Octave Spectrum

Octave analysis divides the frequency axis into logarithmically spaced bands whose widths are proportional to their center frequencies. This constant-percentage bandwidth approach mirrors the frequency resolution of human hearing and is widely used in building acoustics, environmental noise assessment, and noise control engineering.

Theory

Octave and Fractional-Octave Bands

A 1/1 octave band spans a frequency range where the upper band edge is exactly twice the lower band edge. Fractional-octave bands subdivide each octave into n equal parts on a logarithmic scale. The most common variant is the 1/3 octave band, which divides each octave into three sub-bands.

The center frequency f_m and band edges of a 1/n octave band are defined as:

f_upper = f_m · 2^1/(2n)
f_lower = f_m · 2^−1/(2n)
Bandwidth = f_upper − f_lower = f_m · (2^1/(2n) − 2^−1/(2n))

Standard Center Frequencies

IEC 61260 and ANSI S1.11 define the preferred center frequencies for octave and 1/3 octave bands. The reference frequency is 1000 Hz.

1/1 Octave Center Freq. (Hz)	Corresponding 1/3 Octave Center Freq. (Hz)
31.5	25, 31.5, 40
63	50, 63, 80
125	100, 125, 160
250	200, 250, 315
500	400, 500, 630
1000	800, 1000, 1250
2000	1600, 2000, 2500
4000	3150, 4000, 5000
8000	6300, 8000, 10000
16000	12500, 16000, 20000

IEC 61260 Compliance

IEC 61260-1:2014 specifies the performance requirements for octave-band and fractional-octave-band filters, including:

Class 1: Tight tolerances for laboratory and precision field measurements.
Class 2: Relaxed tolerances for general field measurements.

V-Listen implements digital IIR filter banks that conform to Class 1 requirements across the full specified frequency range. Filter attenuation outside the passband meets the minimum rejection requirements defined in the standard.

The filter implementation uses base-2 center frequencies as defined in IEC 61260-1:2014. Older standards used base-10 definitions, which produce slightly different center frequencies. Ensure consistency when comparing results with legacy systems.

Frequency Weighting

A-Weighting

A-weighting approximates the frequency response of human hearing at moderate sound levels. It attenuates low frequencies (below 500 Hz) and high frequencies (above 6 kHz), with maximum sensitivity near 2–4 kHz. The result is expressed in dB(A).

C-Weighting

C-weighting has a nearly flat response across the audible range with slight roll-off at very low and very high frequencies. It is used for peak sound level measurements and in contexts where the full spectral energy is relevant. The result is expressed in dB(C).

Center Freq. (Hz)	A-Weighting (dB)	C-Weighting (dB)
31.5	−39.4	−3.0
63	−26.2	−0.8
125	−16.1	−0.2
250	−8.6	0.0
500	−3.2	0.0
1000	0.0	0.0
2000	+1.2	−0.2
4000	+1.0	−0.8
8000	−1.1	−3.0

Parameters

Parameter	Options	Description
Band Resolution	1/1 Octave, 1/3 Octave	Width of each frequency band.
Frequency Weighting	Z (Linear), A, C	Frequency weighting curve applied before band integration.
Time Weighting	Fast (125 ms), Slow (1 s)	Exponential time constant for level detector.
Frequency Range	20 Hz – 20 kHz (typical)	Range of center frequencies to display.
Averaging	Linear / Exponential	Temporal averaging mode.

Practical Tips

Use 1/3 octave analysis for noise regulation compliance (ISO 3744, ISO 11201).
Use 1/1 octave for a quick overview when detailed spectral structure is not required.
Always verify that the sampling rate provides sufficient coverage for the highest octave band of interest (the sampling rate must be at least 2.6 times the upper band edge).
When comparing octave levels with narrowband FFT results, remember that the octave band integrates all energy within the band, so a single-tone signal will show the same level in both representations but broadband noise will appear higher in wider bands.

Do not apply A-weighting to acceleration signals. Frequency weightings defined in IEC 61672 are intended exclusively for sound pressure measurements.