Technical Report: What is Variable Sound Analysis? 1

Loudness and other sound quality evaluation metrics are now widely used in various fields as techniques to quantify human auditory impressions. Recently, there has been much discussion about timbre evaluation or abnormal sound detection based on time-varying components. Common metrics for detecting these include roughness and fluctuation intensity, but both are metrics that extract only specific time-varying components. However, mechanical fluctuation sounds emitted from industrial products often contain various fluctuation periods, and these metrics have frequently been insufficient to extract their characteristic quantities. Therefore, by using a metric that can quantify various time-varying components based on loudness (fluctuation sound analysis), it becomes possible to quantify not only the timbre (pitch) of a sound but also its time-varying period.

There are many sounds in the world that are "annoying" even though they aren't particularly loud. For example, the rattling and buzzing sounds that you sometimes hear from interior parts while driving a car, or the buzzing noise that mixes with the rotation of a small motor. There are several reasons why these sounds are "annoying," but sounds that fluctuate significantly over time often feel irritating even if their volume (level) isn't very high.

Fluctuation sound analysis is an analysis method that can extract only the components with large time variations that are not affected by the level. This makes it possible to quantify various time variation characteristics that were difficult to detect with conventional methods such as FFT, basic roughness, and variation intensity. In addition, it is possible to evaluate various sound designs (flavoring) on two axes: timbre (pitch) and time variation period, enabling deeper analysis than conventional techniques.

The unit for fluctuation sound analysis (DLF) is an abbreviation for Depth of Loudness Fluctuation, and represents the depth (difference) of the peaks and troughs in the time variation of loudness. The analysis results are expressed in mDLF, so the actual value is multiplied by 1000. The (s) after DLF indicates linear display, and (p) indicates logarithmic display. (The 's' is derived from the initial letter of the loudness unit 'sone', and the 'p' from the initial letter of the loudness level unit 'phon'.)

The basic fluctuating sound analysis indices, roughness (which expresses the perceived roughness of sound) and fluxivity strength (which expresses the perceived wavering of sound), are also parameters that can extract the time-varying components of sound. Each of these parameters limits the fluctuation frequencies that can be evaluated. For example, roughness, which evaluates the perceived roughness of sound, has a peak fluctuation frequency of 70 Hz, and the weighting of frequencies before and after this is low. On the other hand, fluxivity strength, which evaluates the perceived wavering of sound, has a peak fluctuation period of 4 Hz, and its sensitivity to fluctuation frequencies farther away from this is low. Therefore, if we consider fluctuating sound in a broad sense, both parameters have their strengths and weaknesses.

The fluctuating sound analysis parameter can handle a wide range of fluctuating frequencies.
While the roughness and fluctuation intensity analysis described above use a single fluctuation frequency filter to make them sensitive to specific frequencies, fluctuation sound analysis uses multiple filters.
As detailed in the next chapter (Fluctuation Sound Analysis Algorithm), by passing the signal through band-limiting filters one by one, from low to high frequency bands, it is possible to extract fluctuation components in more detail.

This section outlines the algorithm for analyzing fluctuating sound.

*If the lower limit of the fluctuating frequency is 10 Hz or higher, it will be fixed at 200 ms. If it is less than 10 Hz, the analysis frame length will be the length corresponding to the lower limit.

As mentioned in the previous chapter, fluctuating sound analysis is a parameter that focuses on the amount of time variation in loudness (sound intensity considering human auditory characteristics). Therefore, spectral masking effects that occur during loudness calculations can also affect fluctuating sound analysis.

The example in the diagram below illustrates the loudness pattern of AM (amplitude modulation) sound. The spectral masking curve extends above the carrier frequency (1 kHz), and this frequency component also fluctuates over time. Since fluctuating sound analysis analyzes the fluctuating components of the carrier region and the masking region without distinction, the result may be that the fluctuations are large in the frequency region affected by masking.

To eliminate this (spectral masking) effect, it is necessary to calculate the fluctuating sound analysis using unmasked loudness (called core loudness).

* The fluctuating sound Core analysis uses core loudness analysis, while the fluctuating sound Mask analysis includes spectral masking effects.

Here, we explain analysis examples using "automobile injector operation noise" and "unusual noise from a small motor" as examples.

Here is an example of an evaluation conducted on the sound of a car engine.

During fuel injection, a knocking sound is produced when the needle valve and stopper collide. While the sound itself isn't particularly loud, it's a periodic, jarring "smacking" sound that can be quite irritating to the ear.
The figure on the left shows the results of an FFT analysis, where a vertical stripe pattern can be seen in the 5 kHz bandwidth. This is the source of the crackling sound. The time interval of the vertical stripes (approximately 40 ms) represents the period of the fluctuation.

Because the background noise level in the low frequency band (below 800 Hz) is high, it is difficult to extract this time-varying component using the level indicator.
The diagram on the right shows the results of a sound fluctuation analysis of the same sound. The grid where the frequency axis (horizontal axis), representing the pitch of the timbre, intersects with the fluctuation frequency axis (vertical axis), representing the period of time fluctuation, is shown in darker shades. In other words, it indicates that the fluctuation of this component is large.

The background noise component (sounds below 800 Hz), which appeared as a significant noise component in the FFT analysis, is a stationary sound (it does not fluctuate) and therefore does not show up in the fluctuating sound analysis.

Next, we will introduce an example of evaluating the operating noise of a small motor.

The purpose of this device is to detect a high-frequency "buzzing" noise that can occur due to abnormal motor current or other issues, and to identify defective products.

Comparing the OK and NG products below, both products show fluctuations in the normal operating sound range (frequency: 1 kHz), but only the NG product shows significant fluctuations in the higher frequency components (8-10 kHz).

This component is the cause of the "buzzing" noise, and to pass/fail judgment, you can do so by observing this frequency band (frequency: 10 kHz, fluctuation frequency: 60 Hz).