In the 10th introductory column, we introduced "sound quality evaluation analysis," which allows us to quantify various impressions of sound. In this column, we will focus on the "fluctuation" of sound and introduce fluctuating sound analysis, which can clearly illustrate its characteristic quantities.
Why the "fluctuation" in sound is attracting attention
In our daily lives, we sometimes hear sounds that are "annoying" or "sticky," but what kind of sounds do you consider "annoying"? While it varies from person to person, one example is a sound that, while not particularly loud, stands out because its tone seems to fluctuate over time. For example, the ringtone of a mobile phone, as shown in Figure 1, has a pattern that fluctuates in short time cycles, making it a tone that people can easily notice even at a relatively low volume.
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Figure 1: Image of a mobile phone (ringtone) ringtone pattern.
On the other hand, many of the abnormal noises (so-called "unwanted sounds") emanating from various industrial products such as automobiles and home appliances are fluctuating noises, and these are among the noises that need to be addressed. When the level of these noises is high, their characteristic quantities (such as frequency) can be found relatively easily using standard sound analysis methods such as FFT analysis and octave analysis. However, when the level of these noises is low, while the fluctuating nature of the sound is noticeable and therefore "annoying," it becomes difficult to capture their characteristic quantities using FFT analysis and other methods. In recent years, with the electrification of automobiles, the interior space of vehicles has become extremely quiet, and small "fluctuating noises" at various levels that were previously unnoticed have become more prominent, leading to an increase in cases where countermeasures are needed. Against this backdrop, there has been a significant increase in the need to grasp the characteristic quantities of the "fluctuating nature" of sound.
Methods for expressing the "fluctuation" of sound
What would a fluctuating sound actually look like if it were depicted as a waveform?
The answer is shown in Figure 2. If we plot time on the horizontal axis, the amplitude of the musical scale = pitch frequency (F: blue line) is drawn as a waveform in which the amplitude repeatedly increases and decreases at a certain frequency (f: red line). This is the waveform of a sound generally called amplitude-modulated sound (AM sound). In this case, the larger the difference (ΔL) between the point where the amplitude of the peak is largest and the point where it is zero, the greater the "feeling of fluctuation" that the human ear perceives.
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Figure 2. Fluctuation sound (waveform on the time axis)
Thus, we can see that fluctuating sounds are composed of two frequency components: "pitch" and "fluctuation." This is called "fluctuating sound analysis," and is shown in Figure 3 as a graph in the form of a color map. The pitch frequency (F) is plotted on the horizontal axis, the fluctuation frequency (f) on the vertical axis, and the depth of the fluctuation (ΔL) is represented by the intensity of the color on the graph. For the actual calculation process, please refer to the Ono Sokki Technical Report "What is Fluctuating Sound Analysis?" introduced at the end of this document.
In the case shown in Figure 2, we are basically dealing with a single fluctuating sound (a specific pitch and a specific fluctuation period). However, for fluctuating sounds generated from various industrial products, there is not always just one; it is not uncommon for multiple fluctuating sounds to be present. As shown in Figure 3, even when two fluctuating sounds with different timbres, such as sound A and sound B, are present, their individual feature quantities can be represented. In this case, sound A has a lower pitch than sound B, but its fluctuation period is faster, indicating that it is a fluctuating sound with a faster timbre.
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Figure 3: Image of fluctuating sound analysis
Examples of fluctuating sound analysis
This case study presents an analysis of abnormal noises contained in the operating sound of an automobile engine component (injector). The injector is a component that injects fuel such as gasoline, and when fuel is injected, the needle valve and stopper, which are components of the injector, interfere with each other, producing a high-pitched, fluctuating "pitter-patter" sound. We wanted to extract the characteristic quantities of this abnormal noise, but because the low-pitched sound (rumbling sound), which is the main component of engine noise, is relatively large, it is difficult to clearly show its characteristics using general sound analysis (FFT analysis) (Figure 4). In this case, a vertical stripe pattern can be seen in the frequency bands of 5 kHz and 10 kHz (red dashed lines), and this is the true nature of the injector's "pitter-patter" sound. In other words, the 5 kHz and 10 kHz sounds repeatedly increase and decrease in volume at the time interval of the vertical stripe (approximately 40 msec), resulting in a "pitter-patter" sound. This sound (a crackling noise) is unpleasant to the ear, but because the sound level itself is not very high, the characteristic frequency is blurred.
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Figure 4. FFT analysis graph of injector operating sound.
Figure 5 shows the results of a fluctuation sound analysis performed on the same sound source.
The crackling sound (= fluctuating sound), which was blurred in the FFT analysis, is clearly shown as two fluctuating components (red dashed lines). The pitch frequencies are 5 kHz and 10 kHz, and the fluctuating frequency is 25 Hz, with the grid cells being darker, indicating that this component fluctuates significantly.
Another point to note is that the engine's main component, the roaring sound, which is displayed in bold in the FFT analysis, is a steady-state sound (a sound without fluctuations), and therefore this sound component does not react in this analysis (white dashed line). In other words, this analysis method is effective when you want to extract only sounds with relatively small fluctuations (in this case, the popping sound) in a sound environment where steady-state sounds like the roaring sound are dominant.
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Figure 5. Graph showing the fluctuations in injector operating noise.
Our living spaces are filled with various kinds of "fluctuating sounds." As discussed in this column, sounds that give a sense of "fluctuation" can sometimes be useful in attracting attention, while at other times they can be irritating and require countermeasures (unpleasant noises).
This time, we introduced fluctuating sound analysis as one method for skillfully extracting fluctuating sounds, which tend to stand out for better or for worse, and representing their characteristic features.
If reading this column has piqued your interest in the calculation principles of fluctuating sound analysis or other analysis examples, please be sure to read our technical report.
【reference】
Ono Sokki Technical Report: "What is Fluctuation Sound Analysis?"
(Excerpt from the email newsletter issued on January 18, 2023)
