Simcenter Testing Solutions Simcenter Testlab Neo: Modulation Metrics

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Simcenter Testlab Neo contains several methods for quantifying the perceived modulation of sounds as shown in Figure 1. These modulation metrics are available with the Sound Quality Analysis add-in (33 tokens) of Simcenter Testlab Neo.
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Figure 1: Available Modulation Methods in Simcenter Testlab Neo.

This article contains background information on modulation sound metrics and an overview of how to use Simcenter Testlab Neo Process Designer to perform this analysis.

1.    What is Modulation?
2.    Envelope Analysis
3.    Modulation Spectrum Method
4.    Modulation Depth Method
5.    Modulation Map Method
6.    Modulation Frequency Method
7.    Roughness and Fluctuation Strength
8.    Getting Started with Modulation Methods in Simcenter Testlab Neo

1. What is Modulation?

Modulation metrics are a measure of the amount of amplitude variation in a sound over time. These metrics are based on studies using human listeners to understand their perception of modulation. For example, these metrics can be used to rate the rumble of an exhaust system, or the lugging sound of an electric motor.

The depth of the modulations, and how often they occur, are considered in the calculation of a modulation metric as shown in Figure 2.
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Figure 2: The amplitude modulation of a sound is described by a modulation frequency and modulation depth.

Why is a modulation metric needed?  Doesn’t sound pressure always rise and fall over time?  

Consider the sound pressure signal (red curve) and overall level (green) shown in Figure 3.
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Figure 3: The actual rapid changes in sound pressure (red curve) can be different than the perceived changes in amplitude of sound (green curve).  In this example, the perceived changes (green curve) are called modulation.

Here the sound pressure level (red) changes very rapidly, on the order of hundred times in one second.  The red sound pressure curve is what is actually measured by a microphone and corresponds to the pressure exerted on the human ear drum. 

The sound pressure also has a slower change (green) in overall amplitude.  The green line is not a directly measured quantity. This slowly changing phenomenon is perceived by a listener and is called amplitude modulation. It is analogous to an up-tempo song being played on a stereo, while the volume knob is slowly being turned up and down over time.  

This results in the perception of modulation of the sound over time (green curve) that are much slower than the actual frequency content of the sound pressure signal (red curve). The green curve is the mathematical envelope of the red curve.

2. Envelope Analysis

As seen in Figure 3, the envelope is an overall outline of the rapid changes in a signal. The mathematical basis of the envelope function was developed by the German mathematician David Hilbert (Figure 4) in the early 1900’s.
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Figure 4: German mathematician David Hilbert (1862-1943).

In the Simcenter Testlab Neo Process Designer, an envelope method is available by turning on the Interactive Analysis add-in (16 tokens) as shown in Figure 5.
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Figure 5: Envelope method in Simcenter Testlab Neo Process Designer is available using the “Interactive Analysis” add-in (16 tokens).
Some properties of the envelope function include:
  • Based on absolute amplitude, it never goes below zero. 
  • Has more low-frequency content than the original signal.

The second property is useful in understanding the perception of a sound for a listener. Consider the red signal from Figure 3.  It has about a hundred fluctuations in the span of one second.  On the other hand, someone listening to the sound would be more likely to key in on the slow changes in amplitude described by the green envelope curve.  

In this case, the listener would hear two fluctuations per second, because the overall amplitude varies twice per second. This difference would be reflected in the Fourier Transform of the original signal versus the Fourier Transform of the envelope signal. This is shown in the next section.

3. Modulation Spectrum Method

By performing a Fourier Transform on the envelope signal, the frequency and amplitude of the sound modulation is shown. The frequency of the perceived modulation is not shown in the Fourier Transform of the original sound pressure signal as shown in Figure 6.
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Figure 6: The Fourier Transform of the modulated time data from Figure 3.  The Fourier Transform of the original sound pressure signal has several frequencies around 100 Hz (red) while the Fourier Transform of the envelope has frequency content at 2 Hz and multiples (green). 

Notice that the Fourier Transform (red) of the original signal has contain several frequencies around 100 Hz, which combine to create the two times per second rise and fall in the signal.  The Fourier Transform (green) of the envelope has a peak at 2 Hz, which corresponds to the perceived modulation of a listener.  

The Fourier Transform of an envelope function is also called a modulation spectrum. It can be calculated via two different methods in Simcenter Testlab Neo as shown in Figure 7
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Figure 7: Two methods for calculating the modulation spectrum of a signal in Simcenter Testlab Neo. On the left, a series of modulation spectrums are calculated via the “Modulation map – tracked” method and then averaged with the “Modulation spectrum” method.  On the right, a “Envelope” method is calculated and then a “Spectrum average” is taken.

