Octave Analysis Explored
A Tutorial
by Kurt Veggeberg, National Instruments
Sound-level measurements offer a conventional
way to measure sound but do not contain frequency information,
making it difficult to compare different sounds or vibration.
Octave analysis filters the signal and measures the energy at
the output to provide useful frequency information. Although
there are other measures such as loudness for the subjective
human perception of sound, octave analysis remains a common
choice for steady-state signals.
Getting Started
Like most human sense organs, the ear
exhibits a response based on a logarithmic scale for both level
and frequency. To produce results related to this human
perception, sound levels are expressed in decibels (dB), and
frequency content is measured with a logarithmic scale.
Sound-level measurements and instrumentation systems feature
three components: sensors, data acquisition, and analysis.
The most common sensor used for acoustic
measurements is the microphone with accelerometers preferred for
vibration. Measurement-grade microphones are different from
typical recording-studio microphones because they offer a flat
frequency response and can provide a detailed calibration
for their response and sensitivity.
A dynamic range of 130 dB(A) is common. The
dynamic range of the human ear is from the threshold of hearing
or a sound pressure level of 0 dB(A) to the threshold of pain
around 130 dB(A).
Microphones come in various classes. Type 0
and Type 1, preferred for accurate and repeatable measurements,
have the best tolerances for frequency range and decibel
variation comparable to the ear. The most effective microphones
provide a tolerance of no more than 1 dB from 2 kHz to 4 kHz,
which doesn’t sound like much but, in linear units, this is
about 12%. The human ear in normal circumstances can perceive a
difference of 3 dB.
Modern data acquisition instruments for
acoustic measurements use 24-bit analog-to-digital converters
(ADCs) with anti-aliasing filters, which are required for
conformance with octave-band and fractional-octave-band analog
and digital filter standards. Anti-aliasing filters minimize the
interference between an input signal and the sampling process
that creates aliased frequency components of the input signal.
Data acquisition hardware based on 24-bit ADCs offers a dynamic
range from 100 to 120 dB(A), which means that the ear,
microphone, and instrumentation are matched.
Frequency Weighting
Various averaging and weighting techniques
are used to correlate this basic measurement with the subjective
evaluation of sound by the human ear. The human sense of hearing
responds differently to different frequencies and does not
perceive sound equally.
A-weighting is the most commonly used of a
family of curves defined by ANSI and IEC standards for
sound-level measurement (Figure 1). This value is
designated as dB(A). In the A-weighting scale, the sound
pressure levels for the lower-frequency bands and high-frequency
bands are reduced by certain amounts before they are combined to
give one single sound pressure level value.
Figure 1. A-Weighting Scale
A-weighting, thought to mimic human hearing
responses to acoustical signals, is based on historical
equal-loudness contours. While it is no longer considered the
ideal frequency weighting, it is the most common legally
required standard for almost all such measurements.
The U.S. Occupational Safety and Health
Administration (OSHA) found that A-weighting gives a better
estimation of the threat to human hearing than other weighting
filters. This is why it is widely used in describing
occupational and environmental noise. In addition, hearing
protection devices are rated by their overall attenuation and
specific attenuation in one-third octave bands up to 8 kHz.
Time Weighting
Averaging successive measurements tends to
improve measurement accuracy. Sound-level meters and octave
analyzers most commonly use exponential averaging with a time
constant of integration. These are designed to handle a wide
variety of signals and have settings for slow (1 s), fast (125
ms), and impulse (35 ms) to reflect the types of sound being
measured (Figure 2). This is especially useful in making
adjustments in real-time displays to match the signal of
interest and reduce fluctuations.
Figure 2. Time Weighting Settings
Some claim the impulse time weighting
approximates the loudness response of the human ear to impulsive
sounds. Others feel that 35 milliseconds are not long enough to
be perceived by the human auditory system and that it is not the
most appropriate way to measure impulsive sounds.
Octave Analysis in Practice
The range of 20 Hz to 20,000 Hz is called the
audible frequency range and used in octave analysis although it
reflects the actual capability of only a small percentage of the
population. The entire audible frequency range can be divided
into eight or 24 frequency bands known as octave bands or
one-third octave bands, respectively, for analysis.
With fractional-octave analysis, you can
select a frequency resolution that is well adapted to the signal
of interest. Typical fractional bands are one-third octave with
three filters per octave and one-twelfth octave with 12 filters
per octave.
Specifications regarding these octave and
fractional-octave filters are defined by ANSI S1.11-2004, IEC
61260, and JIS C 1514:2002. Although some acoustics engineers
argue that the ear is better, most believe the one-third octave
spectrum paints a picture closest to human-ear perception.
One-third octave analysis is widely accepted in many industries,
such as the automotive industry, because of its repeatability
and not necessarily its suitability.
Octave analysis is a valuable tool for visual
inspection and comparison. For example, the Korean Aerospace
Research Institute (KARI) uses octave analysis as a component in
its real-time control system for testing satellites that go into
its high-intensity acoustic chamber. It produces acoustic levels
up to 152 dB over a range of 25 Hz to 10 kHz, depending on the
spectrum of the launch vehicle for which the satellite is being
tested.
