This time, following on from the previous two articles (Sound Measurement Examples - Part 5 "FFT Analysis and Octave Band Analysis (Part 1)" and Part 6 "FFT Analysis and Octave Band Analysis (Part 2)"), we will introduce the analysis results using two methods: octave band analysis and FFT analysis.
The subjects of this analysis are two sounds: the sound of a coffee can being struck and the sound of a bicycle bell. Both are impactful sounds with short durations, and even when measuring their sound pressure levels, the measurement results will differ depending on the analysis method and conditions. This phenomenon particularly affects how thresholds are determined when verifying the operation of the measured object and pass/fail judgment.
Analysis of the sound of a coffee can being struck.
The sound of hitting a coffee can is represented by the following signal (clicking within the waveform data will open a WAV file where you can hear the actual sound).
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Figure 1. Sound of a coffee can being struck (data length: 1 second)
(1) FFT analysis of the sound of a coffee can being struck
For impact sounds like the sound of a coffee can being struck, which are short in duration and almost silent within the FFT time, a triggered FFT analysis method is used.
Figures 2 and 3 show the results of FFT analysis of the sound of a coffee can being struck. The frequency range was 25 kHz, the window function was a rectangular window, and the analysis was performed with triggering. The number of sample points was 4096 and 16384, and the FFT time lengths were 64 ms and 256 ms, respectively.
The overall value does not match: 83.56 dB with 4096 samples (64 ms) and 77.72 dB with 16384 samples (256 ms). Similarly, the values for each frequency component of the power spectrum and the values for each band of the bundled octave do not match. The overall value matches the average of the squared amplitude values of the time waveform, so if the FFT time length is long, the silent portion in the latter half is also added to the average, and the measured value becomes smaller as the number of samples increases (FFT time length increases). Theoretically, doubling the time length should reduce the value by 3 dB.
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Figure 2. FFT analysis results of the sound of a coffee can being struck (25 kHz range, 4096 points).
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Figure 3. FFT analysis results of the sound of a coffee can being struck (25 kHz range, 16,384 points).
(2) FFT time-scheduled analysis of the sound of a coffee can being struck
FFT scheduled analysis involves repeatedly performing FFT analysis at fixed time intervals and measuring the time evolution of the overall value or specific frequency components from the results.
Figure 4 shows the results of the analysis of the sound of tapping a coffee can (overall value and partial overall value from 1.9 kHz to 2.1 kHz). The frequency range was 25 kHz, the window function was the Hanning window, and the time interval was 10 ms. There were three types of sample counts: 1024 points, 4096 points, and 16384 points, with FFT time lengths of 16 ms, 64 ms, and 256 ms, respectively.
The maximum overall values were 88.31 dB, 86.20 dB, and 81.61 dB, respectively. While the values tend to decrease with a larger sample size, it is theoretically impossible to determine how many dB the results will change when the sample size is changed. Furthermore, the shape of the graph is highly dependent on the analysis conditions, making it unsuitable for analyzing signals with rapid time changes, such as impact sounds.
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Figure 4. FFT time-scheduled analysis of the impact sound of a coffee can (25 kHz range, 10 ms intervals). Sample counts: 1024 points (top), 4096 points (middle), 16384 points (bottom).
(3) Octave time trend analysis of the sound of a coffee can being struck
Octave time trend analysis arranges the results of octave analysis at regular time intervals, and from these results, it measures the time changes of the overall value and specific octave bands.
Figure 5 shows the results of the analysis of the impact sound of a coffee can (overall value and 2 kHz band). The analysis conditions were 1/3 octave, calculation interval was 1 ms, frequency weighting was Z, and dynamic characteristics (time weighting characteristics) were 10 ms and 125 ms.
The maximum overall value differs depending on whether the dynamic response is 10 ms (87.36 dB) or 125 ms (79.23 dB). Furthermore, it does not match the results of the FFT fixed-time schedule.
For dynamic characteristics, if you want to evaluate how a person perceives the sound of the object being measured, you should analyze it at 125 ms, the same as the noise level measurement conditions. In cases of checking the operation or pass/fail judgment, if the duration of the sound is short, you may use a value shorter than 125 ms. However, since the measured values will vary depending on the measurement conditions, thresholds for operation checks and pass/fail judgment must be determined after deciding on the analysis method and conditions.
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Figure 5. Octave time trend analysis of the sound of a coffee can being struck (Z-characteristics, 10ms intervals). Dynamic characteristics (time-weighted characteristics): 10ms (upper panel), 125ms (lower panel).
Analysis of bicycle bell sounds
The sound of a bicycle bell is represented by the following signal (clicking within the waveform data will open a WAV file where you can hear the actual sound).
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Figure 6. Bicycle bell sound (data length: 2 seconds)
(1) FFT analysis of bicycle bell sound
When there are two or more sounds, such as a bicycle bell, and the duration is long, the signals will not fit within a single FFT time period. Therefore, the entire signal may be averaged during FFT analysis. There are several methods for averaging, including power spectrum averaging, power spectrum MAX OA, and power spectrum peak retention.