The main difference in these two methods is related to the mean of the signal.  In the Modulation Spectrum method, the mean (which is the value at zero Hz) is removed from the spectrum as shown in Figure 8.  
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Figure 8: Left – The Fourier Transform of an envelope function magenta) has an offset at zero Hz while a modulation spectrum (green) does not. Right – A envelope function (green) versus time is all positive with a mean offset (dotted green) from zero.  
The Fourier Transform of an envelope function and the modulation spectrum are identical, except at zero Hz. The direct Fourier Transform of an envelope function has a mean, or offset, at zero Hz.  This is because the envelope of a signal is an all positive function, which ensures it has a mean, or offset from zero.

Typically, it is more convenient to look a modulation spectrum without content at zero Hz.  However, the envelope analysis in Simcenter Testlab Neo can be performed with fewer tokens (Interactive analysis: 16 tokens versus Sound Metrics Analysis: 33 tokens).

4. Modulation Depth Method

Besides the modulation frequency, the modulation depth is also important. Consider the two modulated signals shown in Figure 9.
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Figure 9: Two signals with same modulation frequency but different modulation depth. Fully modulated signal (top, red) and partially modulated signal (bottom, green).  

The two signals will have the same modulation frequency, but different “modulation depths”. The red curve (top) has more modulation depth than the green curve (bottom). This difference in depth can be perceived by a listener.  

To calculate the depth, the “Modulation Depth” method is attached to the “Modulation map – tracked” method as shown in Figure 10.
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Figure 10: Modulation Depth method in Simcenter Testlab Neo Process Designer.

The “Modulation map – tracked” method has settings for how often the depth should be calculated versus time or another tracking parameter.  For example, the default time increment is 0.1 seconds when calculating the depth tracked versus time.

An example output of modulation depth versus time is shown in Figure 11.
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Figure 11: Left - Fully modulated signal (top, red) and partially modulated signal (bottom, green).  Right – Modulation depth versus time for the two signals on the left.

Modulation depth can be expressed in different ways:
  • Absolute: The amount of modulation in dB (referenced to Pascals).
  • Number: A number between zero and one, where zero is no modulation depth and one is fully modulated.
  • Percentage: Where zero percent is no modulation depth and 100% is fully modulated. 

Not all signals have the same modulation depth or frequency over time.  This is where a modulation map can be useful.

5. Modulation Map Method

Before explaining a modulation map, it is helpful to know the potential causes of modulation.  If two sounds have similar (but not the same) frequency, and similar magnitude, they will form a modulated sound as their phase changes relative to each other over time as shown in Figure 12.
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Figure 12: When two signals of similar frequency (red and green, top and middle display) and the same amplitude are present at the same time, a modulated signal (blue, bottom display) is created through construction and interference.  The frequency of the modulation is the difference in frequency between the two sines.

If the two sine waves were 100 Hz and 120 Hz respectively, the resulting sound will modulate 20 times per second.  This is called a 20 Hz modulation, even though the actual sine tones in the signal are at 100 Hz and 120 Hz.

A modulation map can determine and display the modulation frequencies present in a signal.  The map function makes it possible to even understand modulation content that changes over time.  This is done with the “Tracked modulation map” method shown in Figure 13.
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Figure 13: Spectral map and tracked modulation map methods.

Suppose a sound signal consisting of two sweeping sine tones was analyzed. One sine tone went from 10 to 1000 Hz, while the other went from 11 to 1100 Hz. The tones will create a modulation with rates equal to the frequency difference in the tones.  In this case, the initial modulation frequency/rate is one time per second (11 Hz minus 10 Hz) which evolves to one hundred times per second (1100 Hz minus 1000 Hz).
Below is a side by side comparison (Figure 14) of a spectral map versus a modulation map of these tones.  
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Figure 14: The spectral map shows the two sine tones, going from 10 and 11 Hz to 1000 and 1100 Hz. The modulation map shows the modulation frequency, which spans a lower frequency range from 1 to 100 Hz. 

In the modulation map, the fact that the modulation changes from one modulation per second to a hundred modulations per second can be clearly seen.

This could also be shown using the “Modulation Frequency” method of Simcenter Testlab Neo.

6. Modulation Frequency Method

The “Modulation Frequency” method calculates the rate, or number of times per second, that a signal modulates.  It is expressed in Hz.

In a signal with multiple modulation components, it finds the frequency for the largest modulating component.

The “Modulation Frequency” method is used in conjunction with the “Tracked Modulation Map” method as shown in Figure 15.
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Figure 15: To calculate the modulation frequency, the “Modulation frequency” method must be attached to the “Modulation map - tracked” method.