To generate the high-intensity sound in a
chamber comparable to the sound experienced in a launch, KARI
uses acoustic modulators with a gaseous nitrogen supply. The
valves in acoustic modulators generate acoustic energy by
modulating gas streams passing through them. The system
continuously monitors the chamber itself and feeds the
information back to the acoustic control program in real time.
The acoustic control system display in the
high-intensity acoustic chamber at KARI shows the sound pressure
level (SPL) at each one-third octave band of the eight channels
being monitored. The light blue lines are the alarm levels for
the upper and lower limits of the SPL within the frequency bands
(Figure 3). You can control the system automatically or
manually aided by visual inspection.
Figure 3. Acoustic Control System Display in the High-Intensity Acoustic Chamber, Space Test Department, KARI
Octave analysis is performed with a bank of
parallel bandpass filters. The output of each filter then is
averaged to compute the power in each band and displayed as a
bar graph. Octave band filters can be either passive or active
analog filters that operate on continuous-time signals or analog
and digital filters that operate on discrete-time signals.
Traditional octave analyzers typically used analog filters, but
computer host-based octave analyzers most often use digital
filters.
Due to the computational load of one-third
octave analysis, analyzers often synthesized one-third octave
bands from FFT data by assigning the energy from appropriate
bins to a particular proportional band filter. This method has
drawbacks due to leakage.
Lower center frequencies and narrower
bandwidths take longer to settle. The settling time of a
1,000-Hz one-third octave band is about 22 milliseconds; the
settling time of a 1-Hz one-third octave band can take 22
seconds. Some low-frequency environmental vibration measurements
are made using one-third octaves between 1 Hz to 80 Hz with 20
bands so you need to know there will be a long settling time
before the filter will begin providing meaningful output.
The most basic computer now can handle
multichannel real-time octave analysis with a range of
additional functionality. My first computer capable of
host-based, real-time one-third octave analysis and display of
four channels had an Intel Pentium III 400-MHz Processor that
replaced my DSP-based analyzer. Recently, I performed benchmarks
with a PC featuring a 2.4-GHz Intel Core 2 Quad Processor using
a multicore technique to share processing across the four cores
and was able to maintain real-time one-third octave analysis of
72 channels from 20 Hz to 20 kHz.
In aero-acoustic measurements of scale models
in a wind tunnel, it may be useful to perform one-third octave
analysis outside the 20-Hz to 20-kHz range. With a host-based
processing system, you can specify the frequency range that your
instrumentation is capable of so that the frequencies of
interest are increased by the ratio of full size to model size.
Digital octave filters are designed in
several ways. You can develop a set of bandpass filters directly
from the time domain at different center frequencies and
bandwidths. ANSI S1.11 uses Butterworth filters to define the
order and attenuation of the octave filters.
One octave band corresponds to the frequency
range between two frequencies with a ratio of 2:1. A typical
example of this is a piano keyboard. Consecutive A tones are
separated exactly by an octave.
Octave band filters do not have infinitely
steep skirts. As a result, an isolated tone may produce a
reading in adjacent octave bands. Also, a tone at the nominal
boundary between two bands produces an equal reading in both.
For example, a 60-dB(A) tone at 707.1 Hz gives readings of 57 dB
each in the 500-Hz and 1,000-Hz octave bands. In the audio
domain, the reference center frequency has been chosen at
1 kHz. Other center frequencies are at 250 Hz, 500 Hz, 2 kHz,
4 kHz, and so on. The actual filter band center frequencies
typically are developed as a series of powers of 21/3
x 1,000 Hz and may not correspond precisely to the nominal band
center frequencies (Table 1).
Table 1. Octave and One-Third Octave Center Frequencies
The Future of Octave Analysis
Octave analysis is a useful technique for
representing subjective perception of sound by the very complex
human ear. There are other frequency analysis techniques, such
as FFT, joint time-frequency analysis, wavelets, and model-based
methods, that may be closer and yield more detail on the
frequency content of sound. The long history and popularity of
octave analysis guarantee the continued use of this technique to
obtain important frequency information about steady-state sound
and vibration levels.
For More Information
• ANSI S1.4-1983: Specification for Sound
Level Meters (R2006), American National Standards Institute.
• ANSI S1.11-2004: Specification for
Octave-Band and Fractional Octave-Band Analog and Digital
Filters, American National Standards Institute.
• IEC 61260, 1st ed. 1995-07: Octave-Band
and Fractional Octave-Band Filters, International
Electrotechnical Commission.
• Y.K. Kim et al., A High Intensity
Acoustic Chamber for Spacecraft Environmental Tests,
Seogwipo, Korea, Inter-noise 2003.
About the Author
Kurt Veggeberg works as a business
development manager for sound and vibration at National
Instruments. He has been with the company since 1985 and in this
position for eight years. National Instruments, 11500 N. Mopac
Expwy., Austin, TX 78759, 512-683-5461, e-mail:
kurt.veggeberg@ni.com