The frequency range was 25 kHz, the number of samples was 4096, the overlap was 75%, the window function was a Hanning window, and the average time (over the entire signal) was 2 seconds for the analysis.
Figure 7 shows the power spectrum averaging results, Figure 8 shows the power spectrum MAX OA results, and Figure 9 shows the power spectrum peak retention results. MAX OA calculates the power spectrum when the Overall value was highest over a 2-second period. Peak retention preserves the maximum value for each frequency component.
The overall values were an averaged 70.07 dB, a maximum overhead (OA) of 84.66 dB, and a peak hold of 85.58 dB.
The power spectrum averaging result includes silent intervals, and while the measured value may appear smaller, it reflects the entire signal. It also shows relatively good agreement with the time-averaged sound level (L eq) measured with a sound level meter. However, the averaging time must always be the same.
The Power Spectrum MAX OA result shows the spectrum at the point where the signal was strongest. However, in the case of a signal consisting of two or more segments, as in this case, the analysis result will only reflect the sound from the segment with the highest signal level.
While the frequency components of the power spectrum peak retention are not necessarily from the same time, they can be used in cases where the difference between good and defective products is significant, such as for pass/fail judgment. Note that the octave band data bundled from the spectrum is meaningless in peak retention and is therefore not shown in the figure.
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Figure 7: FFT analysis of bicycle bell sound (power spectrum averaging)
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Figure 8. FFT analysis of bicycle bell sound (power spectrum MAX OA)
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Figure 9. FFT analysis of bicycle bell sound (power spectral peak retention).
(2) FFT time-scheduled analysis of bicycle bell sounds
FFT scheduled analysis involves repeatedly performing FFT analysis at fixed time intervals and measuring the time evolution of the overall value or specific frequency components from the results.
Figure 10 shows the results of the analysis of the impact sound of a bicycle bell (overall value and partial overall value from 1.9 kHz to 2.1 kHz). The frequency range was 25 kHz, the window function was the Hanning window, and the time interval was 10 ms. The number of sample points was 1024, 4096, and 16384, with FFT time lengths of 16 ms, 64 ms, and 256 ms, respectively.
The maximum overall values were 86.19 dB, 84.55 dB, and 81.56 dB, respectively. While the values tend to decrease with a larger sample size, it is theoretically impossible to determine how many dB the results will change when the sample size is changed. Furthermore, the shape of the graph also depends heavily on the analysis conditions, so when analyzing or comparing the time evolution of such signals, the analysis conditions should be defined in advance before measurement.
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Figure 10. FFT time-scheduled measurement of bicycle bell sound (25 kHz range, 10 ms intervals). Sample count: 1024 points (top), 4096 points (middle), 16384 points (bottom).
(3) Octave time trend analysis of bicycle bell sounds
Octave time trend analysis arranges the results of octave analysis at regular time intervals, and from these results, it measures the time changes of the overall value and specific frequency components.
Figure 11 shows the results of time-trend measurement of bicycle bell sounds (overall value and 2 kHz band). The analysis conditions were 1/3 octave, calculation interval was 1 ms, frequency weighting was Z, and dynamic characteristics (time-weighted characteristics) were 10 ms and 125 ms.
The maximum value of the overall value differs depending on whether the dynamic response is 10 ms (85.23 dB) or 125 ms (79.77 dB). Furthermore, it does not match the results of the FFT fixed-time schedule. Regarding dynamic response, if you want to evaluate how a person perceives the sound of the object being measured, analyze it at 125 ms, the same condition used for noise level measurement. For operational checks or pass/fail judgment of an object, if the sound duration is short, a value shorter than 125 ms may be used. However, since the measured values vary depending on the measurement conditions, thresholds for operational checks and pass/fail judgment must be determined after deciding on the analysis method and conditions.
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Figure 11 Octave time trend analysis of bicycle bell sound (Z characteristics, 10 ms intervals) Dynamic characteristics (time-weighted characteristics): 10 ms (upper panel), 125 ms (lower panel)
(Excerpt from the email newsletter issued on August 22, 2013)
summary
This time, we'll discuss octave band analysis and FFT analysis, comparing the sound of a coffee can being struck with a bicycle.
We presented the analysis results for "bell sounds" and showed how the analysis methods differ.
If a real-time octave analyzer is not available, consider performing FFT analysis using an FFT analyzer.
While this may sometimes be the case, the results generally do not match, and the difference lies in the nature of the signal being analyzed and the analytical conditions.
Therefore, it will vary.
In particular, when performing operational checks or pass/fail judgment of the object being measured, the analysis method and conditions must be determined.
Above, you need to define thresholds. Once you have defined thresholds for operational verification and pass/fail judgment, analysis
The method and analysis conditions will also be recorded. If the analysis conditions are unclear, it will be difficult to obtain the same results at a later date.
It becomes difficult to do so.
If it becomes necessary to change the analysis method or conditions due to unavoidable circumstances, the threshold
A correction is necessary. It is rare that this correction amount can be theoretically determined; in most cases,
We analyze the actual data using two methods, confirm the correlation, and then determine the correction amount.
This will be necessary.
