Octave Analysis Explored
By Kurt Veggeberg, National Instruments, August 2008
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.
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.
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.
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: