Simcenter Testing Solutions Sharpness in Simcenter Testlab

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The sound quality metric Sharpness provides an objective way of quantifying the amount of high frequency content present in a sound.  The greater the proportion of high frequencies to the rest of the energy in a sound the “sharper” the sound is.  High frequency noise often plays a crucial role in whether we perceive a sound as being harsh or irritating to listen to, so Sharpness is often included in sound quality pleasability studies.

There exist three commonly used formulations for the calculation of Sharpness, this article will review the different formulations and provide some practical examples of the metric in use.

This article has the following sections:

1.  Introduction
1.1  Unit and Values of Sharpness
1.2  Specific Loudness as a basis for Sharpness
2.  Formulations of Sharpness
2.1  Zwicker Sharpness
2.2  DIN45692 Sharpness
2.3  Aures Sharpness
3.  Application examples
3.1  Vacuums
3.2  Motorcycles
3.3  Using Sharpness in sound quality – Washing machines

1.  Introduction

Sharpness provides an objective way to quantify the balance of the spectral content of a sound between low and high frequencies.  If the energy of a spectrum is mostly concentrated in the low frequency range, it will produce a low sharpness value.  If the energy of the signal is biased toward the high frequency end of the hearing spectrum, the sharpness value will be high.  A flat spectrum, featuring energy well-balanced across the frequency spectrum will produce an intermediate sharpness value.  In this way, Sharpness acts as another sound quality tool (along with Loudness, Tonality, etc) that can be used to differentiate between sounds which may all have the same overall decibel level but produce very different subjective impressions.
1.1  Unit and Values of Sharpness

Sharpness is reported in the unit of acum, which is derived from the Latin root meaning “sharp”.  The definition of 1.0 acum is a narrowband noise one critical band wide centered at 1 kHz, and a level of 60 dB RMS.  The values produced by the sharpness calculation are always non-negative integers, and theoretically unlimited in value (depending on the formulation used, more on that in the next section).  A signal with no content in the audible frequencies will produce a sharpness of 0.0 acum.
1.2  Specific Loudness as a basis for Sharpness

**Note:  Calculation of Sharpness is directly available in Simcenter Testlab, there are no preprocessing steps required.  However, as will be further detailed in the next section, the various formulations of sharpness all rely on the specific loudness spectrum.  To better detail how the Sharpness formulations work, it is necessary to first describe the calculation of specific loudness and total loudness for the purposes of this article.** 
The calculation of sharpness really begins with the specific loudness spectrum, or loudness versus the Bark scale.  From the specific loudness spectrum, the total loudness can be calculated and used in the calculation of sharpness.  To illustrate this process, consider two familiar test signals, White and Pink Noise.  The narrow band frequency spectra of these two signals is shown below in Figure 1
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Figure 1.  Narrow-band frequency spectra for white and pink noise. 
White noise is characterized by equal energy across the narrow-band frequency spectrum, or equal amplitude across all frequencies as shown by the flat white line in Figure 1.  Pink noise is energy-biased toward low frequency, and the amplitude level drops off continuously as a function of narrow-band frequency, as shown by the pink trace in Figure 1.   

The first step in the calculation of sharpness is to calculate the specific loudness spectrum for each signal.  The specific loudness spectrum represents the psycho-acoustic loudness of a signal, distributed over the frequency bands that humans hear in, called Bark bands, or the Bark scale.  The specific loudness spectra for white and pink noise are shown below in Figure 2
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Figure 2.  Specific loudness spectra for white and pink noise.  Specific loudness specifies the distribution of loudness over the 24 Bark bands.
Figure 2 highlights how spectral energy is distributed differently between these two signals: the loudness of pink noise is relatively balanced between low and high Bark bands, while white noise is biased toward the higher Bark bands. 

The next step in the calculation of sharpness is to determine the total loudness (N), which is calculated from the specific loudness spectrum.  The equation for total loudness is shown below in Figure 3.  Total loudness is determined by integrating the specific loudness spectrum over the 24 Bark bands, resulting in a total loudness in Sones.
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Figure 3.  Formulation of total loudness (N) calculated from specific loudness spectrum (N’).

As will be shown in detail in the next section, the various formulations of Sharpness utilize the band-wise approach of the total loudness calculation to weight the higher Bark bands for their influence on the perception of sharpness.  The more spectral energy that appears in the higher Bark bands, the higher the calculated sharpness value.  Based on the specific loudness spectra shown in Figure 2, it follows that white noise will produce a higher sharpness value than pink noise, due to the higher levels in the upper Bark bands.  This is demonstrated in Figure 4 below, which shows the Zwicker sharpness for white and pink noise versus time. 
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Figure 4.  Time-varying sharpness (Zwicker formulation) for White noise and Pink noise.  White noise is “sharper” than Pink noise due to the higher levels of loudness in the upper frequency range.

Listen to white noise and pink noise in the video below (Video 1). 

Video 1: Sharpness of White and Pink Noise - Direct YouTube link:  

The Sharpness method provides another way to quantify objectively the subjective difference one experiences when listening to different sounds, in this case the difference in the spectral energy balance between low and high frequency.

2.  Formulations of Sharpness

There are several different formulations and standards for the calculation of sharpness.

2.1  Zwicker Sharpness

Zwicker sharpness is calculated using the formula shown below in Figure 5.  The equation shows sharpness to be a ratio of the weighted total loudness of the spectrum to the total loudness.  The weighting function g(z) is shown in Figure 6.
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Figure 5.  Formulation of Sharpness (S) for Zwicker and DIN45692 methods.
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Figure 6.  Weighting function g(z) for Zwicker formulation of sharpness.
The weighting function g(z) begins to increase above unity at 15.8 Bark (around 3 kHz) and the normalization constant k is to ensure a narrow-band tone at 1,000 Hz with a level of 60 dB produces 1.0 acum.  The weighting function g(z) determines the extra emphasis the loudness in the higher Bark bands have on the overall sharpness value.  In the case of Zwicker Sharpness, the spectral content of the analyzed signal below 15.8 Bark does not contribute to the sharpness value, as the weighting function is 1.0 for these bands.  Only the spectral content above 15.8 Bark influences the Zwicker Sharpness value, and the higher the Bark band, the more the influence on sharpness. 

2.2  DIN45692 Sharpness

A version of the Sharpness calculation has been standardized in the German standard DIN 45692.  The formulation for DIN sharpness is identical to Zwicker discussed in the previous section, but with a slightly modified weighting function g(z), shown in Figure 7 below. 
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Figure 7.  Sharpness weighting function g(z) for both Zwicker (yellow) and DIN45692 standard (dashed purple line).

The difference between the Zwicker and DIN frequency weighting functions will result in slight differences between the sharpness values when comparing the two methods.  Zwicker adds more weight to Bark bands 16-22 (roughly 3 kHz – 10 kHz), while DIN more aggressively weights the upper Bark bands (above roughly 10 kHz).  For most signals this difference in weighting strategy results in slightly higher sharpness values from Zwicker than the DIN standard, though this trend is entirely signal-dependent.  For sounds with most or all their energy above 10 kHz, DIN45692 will produce a higher acum level. 

2.3  Aures Sharpness

Aures Sharpness is similar to Zwicker and DIN45692 Sharpness, but with one major difference: Both Zwicker and DIN Sharpness are loudness-normalized, meaning they will produce the same acum value regardless of the overall loudness level of the signal.  Aures Sharpness, however, is loudness-dependent and will produce a higher sharpness value with increasing loudness.

The formulation for Aures sharpness appears as an appendix to the DIN45692 standard and is shown below in Figure 8
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Figure 8. Formulation of Aures sharpness.  This formulation features a frequency weighting function gA(z) that incorporates signal loudness.

Note the new weighting function gA(z), identified with a subscript A.  This weighting function incorporates the signal loudness into the weighting function, and the formulation is shown in Figure 9.
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Figure 9.  Weighting function gA(z) for Aures sharpness.  This function scales with increasing loudness, making Aures sharpness loudness dependent.

As the overall loudness (N) of the signal increases, the weighting function gA(z) also changes and becomes increasingly aggressive as shown in Figure 10 below.  Here, three sample loudness levels (N=1, 10 & 100 sones) are compared to highlight the effect of increased loudness on the shape of the weighting function, gA(z). 
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Figure 10.  Example weighting curves gA(z) for Aures sharpness.  Three overall loudness values are shown N=1 sone, N=10 sone, N=100 sone.     

The effect of this loudness scaling on Aures sharpness is shown in Figure 11 below.  First, white noise was used to calculate Zwicker, DIN45692 and Aures sharpness values versus time (Figure 11a).  Next, the white noise signal was scaled by a factor of 10 (Figure 11b), and finally by a factor of 100 (Figure 11c), with the three sharpness values being calculated in each case.  Notice the DIN and Zwicker values of sharpness (green & blue, respectively) remain constant, but the Aures sharpness value (shown in red) increases with the increased signal amplitude. 
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Figure 11.  Aures, DIN45692 and Zwicker Sharpness values for white noise versus time, for various noise levels: a) baseline white noise, b) scaled by a factor of 10, c) scaled by a factor of 100. 

So, which method should be used? Zwicker and DIN45692 weight the Bark scale differently, and do not account for overall signal loudness.  Aures factors the overall signal loudness into account, and as the amplitude of a given signal increases, so will the reported sharpness according to Aures. 

Ultimately, the selection of a Sharpness formulation is a matter of personal preference.   What is important is to use the chosen method consistently when comparing results, and to always note the formulation used when reporting results to avoid confusion. 

