The noise level displayed by a sound level meter is calculated from the instantaneous sound pressure multiplied by frequency weighting characteristic A, and includes signal components across all frequency bands (20 Hz to 8 kHz for a standard sound level meter, and 10 Hz to 20 kHz for a precision sound level meter).
When implementing noise countermeasures, the appropriate countermeasures vary depending on the noise frequency, so frequency analysis of the noise is necessary. One method of frequency analysis is octave band analysis, as defined in JIS C 1513:2002 "Octave and 1/3 Octave Band Analyzers for Acoustics and Vibration".
If an octave band analyzer conforming to JIS C 1513 is not available, an FFT analyzer may be used to perform FFT analysis, and the FFT analysis results may be bundled for each octave band to calculate octave band analysis data (so-called bundled octaves).
For stationary signals, the results of octave band analysis and the bundled octave results from FFT analysis will match, but they will not match if the signal fluctuates. In this and the next (June 2013) measurement column, we will introduce each analysis method and the results of the analysis of actual measurement data.
Octave band analysis
Octave band analysis analyzes the signal levels passing through multiple bands with a given frequency bandwidth. A 1/1 octave analysis uses a filter with a bandwidth of one octave (Figure 1). For a 1 kHz band (fm = 1000 Hz), f1 = 707.11 Hz and f2 = 1414.2 Hz.
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Figure 1 1/1 octave band filter
1/3 octave analysis uses a filter with a bandwidth of 1/3 octave (Figure 2). For a 1 kHz band (fm = 1000 Hz), f1 = 890.90 Hz and f2 = 1122.5 Hz.
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Figure 2 1/3 octave band filter
Figure 3 shows an example of a 1/3 octave band analysis. For 30 bands from 25 Hz to 20 kHz, the values are shown for the signal levels after passing through each band filter, with frequency-weighted A-weighting applied. "Overall" is the sum of the levels from the 25 Hz to 20 kHz bands, applied with A-weighting. "AllPass" is the level of the signal across the entire frequency band without passing through band filters. Since "AllPass" is a FLAT characteristic (no A-weighting applied) value, it is approximately 3 dB higher than "Overall." Also, because the original data does not contain components above 18.75 kHz, the 20 kHz band is displayed as -400 dB.
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Figure 3: Example of 1/3 octave band analysis results.
Octave band analyzer
Block diagrams (examples) of a time-weighted sound level meter and octave band analyzer are shown in Figures 4 and 5. Among sound level meters (noise meters), those that can measure time-weighted sound levels are called time-weighted sound level meters, and as shown in Figure 4, they have an RMS detection/time-weighting circuit (dynamic characteristic circuit) and a logarithmic calculation circuit. Note that the term "dynamic characteristic" is used in the old noise meter standards (JIS C1502, C1505), and in the new standard (JIS C1509), it is called "time-weighted characteristic".
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Figure 4. Block diagram of a time-weighted sound level meter (example).
The block diagram of the octave band analyzer (for acoustics) shown in Figure 5 is almost identical to that of a sound level meter, but with an octave band bandpass filter in between. Also, frequency correction is usually not performed, and a flat characteristic (FLAT) is used. This type of analyzer can only analyze one octave band at a time.
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Figure 5. Block diagram of an octave band analyzer (example)
An analyzer that performs analysis of multiple octave bands simultaneously is called a real-time octave analyzer (Figure 6). For 1/1 octave analysis from 31.5 Hz to 16 kHz, 10 octave band filters, an RMS detection/dynamic characteristic circuit, and a logarithmic calculation circuit are required. For 1/3 octave analysis from 25 Hz to 20 kHz, 30 filters are required. In addition, it has a circuit that analyzes the AllPass value, which is the level of the signal across the entire frequency band without passing it through a band filter.
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Figure 6: Block diagram of a real-time octave analyzer (example)
FFT analyzer
An FFT analyzer is a device that performs FFT analysis. For example, with a frequency range of 20 kHz and 16,384 sample points, the frequency resolution is 3.125 Hz increments, resulting in a power spectrum of 6,401 lines (including 0 Hz) from 0 Hz to 20 kHz, in 3.125 Hz increments.
In the 1 kHz band of a 1/3 octave band, f1 = 890.90 Hz and f2 = 1122.5 Hz. Therefore, by combining the components of this power spectrum from 890.625 Hz to 1121.875 Hz, the signal level of the 1 kHz band can be calculated from the power spectrum (*). In this way, the data obtained by calculating the signal levels of each octave band from the power spectrum obtained by FFT analysis is bundled together and called an octave.
* In practice, frequency components below f1 or above f2 are not ignored; the spread of the octave filter (the characteristic shown by the red line in Figures 1 and 2) is taken into account during synthesis.
Comparison of bundled octaves using real-time octave analysis and FFT analysis.
Figures 7 and 8 show the results of a 1/3 octave analysis of a 4 kHz repeating tone burst signal (sound pressure level: 91 dB, duration: 200 ms, repetition period: 2 s). The dynamic characteristics (time weighting characteristics) of the real-time octave analysis were set to fast (125 ms). The FFT analysis was performed with a frequency range of 20 kHz, 16,384 sample points, and a Hanning window function. The FFT frame time was 0.32 seconds.
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Figure 7: Color map of real-time octave analysis (top) and bundled octaves from FFT analysis (bottom).
In the real-time octave analysis results, when the burst signal is interrupted, the overall value and the values of each octave band decrease at a slope of approximately -4.3 dB every 125 ms due to the influence of dynamic characteristics. On the other hand, in the FFT analysis results, the frame time length is 0.32 seconds, so the signal level becomes 0 (decibels become negative infinity) 0.32 seconds after the burst signal is interrupted.
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Figure 8: Time trend diagram of overall values for real-time octave analysis (top) and bundled octaves from FFT analysis (bottom).
The maximum overall value in the real-time octave analysis results was 90.0 dB, which is 1.0 dB lower than the sound pressure level of the tone burst signal, 91.0 dB. On the other hand, the FFT analysis result was approximately 91.0 dB, showing a difference of about 1.0 dB depending on the analysis method. The time trend graphs also differ significantly.
summary
This time Otreble band analysis and FFT analysis of bundled octaves of We have provided an overview of the analysis method. We also presented the analysis results of a repeated tone burst signal and showed that there are differences between the two analysis results. In the next update (June 2013), we plan to present several more analysis results.
- JIS C 1509-1:2005 Sound level meters (noise meters) - Part 1: Specifications
- JIS C 1513:2002 Octave and 1/3 Octave Band Analyzers for Acoustics and Vibrations
- JIS C 1514:2002 Octave and 1/N Octave Band Filters
(Excerpt from the email newsletter issued on April 18, 2013)