The modulation frequency result will be displayed on the same tracking axis as defined in the “Modulation map - tracked” method.  For example, if tracking on time was used, the modulation frequency is also plotted against time as shown in Figure 16.
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Figure 16: Top– Modulation map (modulation amplitude, time, modulation frequency) for two sweeping sine tones.  Bottom – Corresponding modulation frequency result versus time (modulation amplitude or depth is not indicated).

It is important to remember that the modulation frequency and actual frequencies in the signals are two different items.  In Figure 17 below, two different sets of frequencies create the same modulation rate of 20 Hz. 
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Figure 17: Modulation frequency is not the same as the frequencies present in the sound.  In the top graph, 100 Hz and 120 Hz sine waves create the same 20 Hz modulation as the 1000 Hz and 1020 Hz sine waves of the bottom graph.
The modulation metrics described so far do not take fully into account the human perception of modulation.  There are additional metrics to describe the perception of modulation.

7. Fluctuation Strength and Roughness

The modulation metrics Fluctuation Strength and Roughness consider one additional aspect of the human perception of modulation.  According to studies, for the same modulation depth, listeners are more sensitive to modulations that occur four times per second and at seventy times per second:
  • Fluctuation Strength: Metric for low frequency modulation perception that range from one to twenty modulations per second.  When modulation depth is the same, Fluctuation Strength has a maximum when modulations occur four times per second.
  • Roughness: Metric for high frequency modulation perception that range from twenty to three hundred modulations per second.  When modulation depth is the same, Roughness has a maximum when modulations occur seventy times per second.
Both Fluctuation Strength and Modulation Depth can be calculated in Simcenter Testlab Neo Process Designer as shown in Figure 18.
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Figure 18: Fluctuation Strength method (left) versus Modulation Depth method (right).

Fluctuation Strength and Modulation Depth metrics for the same signal (two equal amplitude tones modulated from one to 100 times a second) are overlaid in Figure 19.
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Figure 19: For the same signal with variable frequency modulation, the modulation depth metric remains at a constant level (green curve – right axis) while the Fluctuation Strength metrics changes (red curve – left axis).  
Unlike modulation depth, which is a constant value throughout the sine sweeps, the Fluctuation Strength varies in amplitude.  Fluctuation Strength metric better reflects human perception of modulation.  The metric peaks at four Hz.

Fluctuation Strength has a twin metric called Roughness for faster modulations of 70 times per second, ranging from 20 to 300 times per second.

For more about these metrics, and some real-world examples, see the article “Roughness and Fluctuation Strength”.

8. Getting Started with Modulation Methods in Simcenter Testlab Neo

After starting Simcenter Testlab Neo, go to “File -> Add-ins” and turn on “Process Designer” (19 tokens) and “Sound Quality Analysis” (33 tokens) as shown in Figure 20
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Figure 20: To use modulation metrics in Simcenter Testlab, turn on “Sound Quality Analysis” in addition to “Process Designer”.

The “Processing” tab has three different areas for analyzing data, including a data selection, display, and process area.
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Figure 21: Simcenter Testlab Neo Process Designer has a Data Selection area (red), Process definition area (blue), and data display area (green).
Just by clicking on data in the data selection area, it will be automatically shown in the Preview tab of the display area.

In the data selection area, right click on a time file and choose “Add to Input Basket” to select it for processing as shown in Figure 22.  

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Figure 22: Right click on the time data to be analyzed and choose “Add to Input Basket”.
Modulation methods can be added to the process area.  See the knowledge article “Simcenter Testlab Neo Process Designer” for instructions on how to create a process.

A typical modulation process is shown in Figure 23.
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Figure 22: Left – Modulation analysis process, Right – Method properties.
By clicking on the “Modulation map – tracked” method, important parameters can be selected:
  • Band type: Frequency range of the input time signal where the method looks for modulations.  Choices are Full Bandwidth, Octaves, Critical Bands, User Defined.
  • Modulation Limit:  Limit on the frequency content of the resulting envelope function.
  • Modulation Depth: Amplitude of modulation can be expressed as a percentage (0 to 100%) or number (0 to 1).
  • Window type: Window used in Fourier Transform of envelope.  Choices include: Uniform, Hanning, Hamming, Blackman, Kaiser-Bessel, Flattop. See knowledge article “Window Types: Hanning, Flattop, more...”.
  • Spectral Resolution: Spectral resolution (delta f) of modulation spectrum. See knowledge article “Digital Signal Processing”.
Questions?  Email or contact the Siemens Support Center.

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KB Article ID# KB000044605_EN_US



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