3.   Application Examples

Some example applications of the use of sharpness with sounds:

3.1  Vacuums

To illustrate how Sharpness can be used in practice, consider two vacuums: Vacuum A & Vacuum B.  Vacuum A is well-known to have some high frequency tones that are not present in Vacuum B, and as a result often scores lower on jury tests for sound quality.  Aside from jury feedback and perhaps applying some tonality metrics, Sharpness should also provide an objective way to differentiate the two vacuum sounds.  The specific loudness spectra of Brand A and B are shown in Figure 12 below.
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Figure 12.  Specific loudness spectra for vacuums Brand A (red) and Brand B (green).  The higher loudness levels in Bark bands 15-24 will result in Brand A having a higher sharpness value than Brand B.
The high frequency tones apparent in Brand A drive up the specific loudness in the upper Bark bands, which will in turn result in a higher sharpness value for Brand A.  The frequency spectra and Zwicker sharpness are compared in the video below (Video 2).

Video 2: Sharpness of Vacuum Cleaners - Direct YouTube link: 

3.2  Motorcycles

Audio recordings of three motorcycles are analyzed for Sharpness in Video 3 below.

Video 3: Sharpness of Motorcycles - Direct YouTube link: 

3.3  Using sharpness in sound quality – Washing machines

In an of itself, calculating the sharpness value for a given product’s sound may not be particularly meaningful: knowing a product produces a certain value of acums of sharpness isn’t necessarily helpful in knowing much about its sound quality, or what it sounds like.  It is only when the sharpness value is used in concert with other sound quality metrics, such as loudness, tonality, fluctuation strength, etc, as well as customer preference information that these individual values become useful and powerful. 
Consider this sound quality example of several washing machines, and the sound they emit during the “Spin” cycle (Video 4).  Five washing machines A, B, C, D and E are considered, and several sound quality metrics are calculated for each: loudness, articulation index, and sharpness.

Video 4: Sound Quality of Washing Machines - Direct YouTube link: 

The time varying sharpness (Aures formulation) values for the five washing machines are shown in Figure 13 below.  Looking solely at the sharpness values, one might conclude that Brand A and C are the best, B and D the worst, and Brand E somewhere in between.  While some of these conclusions may match the perception of the five washing machines, some may not.  The proportion of high frequency noise is not the only factor in determining how irritating or annoying the different machines are to listen to, there are other key features to the five recordings that need to be included in our analysis.

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Figure 13.  Aures sharpness values for each of the 5 washing machines versus time.  The maximum sharpness value is shown in the curve legend.

In order to get a clearer picture on the annoyance level for each of the machines, one may consider what aspects of the sound a washing machine makes during use that a customer may find particularly irritating and troublesome in their home.  High frequency noise is often more irritating to listen to, so sharpness will certainly be included.  In addition, the loudness of the machine will certainly play a part in how annoying the machine is: the louder the noise, the more intrusive it will likely be.  Lastly, perhaps the washing machine will be installed in a multi-use portion of the home where conversations often take place, making communication difficult.  Articulation Index is a metric used to measure how much a noise interferes with speech intelligibility, and will be included in our “annoyance” analysis of the five machines. 

As of Simcenter Testlab 2021.1, the output of certain methods, such as a statistical value, can now be used as the input of a subsequent method.  This is convenient for calculating customized metrics (i.e.- the “golden equation”) in sound quality analysis and jury testing.  In this example this functionality will be used to calculate our “annoyance” metric on the washing machines, based on the output of the Loudness time varying, Sharpness time varying and Articulation Index methods, as shown in Figure 14.

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Figure 14.  Simcenter Testlab Neo process to calculate the “annoyance metric” for the washing machines.  The Calculate method uses the output of the Statistic methods as input.

For the Annoyance metric calculation, we have the N10 Loudness (or 90th percentile), the maximum value of the Sharpness, and the minimum of the Articulation Index (AI%).  Typically, the relationships between sound quality metrics and sound quality performance are derived from detailed statistical analysis from jury testing results.  “Annoyance” will be defined for this example as described in the equation below in Figure 15.  High loudness and high sharpness are deemed more annoying, so appear in the numerator.  The lower the AI% the more difficult speech communication, so AI% appears in the denominator.  Though simple, this Annoyance metric could be effectively used for the assessment of future product variants and performance ranking, provided it continues to accurately model jury results related to product preference. 

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Figure 15.  A new metric termed “Annoyance” is built out of several other sound quality metrics.  The higher the Annoyance, the harsher and more irritating the sound.
The results of the Annoyance metric calculation are shown in Figure 16.  The results show Brand B to be the most annoying, followed by Brand D.  These two brands performed the worst according to all the included metrics: highest loudness, highest sharpness, and lowest AI%.  Perhaps in the next round the recordings could be modified to equalize the loudness of all the machines and see how the updated results compare to jury feedback.   

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Figure 16.  Tabulated results for three included metrics and new calculated “Annoyance” metric for the washing machines. 
How does the custom "Annoyance" metric compare to your impressions of the washing machine sounds?  Let us know in the comments! 

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