You are here: NI Home > Support > Product Reference > Manuals > Sound and Vibration Measurement Suite 6.0 Help

Fractional-octave analysis primarily depends on filters. This topic discusses filter design in relationship to fractional-octave analysis.

Octave Filters

An octave is the interval between two frequencies, one of which is twice the other. For example, frequencies of 250 Hz and 500 Hz are one octave apart, as are frequencies of 1 kHz and 2 kHz. The following illustration shows an octave filter, a filter whose passband covers one octave.

Just as a tuning fork provides a 440 Hz reference frequency for musicians, a reference frequency is needed to fully define octave filters. Instrumentation equipment typically uses a 1 kHz reference frequency.

Bandedge Frequencies

The quality constant Q is defined as the ratio of the bandwidth over the center frequency of the filter. Q remains constant across all octave bands for octave filters. For example, an octave filter with a center frequency of 1,000 Hz leads to the following bandedge frequencies:

where

f₁ and f₂ are bandedge frequencies

Q is the quality constant

BW is the bandwidth

An octave filter with a center frequency of 8,000 Hz leads to the following bandedge frequencies:

where

f₁ and f₂ are bandedge frequencies

BW is the bandwidth

Q is the quality constant

The results obtained from calculating the bandedge frequencies indicate the following bandwidth characteristics:

• The bandwidth of the octave filters is narrow when the center frequency is low.
• The bandwidth of the octave filters is wider when the center frequency is higher.

Because of the bandwidth characteristics, fractional-octave analysis uses a logarithmic frequency scale to compute and display octave spectra.

Fractional-Octave Filters

Octave filter resolution is limited because only 11 octaves exist in the 16 Hz–16 kHz range. To overcome the limited resolution of octave filters, you can use other filters known as fractional-octave filters. Rather than covering one octave with a single filter, N filters are applied per octave in order to improve resolution. Of the fractional-octave filters, the third-octave (1/3) filter is used widely for fractional-octave analysis. The following front panel shows the 1/3 octave response at frequencies of 500 Hz, 630 Hz, and 800 Hz.

Fractional-octave analysis is a CPU-intensive operation. Increasing the number of filters applied to a signal increases the demands placed on the CPU and can result in increased computation time.

Filter Settling Time

When starting or resetting the filtering operation of fractional-octave filters, a settling time is required before the measurements are valid. The settling time is related to the bandwidth of any particular filter. The lowest frequency band has the smallest bandwidth and defines the settling time required before you can consider the complete fractional-octave measurement valid. In the NI Sound and Vibration Measurement Suite, settling time is defined as five divided by the bandwidth of the filter used for the lowest frequency band. The filter settled indicator returns TRUE when all the filters are settled.