure 13):
Calculate away! See throughput processing tips article for more information on settings.
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'.
Standards like 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.
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.