Frequently Asked Questions about Measurement - Part 10: "About the Frequency Weighting Characteristic ACZ"

This measurement column addresses frequently asked questions received by our customer support center and provides answers to those questions.

When measuring sound using a sound level meter (noise meter) or FFT analyzer, there is an item called "frequency weighting characteristics (A/C/Z)" in the settings, and we receive many questions about this, such as "Which setting should I use?", "What does A mean?", and "When should I use C?".

This time, we will delve into the background behind the definition of A/C/Z and introduce the frequency weighting characteristic A/C/Z used in sound measurement.

Human hearing perception and loudness levels

Sound is a fluctuation in the pressure of air (or similar material). Even if the amount of pressure fluctuation is the same, people will not perceive the sound as being the same loudness if the sound frequency is different. Therefore, in order to evaluate the loudness of sound as perceived by a person, it is necessary to understand human hearing and correct for its characteristics.

For steady-state sounds, the "loudness level" is defined as the sound pressure level of a 1 kHz pure tone that a person with normal hearing would perceive as being the same loudness as the sound.

Measurements of how human hearing changes with frequency were started by Fletcher-Munson and re-measured in 1957 by Robinson et al. The sound pressure levels of pure tones that a person with normal hearing would perceive as equal in volume, as measured by Robinson et al., and
Figure 1 shows a curve illustrating the relationship between frequencies, labeled as the old standard (blue). This curve is called an equal-loudness curve or equal-sensitivity curve.

Subsequently, it was discovered that the equal-loudness curves measured by Robinson et al. contained significant errors, and in 2003, new equal-loudness curves were standardized internationally as ISO 226. The curves of the new standard are shown in Figure 1 as the new standard (red line).

Frequency weighting characteristic A is

The A-weighting characteristic is a frequency weighting characteristic defined in JIS C1509 for measuring noise intensity (noise level). The A-weighting characteristic is used when measuring noise in factories or on roads, or when it is specified to measure noise level or A-weighted sound pressure level.

When briefly explaining the characteristics of a particular frequency response, it is sometimes described as "a frequency response that mimics human hearing," but this is merely an approximation and does not strictly reflect human hearing.

The A characteristic is an approximation of the loudness curve for quiet sounds in Figure 1, the equal loudness curve for pure tones (old standard). There is also the C characteristic, which is an approximation of the equal loudness curve for loud sounds, and in the past, these characteristics were used interchangeably depending on the loudness of the sound during measurements.

Subsequent research has shown that this characteristic represents auditory loudness, but not noise level.
It was found that this approach is not suitable, and it became clear that using the A-weighting curve is better for representing noise levels, even at high volumes.

In 2003, new equal-loudness curves were standardized as ISO 226, but the A-weighting, which was created by approximating the equal-loudness curves (old standard), remained unchanged and continues to be used as a weighting characteristic when measuring noise level.

What is the frequency weighting characteristic C?

The C-weighting curve is a characteristic created to approximate the perceived loudness of loud sounds using the equal-loudness curves (old standard). In the past, this characteristic was used depending on the loudness of the sound, but it became clear that the A-weighting curve is better for representing the loudness of noise even at high volumes, and the C-weighting curve is rarely used nowadays. However, some European standards still specify the use of the C-weighting curve for certain measurements.

The C characteristic is still sometimes used today when calibrating sound level meters and microphones with acoustic calibrators to avoid the influence of ambient noise.

In practice, unless the background noise is considerably high, there will be no effect from calibration using the Z-weighting. However, if the calibration signal frequency is other than 1 kHz, the effect cannot be ignored, so the A-weighting is not used during calibration.

What is the frequency weighting characteristic Z?

The Z characteristic is a frequency-weighted characteristic that exhibits a flat response within a specified frequency range. It is used to measure the physical phenomenon of sound (pressure fluctuation) itself, regardless of human perception.

Furthermore, while some general-purpose analysis devices that can be used for measuring sound, vibration, voltage, and other parameters are equipped with frequency weighting characteristics A/C/Z for sound measurement, when analyzing anything other than sound with such devices, the Z characteristic must always be used.

The Z characteristic was defined as a flat characteristic (FLAT) in the old standards for sound level meters, JIS C1502/1505. In the new standard, JIS C1509, the frequency range was expanded to 10 Hz to 20 kHz, and it was defined as a frequency-weighted characteristic Z.

Other frequency weighting characteristics

Other frequency weighting characteristics used in sound measurement are hardly used today.
There are B-weighting, D-weighting, and G-weighting used when evaluating infrasound, but I will omit the details.

Values of the frequency weighting characteristics A/C/Z

Table 1 and Figure 2 show the values of the frequency weighting characteristics A/C/Z as specified in JIS C1509, along with their graphs.

Table 1 Frequency Weighting Characteristics A/C/Z (1/3 Octave Band)

The nominal frequency is the center frequency of each 1/3 octave band expressed as a round number. The exact frequency is the exact center frequency value of each band, calculated using Equation 1, where band number n is an integer between 10 and 32.

f = 1000 × 10^{0.1 × (n − 30)} [Hz] 

Table 1 shows the frequency weighting characteristics for each 1/3 octave band. If you delete the rows from Table 1 and keep only the rows for the 1/1 octave band frequencies (16 Hz, 31.5 Hz, 63 Hz, 125 Hz, 250 Hz, 500 Hz, 1 kHz, ..., 16 kHz), you will get a table for the 1/1 octave bands.

Formula for calculating frequency weighting characteristics A/C/Z

The formulas for calculating the frequency weighting characteristic A/C/Z are defined in JIS C1509 as equations (2) to (4), where f is the frequency [Hz].

Z ( f ) = 0 [dB]

Here, the constants are as follows:

fr =1000 [Hz]

f_L =10 ^1.5 [Hz]

f_H=10 ^3.9 [Hz]

f_A=10 ^2.45 [Hz]

c = f_L²f_H²

Furthermore, A ₁₀₀₀ and C ₁₀₀₀ are normalization constants used to ensure that the frequency weighting characteristic at 1 kHz is 0 dB.

Example of calculation for frequency weighting characteristics A/C/Z

An example of frequency weighting characteristic A/C/Z calculation is available as an Excel file. You can download it from the URL below.

Example of calculating frequency weighting characteristics A/C/Z

(Excerpt from the email newsletter issued on December 22, 2016)