What is modulation effect (fluctuation strength or roughness)?


Sound modulation occurs when the amplitude or frequency of the sound presents a periodical variation over time. There are two different types of modulation:

Level changes along time Frequency changes along time

There are three modulation aspects one can consider :

  • The modulation frequency (f_mod): the number of modulations per second
  • The modulation depth: the relative level of the modulation
  • The center frequency (f_c): the frequency of the signal before modulation
    (also called carrier frequency)

Complex sounds can combine both frequency- and amplitude-modulation.

Psychoacoustics metrics

There are two psychoacoustic metrics aiming to quantify the amount of perceived modulation present in a sound : roughness and fluctuation strength. They take into account, in a single value, how the modulation parameters affect the human ear perception. The more noticeable a modulation, the higher the fluctuation strength/roughness value.

The use of one or the other depends on the number of modulations per second :

  • Fluctuation strength (in vacils) is used for sounds with 20 modulations per second or less.
    At those frequencies, human ear is capable to detect the changes over time and perceive a pulsation or a beat. The fluctuation strength peak reached at 4Hz modulation frequency is the most noticeable by the human ear.
  • Roughness (in aspers) is used for sounds with a number of modulations per second between 20 and 300
    In this frequency interval, modulation temporal changes are no longer perceived but a new “rough” impression appears. Noises with high roughness value are perceived as unpleasant, annoying and aggressive even if their overall loudness stays the same along time. The roughness peak is reached at 70 Hz for a 1kHz sound.
  • Over 300 modulations per second, the human ear is no longer able to detect a modulation.

Modulation metrics calculation have not been standardized yet, but the most used method to calculate roughness is the one from Daniel and Weber, presented in "Psychoacoustical roughness: implementation of an optimized model," Acustica, vol. 83, pp. 113-123, 1997. Considering a sine tone of 1 kHz at a level of 60 dB, with an amplitude-modulation centered at 70 Hz with a depth of 1, its roughness is defined to 1 asper.

e-NVH application: roughness due to eccentricity

Modulation effects can be introduced by PWM, speed ripple, uneven magnetization or dynamic eccentricity.

The two following sounds from EOMYS e-NVH benchmark have been recorded at 2270 and 2330 RPM, in the exact same conditions. However, there is a strong difference between these two sounds: the first one sounds very rough while the other one more tonal.

Test bench at 2270 RPM

Test bench at 2330 RPM

The testbench is an electric motor with 12 slots and 10 poles. The slotting harmonics of such a motor occur at ten times the mechanical frequency (H10) and multiples. Moreover the testbench has a high level of eccentricity, producing many additional harmonics.

Testbench spectra comparison between 2270 and 2330 RPM

When the frequencies of the different harmonics do not excite any structural mode of the motor, the main harmonics (around H20) have almost the same level (see blue spectrum at 2270 RPM). The harmonics frequencies being close enough to be part of the same critical band, a sensation of roughness is created. On the other hand, when one of the harmonics excites a structural mode, creating a resonance, the noise level radiated at this specific frequency becomes dominant. A feeling of tonality is then produced.

At 2270 RPM, calculated roughness is 0.55 asper, while at 2330 RPM it only reaches 0.09 asper. This example shows that calculated roughness correctly reflects auditory perception. It also demonstrates that it is not straightforward to improve e-motor sound quality: a slight change in the operating conditions can improve one psychoacoustic aspect but also degrade another one.

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