Sound Measurement Case Study - 5th Session "FFT Analysis and Octave Band Analysis (Part 1)"

The sound level displayed by the sound level meter is a value calculated from the instantaneous sound pressure weighted by frequency characteristic A, and includes signal components from all frequency bands (for a standard sound level meter, 20 Hz to 8 kHz, and for a precision sound level meter, 10 Hz to 20 kHz).

騒音対策をおこなう場合、騒音の周波数によって対策方法が異なるため、騒音の周波数分析が必要になります。周波数分析の手法の1つにJIS C 1513:2002「音響・振動用オクターブ及び 1/3オクターブバンド分析器」に定められたオクターブバンド分析があります。

JIS C 1513に準拠したオクターブバンド分析器がない場合、FFTアナライザによりFFT分析をおこない、FFT分析結果をオクターブバンドごとに束ねてオクターブバンド分析データを算出すること（いわゆる束ねオクターブ）があります。

定常的な信号であれば、オクターブバンド分析の結果とFFT分析による束ねオクターブの結果は一致しますが、信号に変動があれば一致しません。計測コラムでは今回と次回（2013年6月）にわたり、それぞれの分析方法と実測データの分析結果をご紹介します。

octave band analysis

Octave-band analysis examines the signal level passing through each of several bands, each with a certain bandwidth. 1/1-octave analysis uses filters with a bandwidth of one octave (Figure 1). For the 1 kHz band (f _m = 1000 Hz), f ₁ = 707.11 Hz and f ₂ = 1414.2 Hz.

One-third-octave analysis uses filters with a one-third-octave bandwidth (Figure 2). For the 1 kHz band (f _m = 1000 Hz), f ₁ = 890.90 Hz and f ₂ = 1122.5 Hz.

Figure 3 shows the results of the 1/3 octave band analysis (example). It displays the values of the signal levels that passed through each band filter from the 25 Hz band to the 20 kHz band, weighted by the A characteristic. The Overall value is the sum of the levels from the 25 Hz band to the 20 kHz band, weighted by the A characteristic. The AllPass value is the leveled signal across the entire frequency range without passing through the band filters. Since AllPass represents a FLAT characteristic (without A weighting), it is approximately 3 dB higher than Overall. Additionally, since the original data does not contain components exceeding 18.75 kHz, the 20 kHz band is displayed as -400 dB.

Octave band analyzer

Figures 4 and 5 show a block diagram of a time-weighted sound level meter and octave band analyzer (one example). Among the sound level meters, those capable of measuring time-weighted sound levels are called time-weighted sound level meters, which, as shown in Figure 4, have an effective value detection and time-weighting circuit (dynamic characteristic circuit) and a logarithmic operation circuit. The term 'dynamic characteristic' is from the old standard for sound level meters (JIS C1502, C1505), while the new standard (JIS C1509) refers to it as time-weighted characteristics.

The block diagram of the octave band analyzer (for acoustics) shown in Figure 5 is almost the same as that of a sound level meter, but it includes octave band bandpass filters in between. Additionally, 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.

A device that performs simultaneous analysis of multiple octave bands is called a real-time octave analyzer (Figure 6). For 1/1 octave analysis, analyzing from 31.5 Hz to 16 kHz requires 10 octave band filters, an effective value detection circuit, dynamic characteristic circuit, and logarithmic operation circuit. For 1/3 octave analysis, analyzing from 25 Hz to 20 kHz requires 30 filters. Additionally, it has a circuit that analyzes the AllPass value, which levels the signal across the entire frequency range without passing through band filters.

FFT Analyzer

The FFT analyzer is a device that performs FFT analysis. For example, with a frequency range of 20 kHz and a sample size of 16,384 points, the frequency resolution will be in increments of 3.125 Hz, resulting in a total of 6,401 lines (including 0 Hz) of power spectrum from 0 Hz to 20 kHz, at 3.125 Hz intervals.

For the 1 kHz band of a 1/3-octave band, f ₁ = 890.90 Hz and f ₂ = 1122.5 Hz. Therefore, by summing the components from 890.625 Hz to 1121.875 Hz in this power spectrum, the signal level of the 1 kHz band can be calculated from the power spectrum (*). Data calculated in this way, in which the signal levels of each octave band are derived from the power spectrum obtained through FFT analysis, are called grouped octaves.

* In practice, rather than ignoring frequency components below f ₁ or above f ₂, they are synthesized by taking into account the spread of the octave filter (the characteristics shown by the red lines in Figures 1 and 2).

Comparison of Real-Time Octave Analysis and Bundled Octave FFT Analysis

The results of the 1/3 octave analysis of a 4 kHz repeating tone burst signal (sound pressure level: 91 dB, duration: 200 ms, repetition period: 2 s) are shown in Figures 7 and 8. The dynamic characteristics of the real-time octave analysis (time weighting characteristics) were set to fast (125 ms). The FFT analysis was conducted with a frequency range of 20 kHz, a sample size of 16,384 points, and a Hanning window function. The FFT frame time length at this time is 0.32 seconds.

In the real-time octave analysis results, when the burst signal is interrupted, the overall values and the values of each octave band decrease with a slope of about -4.3 dB at 125 ms due to the influence of dynamic characteristics. On the other hand, regarding the FFT analysis results, since the frame duration is 0.32 seconds, the signal level becomes 0 (the decibel value is minus infinity) 0.32 seconds after the burst signal is interrupted.

The maximum overall value in the real-time octave analysis results is 90.0 dB, which is 1.0 dB lower than the sound pressure level of the tone burst signal at 91.0 dB. On the other hand, the FFT analysis result is approximately 91.0 dB, showing a difference of about 1.0 dB depending on the analysis method. Additionally, the time trend graphs also differ significantly.

(Excerpt from the email newsletter published on April 18, 2013)